Continuous separation of alpha-mangostin and gamma-mangostin fractions from xanthone extracted from mangosteen pericarps using a preparative three-zone simulated moving bed system

Continuous separation of alpha-mangostin and gamma-mangostin fractions from xanthone extracted from mangosteen pericarps using a preparative three-zone simulated moving bed system | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Continuous separation of alpha-mangostin and gamma-mangostin fractions from xanthone extracted from mangosteen pericarps using a preparative three-zone simulated moving bed system Preuk Tangpromphan, Amaraporn Kaewchada, Attasak Jaree This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6102236/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 03 Jul, 2025 Read the published version in Waste and Biomass Valorization → Version 1 posted 5 You are reading this latest preprint version Graphical Abstract Abstract Mangosteen pericarps, a rich source of bioactive xanthones, particularly α-mangostin and γ-mangostin, were the focus of this study. The primary objective was to design and experimentally implement a continuous separation process using a three-zone simulated moving bed (TZ-SMB) system to isolate and purify these valuable compounds. Xanthone powder, extracted from mangosteen pericarps using acetonitrile and purified by anti-solvent precipitation, served as feedstock. This powder, with an initial α-mangostin purity of 71.56%, was subjected to separation on a single C18 preparative column to determine crucial adsorption parameters, including linear adsorption isotherms and mass transfer coefficients. A mobile phase consisting of 75% v/v acetonitrile was found to effectively separate α-mangostin and γ-mangostin. Subsequently, computational simulations based on triangle theory were employed to optimize TZ-SMB operating parameters. The optimal conditions involved a 20-min switching time and flow rates of 5.00, 1.062, 2.425, and 3.637 mL/min for the mobile phase, feed, extract, and raffinate, respectively. Under these conditions, the system achieved a maximum productivity of 0.56 mg/mL·h while maintaining high purities for both α-mangostin and γ-mangostin in the respective products. Experimental validation of the TZ-SMB system, using slightly adjusted flow rates, resulted in an α-mangostin purity of 100% in the extract product and a γ-mangostin purity of 98.79% in the raffinate product. The dried extract product exhibited an α-mangostin purity of 99.4% (HPLC grade). This research highlights the potential of TZ-SMB as a promising technology for the efficient and scalable purification of bioactive compounds from natural sources. alpha-mangostin gamma-mangostin xanthone mangosteen pericarps simulated moving bed Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Statement of Novelty This study presents the pioneering experimental demonstration of alpha-mangostin and gamma-mangostin separation using a preparative three-zone simulated moving bed (SMB) system. This is the first reported application of this technique for the purification of these valuable xanthones directly from mangosteen pericarp extracts, pretreated via anti-solvent precipitation. Achieving a remarkable 99.4% purity for alpha-mangostin from a pretreated extract of 71.56% purity, this work establishes a critical foundation for the development of commercial-scale alpha-mangostin production. 1. Introduction Thailand has embraced a sustainable development model known as the BCG (Bio-Circular-Green) Economy, prioritizing the valorization of agricultural waste materials for various applications, including the production of pharmacological products for the health and medical sectors [ 1 ]. The high consumption of mangosteen (regarded as the queen of fruits in Thailand) generates substantial quantities of pericarp waste. This underutilized biomass is a rich source of bioactive compounds with pharmacological properties, so-called xanthones [ 2 , 3 ]. These compounds consist of derivatives such as alpha-mangostin as the major component, and others like gamma-mangostin, beta-mangostin, etc. Alpha-mangostin has been extensively studied for various pharmacological effects, such as antioxidant, anti-inflammatory, anti-diabetic, anti-microbial, and anticancer properties [ 4 – 8 ]. Gamma-mangostin exhibits similar pharmacological effects, including antibacterial, anti-inflammatory, and anticancer properties [ 9 – 12 ]. To harness the potential of these valuable compounds, efficient extraction and separation techniques are crucial for their recovery from mangosteen pericarps. Various solid-liquid extraction techniques, such as solvent extraction and maceration, have been employed to recover xanthones from mangosteen pericarps [ 6 , 13 – 17 ]. Subsequent purification of target compounds, including alpha-mangostin, often involves column chromatography [ 18 ]. Batch chromatography is based on the principle of adsorption of solutes in the liquid phase on the surface of the solid adsorbent packed in the column [ 19 ]. While it offers advantages like high yield and purity, it suffers from drawbacks such as high solvent consumption and low product concentration, leading to increased energy consumption during downstream solvent removal. To address these limitations, the implementation of continuous separation processes is essential. Simulated Moving Bed (SMB) chromatography is a highly efficient continuous separation technique that employs a multi-column system. By periodically shifting the inlet and outlet ports in the direction of fluid flow while keeping the columns stationary, SMB simulates countercurrent flow between the solid adsorbent and liquid phase. This configuration offers numerous advantages, including high yield, purity, product concentration, and reduced solvent consumption. Consequently, SMB has been widely applied in various industries, such as petrochemicals for the separation of p-xylene and n-paraffins, and the sugar industry for the separation of glucose and fructose [ 20 , 21 ]. Additionally, bioactive compounds such as chlorogenic have been successfully separated with this method [ 22 ]. This study aimed to demonstrate the feasibility of a three-zone simulated moving bed (TZ-SMB) system for the continuous recovery of alpha-mangostin from xanthones extracted from mangosteen pericarps [ 23 – 25 ]. In the proposed TZ-SMB process, alpha-mangostin and gamma-mangostin fractions were targeted as the extract and raffinate products, respectively. To establish optimal operating conditions of the TZ-SMB, initial experiments were conducted using a single preparative C18 column. Pulse injection experiments were performed to determine key parameters, including total and external bed porosities, as well as the optimal mobile phase composition (% acetonitrile). Additionally, adsorption isotherms and mass-transfer coefficients were estimated by fitting mathematical models to experimental breakthrough curve data. Subsequently, a TZ-SMB process was simulated using triangle theory to identify operating conditions that maximized productivity while ensuring high purity (> 98%) for both alpha-mangostin and gamma-mangostin. Finally, experimental validation of the TZ-SMB process was conducted, and the purity of the recovered alpha-mangostin fraction was assessed by HPLC analysis. A three-zone simulated moving bed (TZ-SMB) system comprises three chromatographic columns connected in series, as illustrated in Fig. 1 . Zone I serves as the regeneration zone, where adsorbed compounds are desorbed using a liquid solvent (desorbent). Zones II and III function as separation zones, selectively adsorbing the more retained component (extract product) and desorbing the less retained component (raffinate product), respectively. The feed (liquid extract) is introduced into Zone III, where the separation of the two compounds occurs. The desorbent is fed into Zone I, eluting the adsorbed compounds and collecting the extract product at the outlet of this zone. The raffinate product is collected at the outlet of Zone III. After a specific switching time, the inlet and outlet ports are shifted one column position in the direction of fluid flow, as depicted in Fig. 1 . A complete cycle is achieved after three such shifts, returning all ports to their original positions. The operating parameters of a TZ-SMB system include flow rates (mL/min) of the desorbent ( \(\:{\text{Q}}_{\text{D}}\) ), feed ( \(\:{\text{Q}}_{\text{F}}\) ), extract ( \(\:{\text{Q}}_{\text{E}}\) ), and raffinate ( \(\:{\text{Q}}_{\text{R}}\) ), as well as the switching time ( \(\:{\text{t}}_{\text{s}}\) ). Assuming constant fluid density, the material balance equations for the liquid flow in each zone of the TZ-SMB system can be expressed as follows: Overall: \(\:{\text{Q}}_{\text{D}}+{\text{Q}}_{\text{F}}={\text{Q}}_{\text{E}}+{\text{Q}}_{\text{R}}\) (1) Zone I: \(\:{\text{Q}}_{\text{I}}={\text{Q}}_{\text{D}}\) (2) Zone II: \(\:{\text{Q}}_{\text{I}\text{I}}={\text{Q}}_{\text{I}}-{\text{Q}}_{\text{E}}\) (3) Zone III: \(\:{\text{Q}}_{\text{I}\text{I}\text{I}}={\text{Q}}_{\text{I}\text{I}}+{\text{Q}}_{\text{F}}={\text{Q}}_{\text{R}}\) (4) where \(\:{\text{Q}}_{\text{j}}\) is the volumetric flow rate of the liquid (mL/min) of zone j (j = I, II, and III). To evaluate the separation performance of the TZ-SMB, key parameters such as relative purity, productivity, capacity, and solvent consumption are calculated. These parameters can be determined based on the average concentrations of alpha-mangostin (AM) and gamma-mangostin (GM) in the extract (E) and raffinate (R) products, measured over a complete switching cycle during cyclic steady-state operation. The average concentration (g/L) is calculated according to Eq. (5). \(\:⟨{\text{C}}_{\text{G}\text{M}}^{\text{R}}⟩\) and \(\:⟨{\text{C}}_{\text{A}\text{M}}^{\text{E}}⟩\) (5) The % relative purities of gamma-mangostin in the raffinate product and alpha-mangostin in the extract product are calculated as follows: $$\:\text{P}{\text{U}}_{\text{R}}=\frac{⟨{\text{C}}_{\text{G}\text{M}}^{\text{R}}⟩}{⟨{\text{C}}_{\text{G}\text{M}}^{\text{R}}⟩+⟨{\text{C}}_{\text{A}\text{M}}^{\text{R}}⟩}\times\:100\:\text{a}\text{n}\text{d}\:\text{P}{\text{U}}_{\text{E}}=\frac{⟨{\text{C}}_{\text{A}\text{M}}^{\text{E}}⟩}{⟨{\text{C}}_{\text{G}\text{M}}^{\text{E}}⟩+⟨{\text{C}}_{\text{A}\text{M}}^{\text{E}}⟩}\times\:100$$ 6 The productivity is expressed in mg/(mL·h) and is defined as shown in Eq. 7 : $$\:\:\text{P}\text{d}=\frac{{\text{Q}}_{\text{F}}\left({\text{C}}_{\text{G}\text{M}}^{\text{F}}+{\text{C}}_{\text{C}\text{A}\text{M}}^{\text{F}}\right)}{(1-{}_{\text{b}}){\text{V}}_{\text{C}}{\text{N}}_{\text{C}}}$$ 7 where \(\:{}_{\text{b}}\) is the bed porosity. \(\:{\text{V}}_{\text{C}}\) is the column volume (mL). \(\:{\text{N}}_{\text{C}}\) is the number of columns in the TZ-SMB system. \(\:{\text{C}}_{\text{G}\text{M}}^{\text{F}}\) and \(\:{\text{C}}_{\text{A}\text{M}}^{\text{F}}\) represent the concentrations (g/L) of gamm-mangostin and alpha-mangostin in the feed (xanthone solution), respectively. The production capacity (mg/h) of both bioactive compound fractions in the raffinate and extract products are calculated according to Eqs. ( 7 ) and ( 8 ). $$\:{\text{C}\text{a}\text{p}}_{\text{G}\text{M}}=⟨{\text{C}}_{\text{G}\text{M}}^{\text{R}}⟩{\text{Q}}_{\text{R}}$$ 8 $$\:{\text{C}\text{a}\text{p}}_{\text{A}\text{M}}=⟨{\text{C}}_{\text{A}\text{M}}^{\text{E}}⟩{\text{Q}}_{\text{E}}$$ 9 The solvent consumption (mL/mg) is calculated as shown in Eq. ( 10 ): $$\:\:\text{S}\text{C}=\frac{{\text{Q}}_{\text{D}}}{{\text{Q}}_{\text{F}}\left({\text{C}}_{\text{G}\text{M}}^{\text{F}}+{\text{C}}_{\text{A}\text{M}}^{\text{F}}\right)}$$ 10 The dynamic adsorption behavior of both bioactive compounds in each TZ-SMB column is modeled using established equations for single-column systems. Key assumptions include isothermal conditions, plug flow liquid phase, and linear driving force mass transfer kinetics. The material balance equations for the liquid and solid phases are presented in Eqs. (11) and (12), respectively [ 26 , 27 ]: Liquid Phase: \(\:\frac{\partial\:{\text{C}}_{\text{i}}}{\partial\:{\theta\:}}+{\gamma\:}\frac{\partial\:{\stackrel{-}{\text{q}}}_{\text{i}}}{\partial\:{\theta\:}}=\frac{{\psi\:}}{\text{P}\text{e}}\frac{\partial\:{\text{C}}_{\text{i}}^{2}}{\partial\:{{\chi\:}}^{2}}-{\psi\:}\frac{\partial\:{\text{C}}_{\text{i}}}{\partial\:{\chi\:}}\) (11) Solid Phase: \(\:\frac{\partial\:{\stackrel{-}{\text{q}}}_{\text{i}}}{\partial\:{\theta\:}}={{\alpha\:}}_{\text{i}}\left({\text{q}}_{\text{i}}^{\text{*}}-{\stackrel{-}{\text{q}}}_{\text{i}}\right)\) (12) where \(\:{\text{C}}_{\text{i}}\:\) is the concentration of solute i in the liquid phase. \(\:{\stackrel{-}{\text{q}}}_{\text{i}}\:\) is the average concentration of solute i in the solid phase. \(\:{\text{q}}_{\text{i}}^{\text{*}}\:\) is the concentration of solute i in the solid phase, which is in equilibrium with \(\:{\text{C}}_{\text{i}}\) . All concentrations are expressed in g/L. The dimensionless parameters in the above equations are defined as follows: $$\:{\gamma\:}=\frac{1-{{\epsilon\:}}_{\text{b}}}{{{\epsilon\:}}_{\text{b}}}\:\text{a}\text{n}\text{d}\:{\psi\:}=\frac{\text{v}{\text{t}}_{\text{s}}}{{\text{L}}_{\text{c}}}$$ 13 $$\:\text{P}\text{e}=\frac{\text{v}{\text{L}}_{\text{c}}}{{\text{D}}_{\text{a}\text{x}}}\:\text{a}\text{n}\text{d}\:{{\alpha\:}}_{\text{i}}={\text{K}}_{\text{i},\text{j}}{\text{t}}_{\text{s}}$$ 14 Dimensionless parameters for time ( \(\:{\theta\:}\) ) and column axial distance ( \(\:{\chi\:}\) ) are written as: $$\:{\theta\:}=\frac{\text{t}}{{\text{t}}_{\text{s}}}\:\text{a}\text{n}\text{d}\:{\chi\:}=\frac{\text{z}}{{\text{L}}_{\text{c}}}$$ 15 \(\:\text{v}\) is the interstitial velocity (m/s), calculated from the ratio of superficial velocity to bed porosity. \(\:{\text{t}}_{\text{s}}\:\) is the switching time for TZ-SMB operation (s) or the operating time for adsorption-desorption in breakthrough curve experiment. \(\:{\text{L}}_{\text{c}}\:\) is the length of the preparative C18 column (m). \(\:{\text{D}}_{\text{a}\text{x}}\) is the axial dispersion coefficient (m 2 /s). The Péclet number (Pe) is a dimensionless number that represents the ratio of convective to dispersive mass transport rates. \(\:{\text{K}}_{\text{i},\text{j}}\:\) is the global mass-transfer coefficient (s − 1 ) calculated by Eq. ( 16 ) [ 28 ]. $$\:\frac{1}{{\text{K}}_{\text{i},\text{j}}}=\frac{1}{{\text{k}}_{\text{i}}}+\frac{{\text{R}}_{\text{p}}}{3{\text{k}}_{\text{i},\text{j}}^{\text{f}}}{\text{H}}_{\text{i}}$$ 16 where \(\:{\text{H}}_{\text{i}}\:\) is the linear adsorption isotherm of compound i. \(\:{\text{R}}_{\text{p}}\:\) is the radius of solid adsorbent (cm). \(\:{\text{k}}_{\text{i}}\:\) is the linear driving force mass-transfer coefficient (s − 1 ) calculated from the correlation proposed by Wilson and Geankoplis, as shown below: $$\:{\text{k}}_{\text{i}}=\left(\frac{{\Omega\:}{\text{D}}_{\text{e}\text{f}\text{f},\text{i}}}{{\text{R}}_{\text{p}}^{2}}\right)\left(\frac{1}{1-{{\epsilon\:}}_{\text{p}}}\right)$$ 17 where $$\:{\text{D}}_{\text{e}\text{f}\text{f},\text{i}}=\frac{{{\epsilon\:}}_{\text{p}{\text{D}}_{\text{m},\text{i}}}}{{\tau\:}}$$ 18 $$\:\tau\:=\frac{{\left(2-{{\epsilon\:}}_{\text{p}}\right)}^{2}}{{{\epsilon\:}}_{\text{p}}}$$ 19 In the above equations, \(\:{\Omega\:}\) is the geometric factor. \(\:{\text{D}}_{\text{e}\text{f}\text{f},\text{i}}\) is the effective diffusivity (cm 2 /s). \(\:{\tau\:}\) is the tortuosity factor. \(\:{\epsilon\:}_{p}\:\) is the particle porosity. The liquid phase convective mass-transfer coefficient, \(\:{\text{k}}_{\text{i},\text{j}}^{\text{f}}\:\) (cm/s), which is valid for 0.0015 < Reynolds number < 55, can be calculated from the correlation shown in Eq. ( 20 ) [ 29 ]. $$\:\text{S}\text{h}=\left(\frac{{\text{k}}_{\text{i},\text{j}}^{\text{f}}{\text{d}}_{\text{p}}}{{\text{D}}_{\text{m},\text{i}}}\right)=\left(\frac{1.09}{{{\epsilon\:}}_{\text{b}}}\right){\left(\frac{{{\rho\:}}_{\text{f}}\text{v}{{\epsilon\:}}_{\text{b}}{\text{d}}_{\text{p}}}{{\eta\:}}\right)}^{0.33}{\left(\frac{{\eta\:}}{{{\rho\:}}_{\text{f}{\text{D}}_{\text{m},\text{i}}}}\right)}^{0.33}$$ 20 Sh, is the dimensionless quantity called Sherwood number. \(\:{\text{d}}_{\text{p}}\:\) is the diameter of solid adsorbent particles (cm). \(\:{{\rho\:}}_{\text{f}}\) is the density of liquid solvent (kg/m 3 ). \(\:{\eta\:}\) is the viscosity of liquid solvent (kg/m⋅s). The diffusivity of a solute adsorbed in the column, \(\:{\text{D}}_{\text{m},\text{i}}\) (m 2 /s), can be calculated from the correlation of Wike and Chang, as shown in Eq. ( 21 ) [ 30 , 31 ]. $$\:{\text{D}}_{\text{m},\text{i}}=7.4\times\:{10}^{-8}\frac{{\left({\upvarphi\:}{\text{M}}_{\text{i}}\right)}^{0.5}\text{T}}{{\eta\:}{\text{V}}_{\text{m},\text{i}}^{0.6}}$$ 21 where \(\:{\upvarphi\:}\) is the association solvent parameter [ 19 ]. \(\:{\text{M}}_{\text{i}}\:\) is the molecular weight of solvent (g/mol). T is the absolute temperature (K). \(\:{\text{V}}_{\text{m}.\text{i}}\) is the molar volume of solute at its normal boiling point (mL/mol). The dimensionless initial and boundary conditions for solving Eqs. (11) and (12) are shown in Eqs. (22), (23) and (24). Initial conditions: \(\:\:{\text{C}}_{\text{i}}\left({\chi\:},0\right)=0\:\) and \(\:{\stackrel{-}{\text{q}}}_{\text{i}}\:\left({\chi\:},0\right)=0\) (22) Boundary conditions: At column entrance: \(\:{\text{C}}_{\text{i}}\left(0,{\theta\:}\right)={\text{C}}_{\text{i}}^{\text{i}\text{n}}+\frac{1}{\text{P}\text{e}}\frac{\partial\:{\text{C}}_{\text{i}}}{\partial\:{\chi\:}}\) (23) At column exit: \(\:\frac{\partial\:{\text{C}}_{\text{i}}}{\partial\:{\chi\:}}\left(1,{\theta\:}\right)=0\) (24) where \(\:{\text{C}}_{\text{i}}^{\text{i}\text{n}}\) is the initial feed concentration (g/L) of solute i fed to the column. 2. Material and Methods 2.1. Chemicals and Raw Materials Mangosteen pericarps were sourced from a local market in Bangkok. Distilled deionized water (DDW) with a resistivity of 18.2 MΩ·cm was used as a solvent. HPLC-grade acetonitrile, methanol, and acetone were purchased from MERCK (Darmstadt, Germany). Alpha-mangostin (α-MG) and gamma-mangostin (γ-MG) standards, with a minimum purity of 98% (HPLC), were obtained from Sigma-Aldrich. Blue dextran (HPLC grade), used as a chromatographic marker, was also procured from Sigma-Aldrich. 2.2. Preparation of Xanthone Powder Mangosteen pericarps were cleaned and dried in a hot air oven (Memmert, UF110) at 60°C for 48 hours to remove moisture. The dried pericarps were ground into a fine powder using a grinder and sieved to obtain particles smaller than 150 µm. A reflux extractor with a 500 mL working volume was used to extract the powdered pericarps. Pure acetonitrile was employed as the solvent, with a solid-to-liquid ratio of 1:8.24 (g/mL), and the extraction was conducted at 70°C for 120 min. The resulting extract was filtered through a 0.45 µm membrane filter to remove solid residues. The filtered extract was concentrated tenfold using a vacuum evaporator. Subsequently, deionized distilled water (DDW) was added in a 4:1 volume ratio to induce the precipitation of xanthones. The precipitated xanthones were collected and dried in a hot air oven at 60°C for 24 h. 2.3. The Single-Column Experiments 2.3.1. Determination of External and Total Porosities of a Preparative C18 Column A C18 preparative column (Visper, USA) with dimensions of 10 x 250 mm and a particle size of 10 µm was used. The HPLC system described in Section 2.6 was employed for this experiment. The column temperature was maintained at 40°C, and a mobile phase consisting of 75% v/v acetonitrile was used. The pump flow rate was varied between 0.6 and 1.4 mL/min, with a wavelength of 330 nm and an injection volume of 50 µL. To determine the external bed porosity, a 0.76 mg/mL solution of blue dextran in DDW water was injected into the column. For the total bed porosity, pure acetone was injected instead of blue dextran. The retention times of both substances were recorded and used to calculate the respective bed porosities using Eq. ( 25 ). $$\:{\text{t}}_{\text{r}}={\epsilon\:}\frac{{\text{L}}_{\text{c}}}{\text{u}}$$ 25 where \(\:{\text{t}}_{\text{r}}\) ​ is the retention time of blue dextran or acetone (min), \(\:{\epsilon\:}\) represents the external bed porosity ( \(\:{{\epsilon\:}}_{\text{b}}\) ​) or total bed porosity ( \(\:{{\epsilon\:}}_{\text{T}}\) ​). \(\:{\text{L}}_{\text{c}}\) ​ is the column length (m), and \(\:\text{u}\) is the superficial velocity (m/min), calculated by dividing the flow rate (mL/min) by the cross-sectional area of the column (m 2 ). 2.3.2. Pulse Injection Experiment in a Preparative C18-Column To determine the linear adsorption isotherms of α-MG and γ-MG, a pulse injection experiment was conducted using the chromatographic setup illustrated in Fig. 2 . This setup comprised a gradient dual-piston pump (Waters, USA), a preparative C18 column (Visper, USA) with dimensions of 10 x 250 mm and a particle size of 10 µm, and a convection oven. The column temperature was maintained at 40°C, and the mobile phase flow rate was varied between 4 and 7 mL/min with a composition ranging from 65–75% v/v acetonitrile. A feed solution, prepared by extracting DMP with pure acetonitrile and diluting with DDW to match the mobile phase composition, was introduced into the column using an isocratic pump (Knauer, Germany) at a flow rate of 1 mL/min for 30 seconds. The injection was controlled by a multi-position valve (VICI-Valco, USA). The product stream was split into two: one directed to a UV detector (Variant 7250, USA) for signal detection at 320 nm, and the other routed to a multi-position valve for periodic fractionation. The volumetric ratio between the two streams was regulated using an isocratic pump (Knauer, Germany) and a needle valve. The retention times ( \(\:{\text{t}}_{\text{r},\text{i}}\) ) of α-MG and γ-MG were recorded and used to calculate the linear adsorption isotherms ( \(\:{\text{H}}_{\text{i}}\) ) using Eq. ( 26 ) and the selectivity of separation ( \(\:{}_{\text{i},\text{j}}\) ) using Eq. ( 27 ). $$\:{\text{t}}_{\text{r},\text{i}}=\left[1+\left(\frac{1-{{\epsilon\:}}_{\text{b}}}{{{\epsilon\:}}_{\text{b}}}\right){\text{H}}_{\text{i}}\right]\left(\frac{{{\epsilon\:}}_{\text{b}}{\text{V}}_{\text{c}}}{\text{Q}}\right)$$ 26 $$\:{}_{\text{i},\text{j}}=\frac{{\text{H}}_{\text{j}}}{{\text{H}}_{\text{i}}}$$ 27 where \(\:\text{Q}\) is the mobile phase flow rate (mL/min) and \(\:{\text{V}}_{\text{c}}\) is the column volume (mL). 2.3.3. Breakthrough Curve Experiment in a Preparative C18 Column The chromatographic system described in Section 2.3.2 was employed for adsorption-desorption experiments. A preparative C18 column, maintained at 40°C, was used. Feed solutions containing 1, 3, and 5 g/L of xanthone powder dissolved in 75% v/v acetonitrile were prepared. During the adsorption phase, a 75% acetonitrile solution was delivered to the column at a flow rate of 5 mL/min. This solution was mixed with the feed solution, delivered at 1 mL/min, resulting in a total flow rate of 6 mL/min. The adsorption phase continued for 40 min until column saturation. Subsequently, the system switched to the desorption phase, where a 75% acetonitrile solution was introduced at a flow rate of 6 mL/min for 40 min to elute all adsorbed components. Effluent samples were collected every minute during both adsorption and desorption phases and analyzed using HPLC (described in Section 2.6 ) to quantify α-MG and γ-MG concentrations. 2.3.4. Computational Simulation of Breakthrough Curve The concentration-time profiles of α-MG and γ-MG at the column's exit, obtained from adsorption-desorption experiments, were modeled using the mathematical approaches outlined in section 1 , as expressed in Eqs. (11)-(24). These models were employed to fine-tune the experimental breakthrough curve data across various concentration levels, enabling the determination of adsorption parameters for each compound, such as the linear adsorption isotherm constant, the global mass-transfer coefficient, and Péclet number. The initial guesses for the linear isotherm were derived from the results of the pulse injection experiment described in section 2.3.2 , while the values for the global mass-transfer coefficient were calculated using Eqs. ( 16 )-( 21 ). All equations were numerically solved using the finite element method in MATLAB® version 2021b and FLEXPDE® version 6.5, running on the Windows® 10 operating system. The effectiveness of the fine-tuning process was assessed by calculating r-squared. The concentration-time profiles of α-MG and γ-MG at the column outlet, obtained from adsorption-desorption experiments, were modeled using the mathematical framework described in Section 1 (see Eqs. (11)-(24)). These models were employed to fit the experimental breakthrough curve data at various concentration levels, enabling the determination of adsorption parameters for each compound, including the linear adsorption isotherm constant, global mass-transfer coefficient, and Péclet number. Initial estimates for the linear isotherm parameters were derived from the pulse injection experiments described in Section 2.3.2 , while the global mass-transfer coefficients were calculated using Eqs. ( 16 )-( 21 ). All equations were numerically solved using the finite element method in MATLAB® version 2021b and FLEXPDE® version 6.5, running on Windows® 10. The goodness-of-fit of the models was assessed by calculating the coefficient of determination (R²). 2.4. Three-Zone Simulated Moving Bed (TZ-SMB) 2.4.1. Simulation of TZ-SMB System The five operating parameters of the TZ-SMB system, namely the flow rates of desorbent ( \(\:{\text{Q}}_{\text{D}}\) ), feed ( \(\:{\text{Q}}_{\text{F}}\) ), extract ( \(\:{\text{Q}}_{\text{E}}\) ), and raffinate ( \(\:{\text{Q}}_{\text{R}}\) ), and the switching time ( \(\:{\text{t}}_{\text{s}}\) ), were determined using separation triangle theory, as detailed in Section 3.3. Each operating condition within the separation triangle was used to simulate the concentration profiles of α-MG and γ-MG along the column length in each zone of the TZ-SMB. The mathematical models for a single column, Eqs. (11)-(24), and the material balance equations for the TZ-SMB, Eqs. (1)-(4), were applied, using the previously determined adsorption parameters from single-column experiments. The system of equations was solved numerically using MATLAB® version 2021b and FLEXPDE® version 6.5 on a Windows® 10 operating system. In the simulated TZ-SMB system, the inlet and outlet ports were periodically shifted to mimic countercurrent flow between the solid and liquid phases. This was computationally achieved by setting the final state of each column as the initial state of the subsequent column at the end of each switching period. Separation performance was evaluated using Equations (5)-( 10 ), based on data obtained during the cyclic steady state. For the TZ-SMB simulations, a feed solution containing α-MG and γ-MG at initial concentrations of 0.30 g/L and 0.05 g/L, respectively, was used. Three preparative C18 columns with dimensions of 10 x 250 mm were employed. The system temperature was maintained at 40°C, and the desorbent flow rate was set to 5 mL/min. The switching time was fixed at 20 min. The optimal operating condition for the TZ-SMB was defined as the one that maximized productivity while ensuring that the relative purities of γ-MG in the raffinate product and α-MG in the extract product were both at least 98%. 2.4.2. Experiment of TZ-SMB system Figure 3 illustrates the three-zone simulated moving bed (TZ-SMB) system employed in this study. The system comprises three HPLC pumps (Shimadzu, Japan) delivering the mobile phase (desorbent), feed solution (xanthone solution), and extract product. The flow rates of the extract product were regulated using a metering valve, while the raffinate product flow rate was uncontrolled and determined by mass balance. Four six-port valves (VICI Valco Instruments) equipped with a control module governed the periodic port switching within the TZ-SMB. Three preparative C18 columns (10 × 250 mm, 10 µm particle size, Visper, USA) were housed in a temperature-controlled convection oven at 40°C and interconnected with check valves to direct flow. The feed solution for the TZ-SMB (liquid extract of xanthone) was prepared by dissolving dried xanthone powder in 75% v/v acetonitrile solution to achieve a concentration of 0.5 g/L. During TZ-SMB operation, the following flow rates were maintained: desorbent 5.00 mL/min, feed solution 0.929 mL/min, extract product 2.292 mL/min, and raffinate product 3.637 mL/min, with a switching time of 20 min. The experiment was conducted for 48 switches (16 cycles). Throughout this period, the extract and raffinate products were continuously collected and analyzed by HPLC to determine α-MG and γ-MG concentrations. The separation performance, including % relative purity and production capacity of bioactive compounds, was evaluated using Eqs. ( 6 ), ( 8 ) and (9), respectively. 2.5. Determination of HPLC Purity of Alpha-Mangostin in the Products To compare the purity of α-mangostin in xanthone powder (prepared as described in Section 2.2 ) and the dried α-mangostin fraction from the TZ-SMB extract product, both samples were analyzed by HPLC. The TZ-SMB extract product was concentrated by vacuum evaporation to obtain dried α-mangostin. The HPLC purity of α-mangostin in both the xanthone powder and the dried α-mangostin fraction was determined using a weighing method. A 5 mg sample of each was dissolved in 5 mL of acetonitrile to create a 1 g/L stock solution. Dilutions of this stock solution were prepared to obtain concentrations ranging from 0.1 to 0.5 g/L. A calibration curve was constructed using these solutions, and the calibration factor (slope) was determined. The % purity of α-mangostin in each sample was calculated by dividing the calibration factor of the sample by the calibration factor of an α-mangostin HPLC standard. 2.6. Analytical Method HPLC analysis was performed on a C18 ACE Excel 5 column (25 cm × 4.6 mm, 5 µm particle size) maintained at 20°C with a detection wavelength of 320 nm. Liquid samples were filtered through a 0.45 µm syringe filter and stored in 2 mL vials. A 10 µL injection volume and a mobile phase flow rate of 1 mL/min were employed. The mobile phase consisted of a gradient mixture of distilled deionized water (A) and acetonitrile (B). The initial composition was 15% A and 85% B, linearly increasing to 30% A and 70% B over 20 min. The solvent composition was then further adjusted to 10% A and 90% B at 22 min and held constant until the end of the analysis at 35 min. Separate calibration curves were generated for α-MG and γ-MG using standards dissolved in 80% methanol. The α-MG standard concentrations ranged from 0.06 to 0.53 mg/mL, while the γ-MG standard concentrations ranged from 0.05 to 0.51 mg/mL. 3. Result and Discussions This work was divided into three primary areas of investigation. First, xanthone powder was prepared using extraction and precipitation methods. This powder served as the feedstock for subsequent separations in both single-column and TZ-SMB systems. Second, adsorption parameters were determined through pulse injection and breakthrough curve experiments conducted on a single preparative C18 chromatographic column. Third, the TZ-SMB system was designed and simulated using the experimentally determined adsorption parameters for the series of preparative C18 columns. The efficacy of this system was experimentally validated through the continuous separation of α-mangostin and γ-mangostin. 3.1. Preparation of Xanthone Powder Xanthone, a mixture containing α-mangostin (α-MG), γ-mangostin (γ-MG), and other minor compounds, was extracted from dried mangosteen pericarps using a solid-liquid extraction method. Due to the extremely low water solubility of α-MG and γ-MG (approximately 2.03 × 10⁻⁴ mg/L for α-MG [ 32 ]), a solvent with a lower polarity index than water (polarity index = 1) was required. While low-polarity solvents like hexane could be considered, their toxicity precluded their use. Considering the molecular structure of α-MG and γ-MG, which primarily consists of a xanthone backbone with hydroxyl, methoxy, and prenyl functional groups, solvents with moderate polarity were deemed suitable. Ethanol (polarity index = 0.654) and acetonitrile (polarity index = 0.46) were identified as promising candidates. Acetonitrile was selected due to its lower viscosity (0.334 cP) compared to ethanol (1.1 cP), which facilitates mass transfer of bioactive compounds from the solid matrix into the solvent. Additionally, acetonitrile is more cost-effective than ethanol, especially in regions with alcohol taxes like Thailand. The HPLC chromatogram of the liquid extract (Fig. 4 ) and the corresponding yields of α-MG and γ-MG, based on the dried weight of mangosteen pericarp, are presented in Table 1 . The predominant peak in the chromatogram corresponds to α-MG, indicating a higher yield compared to γ-MG, as confirmed by the quantitative data in Table 1 . The obtained yields of α-MG (21.10 mg/g DMP) and γ-MG (2.48 mg/g DMP) are comparable to those reported in the literature using ethanol and microwave-assisted extraction (27.03 mg/g for α-MG and 5.56 mg/g for γ-MG [ 34 ]). Table 1 The yields of α-MG and γ-MG, reported based on the weights of DMP and dried xanthone. Bioactive compounds Yield (mg/ g DMP) Yield (mg/ g xanthone) Alpha-mangostin (α-MG) 21.10 205.81 Gamma-mangostin (γ-MG) 2.48 36.82 To obtain xanthone powder, the liquid extract was concentrated by evaporation to remove excess solvent. The resulting concentrated liquid extract, primarily composed of acetonitrile, was then subjected to a precipitation process. Given the low water solubility of both α-MG and γ-MG, the addition of excess water induced the precipitation of insoluble xanthones, effectively separating them from polar, water-soluble impurities. The precipitated solid was isolated from the supernatant and dried to yield xanthone powder. This powder was subsequently dissolved in acetonitrile and analyzed by HPLC to confirm the presence of α-MG and γ-MG. The chromatogram in Fig. 10 a and the corresponding yields in Table 1 indicate that the composition of the xanthone powder closely resembled that of the initial liquid extract. The obtained xanthone powder served as the feedstock for both batch single-column and continuous TZ-SMB separation processes. Based on the chromatogram in Fig. 10 a, α-MG and γ-MG were identified as the major and minor components, respectively. To accurately determine the purity of α-MG in the xanthone powder, calibration curves were constructed for both the sample and a commercial α-MG standard (HPLC grade) using various concentrations in acetonitrile (Fig. 5 ). The ratio of the slopes of these calibration curves provides the true HPLC purity of the xanthone powder, which was found to be 71.56%. To further enhance the purity of α-MG to at least 98%, the implementation of a TZ-SMB system was explored. 3.2. Separation of Alpha-Mangostin and Gamma-Mangostin in a Single Preparative C18 Chromatographic Column. 3.2.1. Determination of Bed and Total Porosities of a Preparative C18 Column The external bed porosity was determined using blue dextran, a high molecular weight substance (approximately 2000 Da). Due to its large size, blue dextran can only permeate the external pores of the column, undergoing size exclusion. Total bed porosity was estimated using acetone, which can access both external and internal pores of the C18 adsorbent. Figure 6 illustrates the retention times of blue dextran and acetone plotted against the ratio of superficial velocity to column length. The slopes of these graphs represent the external ( \(\:{\epsilon\:}_{b}\) ) and total ( \(\:{\epsilon\:}_{T}\) ) porosities, respectively. The calculated values were \(\:{\epsilon\:}_{b}\) = 0.3238 and \(\:{\epsilon\:}_{T}\) = 0.6717. The external porosity of 0.3238 is consistent with the typical range for nearly spherical adsorbent particles (around 0.4). The total porosity, which accounts for both external and internal pore volumes, is naturally higher than the external porosity. Particle porosity ( \(\:{\epsilon\:}_{p}\) ) was calculated using Eq. ( 28 ), yielding a value of 0.5145. $$\:{\epsilon\:}_{T}={\epsilon\:}_{b}+\left(1-{\epsilon\:}_{b}\right){\epsilon\:}_{p}\:\:$$ 28 3.2.2. Determination of Linear Isotherm Parameters Using Pulse Injection Method Linear adsorption isotherms for α-mangostin and γ-mangostin were calculated using Eq. 26 at various acetonitrile concentrations in the mobile phase, considering the predetermined external bed porosity. As shown in Table 2 , a decrease in acetonitrile concentration led to a corresponding increase in the linear adsorption isotherm values for both compounds. This phenomenon can be attributed to the increased polarity of the mobile phase with a higher water content. Due to their low water solubility and non-polar nature, α-mangostin and γ-mangostin exhibit stronger retention or adsorption on the C18 phase in a more polar environment, resulting in increased retention times as the acetonitrile concentration decreases. Furthermore, the linear isotherm of α-mangostin was consistently higher than that of γ-mangostin across all mobile phase compositions, indicating stronger retention of α-mangostin compared to γ-mangostin. Consequently, in the continuous separation using a three-zone simulated moving bed, α-mangostin was designated as the extract product, while γ-mangostin was considered the raffinate product. Table 2 The linear adsorption isotherms of α-MG and γ-MG in a preparative C18 column Acetonitrile concentration (%v/v) Linear adsorption isotherm of alpha-mangostin, H α−MG Linear adsorption isotherm of gamma-mangostin, H γ−MG Selectivity (H α−MG / H γ−MG ) 75 4.15 2.68 1.55 70 5.67 3.58 1.58 65 12.32 7.81 1.58 The selectivity of the separation on the preparative C18 column, calculated as the ratio of the linear isotherm of α-mangostin to that of γ-mangostin (Eq. ( 27 )), was approximately 1.6 across all mobile phase concentrations. This selectivity value, greater than unity, indicated the feasibility of the separation. Considering these results, an acetonitrile concentration of 75% v/v was selected for subsequent experiments. While this concentration resulted in the lowest linear adsorption isotherms, it offered a suitable balance between selectivity, resolution, and retention time, which are crucial factors for efficient TZ-SMB operation. Shorter retention times enable the system to reach cyclic steady-state operation more rapidly. The chosen conditions, 75% v/v acetonitrile and a flow rate of 6 mL/min, were employed for the breakthrough curve experiments described in the following section. 3.2.3. Breakthrough Curve Experiments of Alpha-mangostin and Gamma-Mangostin Xanthone solutions prepared at initial concentrations of 1, 3, and 5 g/L in 75% v/v acetonitrile were used as feed for adsorption and desorption experiments. The concentration profiles of γ-mangostin and α-mangostin during adsorption are depicted in Figs. 7 a and 7 c. Initially, neither compound was detected in the effluent, as both were fully adsorbed onto the column. Subsequently, γ-mangostin appeared at 7 min, followed by α-mangostin at 12 min. The concentrations of both compounds gradually increased until reaching a plateau, indicating saturation of the column. The sharp S-shaped breakthrough curves suggest minimal mass transfer resistance during the adsorption process. The 5-min time gap between the breakthrough of α-mangostin and γ-mangostin highlights the successful separation, attributable to the differing adsorption affinities of the two compounds. γ-Mangostin, being less retained, eluted earlier, while α-mangostin, the more strongly retained compound, eluted later. During the desorption process, as shown in Fig. 7 b and 7 d, the concentrations of both compounds decreased over time, eventually reaching zero, indicating complete elution. The less retained γ-mangostin was eluted first, followed by the more retained α-mangostin. The time gap between the two compounds persisted during desorption, further emphasizing their distinct adsorption behaviors. The simulated concentration profiles for all initial xanthone concentrations are overlaid as lines in Fig. 7 a- 7 f. The fitted parameters obtained from the breakthrough curve experiments are presented in Table 3 . Model validation was performed using an initial xanthone concentration of 2 g/L, as shown in Fig. 7 e and 7 f. The good agreement between the experimental data and the model predictions, as indicated by the R-squared values in Table 4 , confirms the accuracy of the model. The adsorption parameters obtained from the single preparative C18 column were subsequently used in the design and simulation of the TZ-SMB system, as detailed in the next section. Table 3 The fitted adsorption parameters from the breakthrough curve experiments and the column parameters for a single preparative C18 column Adsorption Parameters Unit Alpha-mangostin Gamma-mangostin Linear adsorption isotherm (H i ) - 5.50 3.18 Global mass-transfer coefficient ( \(\:{\text{K}}_{\text{i},\text{j}}\) ) s − 1 73.27 90.65 Péclet number (Pe) - 500 500 Column Parameters External bed porosity ( \(\:{\epsilon\:}_{b}\) ) - 0.3238 Total porosity ( \(\:{\epsilon\:}_{T}\) ) - 0.6717 Particle porosity ( \(\:{\epsilon\:}_{p}\) ) - 0.5145 Column length mm 250 Column diameter mm 10 Table 4 The R-squared values for the simulation of breakthrough curve experiments Xanthone Alpha-mangostin Gamma-Mangostin concentration Adsorption Desorption Adsorption Desorption (g/L) R-squared R-squared R-squared R-squared 1 0.9976 0.9989 0.9993 0.9965 3 0.9956 0.9803 0.9972 0.9812 5 0.9873 0.9644 0.9753 0.9216 2 0.9856 0.9573 0.9930 0.9592 3.3. Design and Simulation of the Separation of Alpha-Mangostin and Gamma-Mangostin in a Three-Zone Simulated Moving Bed System The triangle theory [ 35 ] was employed to determine the optimal operating parameters of the TZ-SMB system, including switching time and flow rates for the desorbent, feed (liquid extract), extract product, and raffinate product. This theory assumes instantaneous equilibrium between the liquid and solid phases (adsorbent) and neglects the effects of mass transfer resistance. To achieve complete separation, each of the three zones in the TZ-SMB must fulfill specific functions: Zone I: Both α-mangostin and γ-mangostin are designed to elute completely, with the extract product predominantly consisting of α-mangostin. The flow rate ratio, as defined by Eq. ( 32 ), must exceed the linear adsorption isotherms of both compounds. Zone II: This zone facilitates the adsorption of α-mangostin while promoting the complete desorption of γ-mangostin. Zone III: α-mangostin adsorption is maintained to prevent its premature elution, while γ-mangostin undergoes desorption, allowing the raffinate product, primarily composed of γ-mangostin, to exit from this zone. Zones II and III are collectively referred to as the separation zones. The flow rate ratios in these two zones must fall between the linear adsorption isotherm values of γ-mangostin and α-mangostin. Based on the above description, the equations representing the triangle separation region are as follows: Zone I: m I > H α−MG (29) Zone II: H γ−MG < m II < H α−MG (30) Zone III: H γ−MG < m III < H α−MG (31) The flow rate ratio ( \(\:{\text{m}}_{\text{j}}\) ) in each zone j of TZ-SMB is defined as: $$\:{\text{m}}_{\text{j}}=\frac{{\text{Q}}_{\text{j}}{\text{t}}_{\text{s}}-{{\epsilon\:}}_{\text{b}}{\text{V}}_{\text{C}}}{\left(1-{{\epsilon\:}}_{\text{b}}\right){\text{V}}_{\text{C}}}$$ 32 where \(\:{\text{Q}}_{\text{j}}\) is the volumetric flow rate in zone j of TZ-SMB (mL/min). The initial step involved determining the optimal flow rate ratio for Zone I (m I ). A flow rate of 5 mL/min (Q I or Q D ) and a switching time (t s ) of 20 minutes were selected based on the breakthrough curve experiments. This flow rate ensured complete elution of all bioactive compounds within the 20-min switching time while minimizing pressure drop across the column. The corresponding flow rate ratio, calculated using Eq. ( 32 ), was 7.053. To construct the separation triangle defined by Eqs. (29), (30), and (31), the coordinates (m II , m III ) were varied within the triangular region, as depicted in Fig. 8 . A total of 22 simulation conditions, derived from Eqs. ( 32 ) and (1)-(4), were generated and listed in Table 5 . Table 5 The simulated results of TZ-SMB for the separation of α-MG and γ-MG Run Q D Q F Q E Q R \(\:⟨{\text{C}}_{\text{A}\text{M}}^{\text{E}}⟩\) \(\:⟨{\text{C}}_{\text{G}\text{M}}^{\text{R}}⟩\) \(\:\text{P}{\text{U}}_{\text{E}}\) \(\:\text{P}{\text{U}}_{\text{R}}\) Pd \(\:{\text{C}\text{a}\text{p}}_{\text{A}\text{M}}\) \(\:{\text{C}\text{a}\text{p}}_{\text{G}\text{M}}\) SC (mL/min) (mL/min) (mL/min) (mL/min) (mg/mL) (mg/mL) % % mg/mL⋅h mg/h mg/h (mL/mg) 1 5.000 0.664 2.425 3.239 0.082 0.010 99.94 99.99 0.35 11.94 1.98 21.52 2 5.000 0.664 2.359 3.305 0.084 0.010 99.98 99.98 0.35 11.93 1.99 21.52 3 5.000 0.664 2.292 3.372 0.087 0.010 99.99 99.94 0.35 11.94 1.99 21.52 4 5.000 0.664 2.226 3.438 0.089 0.010 100.00 99.84 0.35 11.93 1.99 21.52 5 5.000 0.664 2.159 3.504 0.092 0.009 100.00 99.63 0.35 11.93 1.99 21.52 6 5.000 0.664 2.093 3.571 0.095 0.009 100.00 99.19 0.35 11.92 1.99 21.52 7 5.000 0.664 2.027 3.637 0.098 0.009 100.00 98.34 0.35 11.90 1.99 21.52 8 5.000 0.797 2.425 3.372 0.098 0.012 99.95 99.94 0.42 14.33 2.38 17.93 9 5.000 0.797 2.359 3.438 0.101 0.012 99.98 99.84 0.42 14.32 2.39 17.93 10 5.000 0.797 2.292 3.504 0.104 0.011 99.99 99.63 0.42 14.32 2.39 17.93 11 5.000 0.797 2.226 3.571 0.107 0.011 100.00 99.20 0.42 14.31 2.39 17.93 12 5.000 0.797 2.159 3.637 0.110 0.011 100.00 98.35 0.42 14.29 2.39 17.93 13 5.000 0.797 2.093 3.704 0.113 0.011 100.00 96.81 0.42 14.25 2.39 17.93 14 5.000 0.929 2.425 3.504 0.115 0.013 99.95 99.64 0.49 16.69 2.78 15.37 15 5.000 0.929 2.359 3.571 0.118 0.013 99.98 99.22 0.49 16.68 2.78 15.37 16 5.000 0.929 2.292 3.637 0.121 0.013 99.99 98.39 0.49 16.66 2.78 15.37 17 5.000 0.929 2.226 3.704 0.124 0.013 100.00 96.90 0.49 16.61 2.78 15.37 18 5.000 0.929 2.159 3.770 0.128 0.012 100.00 94.28 0.49 16.53 2.78 15.37 19 5.000 1.062 2.425 3.637 0.131 0.015 99.95 98.41 0.56 19.04 3.17 13.45 20 5.000 1.062 2.359 3.704 0.134 0.014 99.98 96.95 0.56 18.99 3.18 13.45 21 5.000 1.062 2.292 3.770 0.137 0.014 99.99 94.43 0.56 18.91 3.18 13.45 22 5.000 1.062 2.226 3.836 0.140 0.014 100.00 90.39 0.56 18.75 3.18 13.45 Theoretically, complete separation (100% purity) is achievable within the boundaries of the separation triangle. The simulated performance parameters at cyclic steady-state, including average concentrations, relative purities, production capacities, productivity, and solvent consumption ratio, were calculated using Eqs. (5)-( 10 ) and presented in Table 5 . In Fig. 8 , operating conditions resulting in relative purities exceeding 98% for both extract and raffinate products are denoted by green squares, while those with lower purities are indicated by red squares. It is noteworthy that some operating conditions within the separation triangle failed to achieve the desired purities due to mass transfer resistance within the system. The optimal condition, yielding the highest productivity while meeting the purity criteria, is represented by a yellow triangle (condition #19 in Table 5 ). At the optimal condition 19, the simulated results were as follows: the extract product exhibited a relative purity of 99.95% for α-mangostin, with a production capacity of 19.04 mg/h. The raffinate product demonstrated a relative purity of 98.41% for γ-mangostin, with a production capacity of 3.17 mg/h. The system achieved a productivity of 0.56 mg/mL·h and a solvent consumption ratio of 13.45 mL/mg. The corresponding flow rates for desorbent, feed, extract, and raffinate were 5.00, 1.062, 2.425, and 3.637 mL/min, respectively. 3.4. Experimental Demonstration of TZ-SMB for the separation of α-MG and γ-MG Condition #16 from Table 5 was selected for the experimental demonstration of the TZ-SMB system. Although it offered a lower productivity compared to the optimal condition, it guaranteed the purity of both α-mangostin and γ-mangostin in the extract and raffinate products, as it resided within the green zone of at least 98% purity. Additionally, this condition provided a buffer against potential flow rate fluctuations in the real experimental system. Figure 9 a and 9 b illustrate the total capacities (mg/h) of α-mangostin and γ-mangostin in the extract and raffinate products, respectively, over the switching time. As calculated using Eqs. ( 8 ) and ( 9 ), all capacities increased over time and reached a plateau upon achieving cyclic steady-state. Table 6 presents a comparison of the separation parameters obtained from both experimental and simulation results for the TZ-SMB system, revealing a strong agreement between the predicted and experimental values. Table 6 Separation parameters from the experimental and simulation results of the TZ-SMB system Separation parameters Unit Experimental Simulation % Diff \(\:⟨{\text{C}}_{\text{A}\text{M}}^{\text{E}}⟩\) mg/mL 0.1811 0.1482 18.18 \(\:⟨{\text{C}}_{\text{G}\text{M}}^{\text{R}}⟩\) mg/mL 0.0138 0.0135 1.85 Pu E % 100.00 99.99 0.01 Pu R % 98.79 98.14 0.66 \(\:{\text{C}\text{a}\text{p}}_{\text{A}\text{M}}\) mg/h 23.73 20.38 14.12 \(\:{\text{C}\text{a}\text{p}}_{\text{G}\text{M}}\) mg/h 3.10 2.95 4.70 The chromatograms of the feed, extract product, and raffinate product from the TZ-SMB system are presented in Fig. 10 a, 10 b, and 10 c, respectively. The extract product was predominantly composed of α-mangostin, aligning with the experimental relative purity of 100%. Similarly, the raffinate product primarily consisted of γ-mangostin, as indicated by the experimental relative purity of 98.79%. The true purity of α-mangostin in the extract product was calculated from Fig. 5 , using the slope of the calibration curve to determine the ratio of the extract product to the HPLC standard. The calculated true purity was 99.4%. Figure 11 b depicts the appearance of the extract product after evaporation, revealing a yellowish dried powder similar to the xanthone powder shown in Fig. 11 a. The significant improvement achieved using the TZ-SMB system, increasing the HPLC purity of α-mangostin from 71.56–99.4%, renders it suitable for pharmaceutical applications. This work successfully demonstrated the application of a continuous separation system to enhance the purity of α-mangostin derived from mangosteen pericarp waste. 4. Conclusion This work successfully demonstrated the application of a three-zone simulated moving bed (TZ-SMB) system for the continuous separation of α-mangostin and γ-mangostin from a liquid extract derived from mangosteen pericarps. Initially, xanthone powder was prepared through solvent extraction and anti-solvent precipitation, yielding an α-mangostin purity of 71.56% as determined by HPLC. This xanthone powder served as the feedstock for a single preparative C18 chromatographic column, enabling the determination of adsorption parameters, including linear adsorption isotherms, mass transfer coefficients, and Péclet numbers, through breakthrough curve experiments for both bioactive compounds. Pulse injection experiments confirmed that a mobile phase composed of 75% v/v acetonitrile effectively separated the two compounds. Subsequently, the design and simulation of the TZ-SMB system, leveraging triangle theory and the experimentally determined adsorption parameters, identified optimal operating conditions. With a switching time of 20 min and flow rates of 5.00, 1.062, 2.425, and 3.637 mL/min for desorbent, feed, extract, and raffinate, respectively, the system achieved a maximum productivity of 0.56 mg/mL·h while maintaining relative purities exceeding 98% for both bioactive compounds in the extract and raffinate products. Experimental validation of the TZ-SMB system, employing flow rates of 5.00, 0.929, 2.292, and 3.637 mL/min for the respective streams, yielded impressive results. The experimental relative purities of α-mangostin in the extract product and γ-mangostin in the raffinate product reached 100% and 98.79%, respectively. Gravimetric analysis of the dried extract product from the TZ-SMB system, coupled with HPLC analysis, revealed an α-mangostin purity of 99.4%. This study underscores the potential of TZ-SMB as a powerful separation technology for the purification of bioactive compounds derived from agricultural sources. Declarations Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data availability Data will be made available on request. Acknowledgement This work received financial support from the National Research Council of Thailand (NRCT), grant number N42A650272. References BCG Model, in, The National Science and Technology Development Agency (NSTDA), 2021. A.F. Aisha, K. Abu-Salah, Z.D. Nassar, M. Siddiqui, Z. Ismail, A.M.S.A. Majid, Antitumorigenicity of xanthones-rich extract from Garcinia mangostana fruit rinds on HCT 116 human colorectal carcinoma cells, Revista Brasileira De Farmacognosia-brazilian, Rev. bras. farmacogn. 21 (2011) 1025-1034, https://doi.org/10.1590/S0102-695X2011005000164. H.T.T. Do, J. 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Silva, General optimization strategy of simulated moving bed units through design of experiments and response surface methodologies, Comput. Chem. Eng. 90 (2016) 161-170, https://doi.org/10.1016/j.compchemeng.2016.04.028. D.M. Ruthven, Principles of Adsorption and Adsorption Processes, 1st ed., Wiley-Interscience, 1984. C. Yao, J. Chen, Y. Lu, S. Tang, E. Fan, Construction of an asynchronous three-zone simulated-moving-bed chromatography and its application for the separation of vanillin and syringaldehyde, Chem. Eng. J. 331 (2018) 644-651, https://doi.org/10.1016/j.cej.2017.09.006. W. McCabe, J. Smith, P. Harriott, Unit Operations of Chemical Engineering 7ed., McGraw Hill, 2004. N. Wathoni, A. Rusdin, K. Motoyama, I.M. Joni, R. Lesmana, M. Muchtaridi, Nanoparticle Drug Delivery Systems for alpha-Mangostin, Nanotechnol. Sci. Appl. 13 (2020) 23-36, https://doi.org/10.2147/NSA.S243017. C. Reichardt, T. Welton, Solvents and Solvent Effects in Organic Chemistry, Wiley‐VCH Verlag GmbH & Co. KGaA, 2011. L. Fang, Y. Liu, H. Zhuang, W. Liu, X. Wang, L. Huang, Combined microwave-assisted extraction and high-speed counter-current chromatography for separation and purification of xanthones from Garcinia mangostana, J. Chromatogr. B. 879 (2011) 3023-3027, https://doi.org/10.1016/j.jchromb.2011.08.040. J.P.S. Aniceto, I.S. Azenha, F.M.J. Domingues, A. Mendes, C.M. Silva, Design and optimization of a simulated moving bed unit for the separation of betulinic, oleanolic and ursolic acids mixtures: Experimental and modeling studies, Sep. Purif. Technol. 192 (2018) 401-411, https://doi.org/10.1016/j.seppur.2017.10.016. Cite Share Download PDF Status: Published Journal Publication published 03 Jul, 2025 Read the published version in Waste and Biomass Valorization → Version 1 posted Reviewers agreed at journal 26 Mar, 2025 Reviewers invited by journal 22 Mar, 2025 Editor invited by journal 16 Mar, 2025 Editor assigned by journal 25 Feb, 2025 First submitted to journal 24 Feb, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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University of Technology North Bangkok","correspondingAuthor":false,"prefix":"","firstName":"Amaraporn","middleName":"","lastName":"Kaewchada","suffix":""},{"id":432369318,"identity":"6dc4500d-660d-4b86-b9ce-e2e5092da2ad","order_by":2,"name":"Attasak Jaree","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAy0lEQVRIiWNgGAWjYBAC9gYwxSYnARVIIKiF5wBEizFUiwHRWhgSZxCvhb338Isff/jSZ85IYPzwg+FPHmEtPOfSLHvb2HJnSyQwS/YwGBQT1GIvkWNmwNvAljtPIoFBGuiwxAaCtsi/MTP884ctXQ5oy2/itEjwGD/mYWNLkJZIYCPSFp4cM2bZNjbDmT0P2yx7DIyJ0MJ+xvjjmz/H5CWOJx++8aNCjrAWIGADxuIxIM0IVGxAhHogYP7AwFBDnNJRMApGwSgYmQAAgHY16URjh8MAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-7751-4494","institution":"Kasetsart University","correspondingAuthor":true,"prefix":"","firstName":"Attasak","middleName":"","lastName":"Jaree","suffix":""}],"badges":[],"createdAt":"2025-02-25 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11:55:56","extension":"png","order_by":40,"title":"","display":"","copyAsset":false,"role":"graphical-abstract","size":81762,"visible":true,"origin":"","legend":"Mangosteen pericarps, a rich source of bioactive xanthones, particularly α-mangostin and γ-mangostin, were the focus of this study. The primary objective was to design and experimentally implement a continuous separation process using a three-zone simulated moving bed (TZ-SMB) system to isolate and purify these valuable compounds. Xanthone powder, extracted from mangosteen pericarps using acetonitrile and purified by anti-solvent precipitation, served as feedstock. This powder, with an initial α-mangostin purity of 71.56%, was subjected to separation on a single C18 preparative column to determine crucial adsorption parameters, including linear adsorption isotherms and mass transfer coefficients. A mobile phase consisting of 75% v/v acetonitrile was found to effectively separate α-mangostin and γ-mangostin. Subsequently, computational simulations based on triangle theory were employed to optimize TZ-SMB operating parameters. The optimal conditions involved a 20-min switching time and flow rates of 5.00, 1.062, 2.425, and 3.637 mL/min for the mobile phase, feed, extract, and raffinate, respectively. Under these conditions, the system achieved a maximum productivity of 0.56 mg/mL\u0026middot;h while maintaining high purities for both α-mangostin and γ-mangostin in the respective products. Experimental validation of the TZ-SMB system, using slightly adjusted flow rates, resulted in an α-mangostin purity of 100% in the extract product and a γ-mangostin purity of 98.79% in the raffinate product. The dried extract product exhibited an α-mangostin purity of 99.4% (HPLC grade). This research highlights the potential of TZ-SMB as a promising technology for the efficient and scalable purification of bioactive compounds from natural sources.","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-6102236/v1/f790aa2353d7f6a1fdd4c5cb.png"},{"id":86179698,"identity":"b7c11f87-0740-4e81-8534-fb36b975f435","added_by":"auto","created_at":"2025-07-07 16:18:32","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":16330125,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6102236/v1/67e1fb35-620c-47a3-a45a-06d06efdb4c5.pdf"}],"financialInterests":"","formattedTitle":"Continuous separation of alpha-mangostin and gamma-mangostin fractions from xanthone extracted from mangosteen pericarps using a preparative three-zone simulated moving bed system","fulltext":[{"header":"Statement of Novelty","content":"\u003cp\u003eThis study presents the pioneering experimental demonstration of alpha-mangostin and gamma-mangostin separation using a preparative three-zone simulated moving bed (SMB) system. This is the first reported application of this technique for the purification of these valuable xanthones directly from mangosteen pericarp extracts, pretreated via anti-solvent precipitation. Achieving a remarkable 99.4% purity for alpha-mangostin from a pretreated extract of 71.56% purity, this work establishes a critical foundation for the development of commercial-scale alpha-mangostin production.\u003c/p\u003e"},{"header":"1. Introduction","content":"\u003cp\u003eThailand has embraced a sustainable development model known as the BCG (Bio-Circular-Green) Economy, prioritizing the valorization of agricultural waste materials for various applications, including the production of pharmacological products for the health and medical sectors [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. The high consumption of mangosteen (regarded as the queen of fruits in Thailand) generates substantial quantities of pericarp waste. This underutilized biomass is a rich source of bioactive compounds with pharmacological properties, so-called xanthones [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. These compounds consist of derivatives such as alpha-mangostin as the major component, and others like gamma-mangostin, beta-mangostin, etc. Alpha-mangostin has been extensively studied for various pharmacological effects, such as antioxidant, anti-inflammatory, anti-diabetic, anti-microbial, and anticancer properties [\u003cspan additionalcitationids=\"CR5 CR6 CR7\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Gamma-mangostin exhibits similar pharmacological effects, including antibacterial, anti-inflammatory, and anticancer properties [\u003cspan additionalcitationids=\"CR10 CR11\" citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. To harness the potential of these valuable compounds, efficient extraction and separation techniques are crucial for their recovery from mangosteen pericarps.\u003c/p\u003e \u003cp\u003eVarious solid-liquid extraction techniques, such as solvent extraction and maceration, have been employed to recover xanthones from mangosteen pericarps [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan additionalcitationids=\"CR14 CR15 CR16\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Subsequent purification of target compounds, including alpha-mangostin, often involves column chromatography [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Batch chromatography is based on the principle of adsorption of solutes in the liquid phase on the surface of the solid adsorbent packed in the column [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. While it offers advantages like high yield and purity, it suffers from drawbacks such as high solvent consumption and low product concentration, leading to increased energy consumption during downstream solvent removal. To address these limitations, the implementation of continuous separation processes is essential.\u003c/p\u003e \u003cp\u003eSimulated Moving Bed (SMB) chromatography is a highly efficient continuous separation technique that employs a multi-column system. By periodically shifting the inlet and outlet ports in the direction of fluid flow while keeping the columns stationary, SMB simulates countercurrent flow between the solid adsorbent and liquid phase. This configuration offers numerous advantages, including high yield, purity, product concentration, and reduced solvent consumption. Consequently, SMB has been widely applied in various industries, such as petrochemicals for the separation of p-xylene and n-paraffins, and the sugar industry for the separation of glucose and fructose [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Additionally, bioactive compounds such as chlorogenic have been successfully separated with this method [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThis study aimed to demonstrate the feasibility of a three-zone simulated moving bed (TZ-SMB) system for the continuous recovery of alpha-mangostin from xanthones extracted from mangosteen pericarps [\u003cspan additionalcitationids=\"CR24\" citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. In the proposed TZ-SMB process, alpha-mangostin and gamma-mangostin fractions were targeted as the extract and raffinate products, respectively. To establish optimal operating conditions of the TZ-SMB, initial experiments were conducted using a single preparative C18 column. Pulse injection experiments were performed to determine key parameters, including total and external bed porosities, as well as the optimal mobile phase composition (% acetonitrile). Additionally, adsorption isotherms and mass-transfer coefficients were estimated by fitting mathematical models to experimental breakthrough curve data. Subsequently, a TZ-SMB process was simulated using triangle theory to identify operating conditions that maximized productivity while ensuring high purity (\u0026gt;\u0026thinsp;98%) for both alpha-mangostin and gamma-mangostin. Finally, experimental validation of the TZ-SMB process was conducted, and the purity of the recovered alpha-mangostin fraction was assessed by HPLC analysis.\u003c/p\u003e \u003cp\u003eA three-zone simulated moving bed (TZ-SMB) system comprises three chromatographic columns connected in series, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Zone I serves as the regeneration zone, where adsorbed compounds are desorbed using a liquid solvent (desorbent). Zones II and III function as separation zones, selectively adsorbing the more retained component (extract product) and desorbing the less retained component (raffinate product), respectively. The feed (liquid extract) is introduced into Zone III, where the separation of the two compounds occurs. The desorbent is fed into Zone I, eluting the adsorbed compounds and collecting the extract product at the outlet of this zone. The raffinate product is collected at the outlet of Zone III. After a specific switching time, the inlet and outlet ports are shifted one column position in the direction of fluid flow, as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. A complete cycle is achieved after three such shifts, returning all ports to their original positions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe operating parameters of a TZ-SMB system include flow rates (mL/min) of the desorbent (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Q}}_{\\text{D}}\\)\u003c/span\u003e\u003c/span\u003e), feed (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Q}}_{\\text{F}}\\)\u003c/span\u003e\u003c/span\u003e), extract (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Q}}_{\\text{E}}\\)\u003c/span\u003e\u003c/span\u003e), and raffinate (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Q}}_{\\text{R}}\\)\u003c/span\u003e\u003c/span\u003e), as well as the switching time (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{t}}_{\\text{s}}\\)\u003c/span\u003e\u003c/span\u003e). Assuming constant fluid density, the material balance equations for the liquid flow in each zone of the TZ-SMB system can be expressed as follows:\u003c/p\u003e \u003cp\u003eOverall: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Q}}_{\\text{D}}+{\\text{Q}}_{\\text{F}}={\\text{Q}}_{\\text{E}}+{\\text{Q}}_{\\text{R}}\\)\u003c/span\u003e\u003c/span\u003e (1)\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eZone I: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Q}}_{\\text{I}}={\\text{Q}}_{\\text{D}}\\)\u003c/span\u003e\u003c/span\u003e (2)\u003c/p\u003e\u003cp\u003eZone II: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Q}}_{\\text{I}\\text{I}}={\\text{Q}}_{\\text{I}}-{\\text{Q}}_{\\text{E}}\\)\u003c/span\u003e\u003c/span\u003e (3)\u003c/p\u003e\u003cp\u003eZone III: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Q}}_{\\text{I}\\text{I}\\text{I}}={\\text{Q}}_{\\text{I}\\text{I}}+{\\text{Q}}_{\\text{F}}={\\text{Q}}_{\\text{R}}\\)\u003c/span\u003e\u003c/span\u003e (4)\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Q}}_{\\text{j}}\\)\u003c/span\u003e\u003c/span\u003e is the volumetric flow rate of the liquid (mL/min) of zone j (j\u0026thinsp;=\u0026thinsp;I, II, and III).\u003c/p\u003e \u003cp\u003eTo evaluate the separation performance of the TZ-SMB, key parameters such as relative purity, productivity, capacity, and solvent consumption are calculated. These parameters can be determined based on the average concentrations of alpha-mangostin (AM) and gamma-mangostin (GM) in the extract (E) and raffinate (R) products, measured over a complete switching cycle during cyclic steady-state operation. The average concentration (g/L) is calculated according to\u003c/p\u003e \u003cp\u003eEq.\u0026nbsp;(5).\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:⟨{\\text{C}}_{\\text{G}\\text{M}}^{\\text{R}}⟩\\)\u003c/span\u003e \u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:⟨{\\text{C}}_{\\text{A}\\text{M}}^{\\text{E}}⟩\\)\u003c/span\u003e\u003c/span\u003e (5)\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe % relative purities of gamma-mangostin in the raffinate product and alpha-mangostin in the extract product are calculated as follows:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\text{P}{\\text{U}}_{\\text{R}}=\\frac{⟨{\\text{C}}_{\\text{G}\\text{M}}^{\\text{R}}⟩}{⟨{\\text{C}}_{\\text{G}\\text{M}}^{\\text{R}}⟩+⟨{\\text{C}}_{\\text{A}\\text{M}}^{\\text{R}}⟩}\\times\\:100\\:\\text{a}\\text{n}\\text{d}\\:\\text{P}{\\text{U}}_{\\text{E}}=\\frac{⟨{\\text{C}}_{\\text{A}\\text{M}}^{\\text{E}}⟩}{⟨{\\text{C}}_{\\text{G}\\text{M}}^{\\text{E}}⟩+⟨{\\text{C}}_{\\text{A}\\text{M}}^{\\text{E}}⟩}\\times\\:100$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe productivity is expressed in mg/(mL\u0026middot;h) and is defined as shown in Eq.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e7\u003c/span\u003e:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\:\\text{P}\\text{d}=\\frac{{\\text{Q}}_{\\text{F}}\\left({\\text{C}}_{\\text{G}\\text{M}}^{\\text{F}}+{\\text{C}}_{\\text{C}\\text{A}\\text{M}}^{\\text{F}}\\right)}{(1-{}_{\\text{b}}){\\text{V}}_{\\text{C}}{\\text{N}}_{\\text{C}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{}_{\\text{b}}\\)\u003c/span\u003e\u003c/span\u003e is the bed porosity. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{V}}_{\\text{C}}\\)\u003c/span\u003e\u003c/span\u003e is the column volume (mL). \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{N}}_{\\text{C}}\\)\u003c/span\u003e\u003c/span\u003e is the number of columns in the TZ-SMB system. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{C}}_{\\text{G}\\text{M}}^{\\text{F}}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{C}}_{\\text{A}\\text{M}}^{\\text{F}}\\)\u003c/span\u003e\u003c/span\u003e represent the concentrations (g/L) of gamm-mangostin and alpha-mangostin in the feed (xanthone solution), respectively.\u003c/p\u003e \u003cp\u003eThe production capacity (mg/h) of both bioactive compound fractions in the raffinate and extract products are calculated according to Eqs.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e7\u003c/span\u003e) and (\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e8\u003c/span\u003e).\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{\\text{C}\\text{a}\\text{p}}_{\\text{G}\\text{M}}=⟨{\\text{C}}_{\\text{G}\\text{M}}^{\\text{R}}⟩{\\text{Q}}_{\\text{R}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{\\text{C}\\text{a}\\text{p}}_{\\text{A}\\text{M}}=⟨{\\text{C}}_{\\text{A}\\text{M}}^{\\text{E}}⟩{\\text{Q}}_{\\text{E}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe solvent consumption (mL/mg) is calculated as shown in Eq.\u0026nbsp;(\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e10\u003c/span\u003e):\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:\\:\\text{S}\\text{C}=\\frac{{\\text{Q}}_{\\text{D}}}{{\\text{Q}}_{\\text{F}}\\left({\\text{C}}_{\\text{G}\\text{M}}^{\\text{F}}+{\\text{C}}_{\\text{A}\\text{M}}^{\\text{F}}\\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe dynamic adsorption behavior of both bioactive compounds in each TZ-SMB column is modeled using established equations for single-column systems. Key assumptions include isothermal conditions, plug flow liquid phase, and linear driving force mass transfer kinetics. The material balance equations for the liquid and solid phases are presented in Eqs.\u0026nbsp;(11) and (12), respectively [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]:\u003c/p\u003e \u003cp\u003eLiquid Phase: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{\\partial\\:{\\text{C}}_{\\text{i}}}{\\partial\\:{\\theta\\:}}+{\\gamma\\:}\\frac{\\partial\\:{\\stackrel{-}{\\text{q}}}_{\\text{i}}}{\\partial\\:{\\theta\\:}}=\\frac{{\\psi\\:}}{\\text{P}\\text{e}}\\frac{\\partial\\:{\\text{C}}_{\\text{i}}^{2}}{\\partial\\:{{\\chi\\:}}^{2}}-{\\psi\\:}\\frac{\\partial\\:{\\text{C}}_{\\text{i}}}{\\partial\\:{\\chi\\:}}\\)\u003c/span\u003e\u003c/span\u003e (11)\u003c/p\u003e \u003cp\u003eSolid Phase: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{\\partial\\:{\\stackrel{-}{\\text{q}}}_{\\text{i}}}{\\partial\\:{\\theta\\:}}={{\\alpha\\:}}_{\\text{i}}\\left({\\text{q}}_{\\text{i}}^{\\text{*}}-{\\stackrel{-}{\\text{q}}}_{\\text{i}}\\right)\\)\u003c/span\u003e\u003c/span\u003e (12)\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{C}}_{\\text{i}}\\:\\)\u003c/span\u003e\u003c/span\u003eis the concentration of solute i in the liquid phase. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\stackrel{-}{\\text{q}}}_{\\text{i}}\\:\\)\u003c/span\u003e\u003c/span\u003eis the average concentration of solute i in the solid phase. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{q}}_{\\text{i}}^{\\text{*}}\\:\\)\u003c/span\u003e\u003c/span\u003eis the concentration of solute i in the solid phase, which is in equilibrium with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{C}}_{\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e. All concentrations are expressed in g/L. The dimensionless parameters in the above equations are defined as follows:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:{\\gamma\\:}=\\frac{1-{{\\epsilon\\:}}_{\\text{b}}}{{{\\epsilon\\:}}_{\\text{b}}}\\:\\text{a}\\text{n}\\text{d}\\:{\\psi\\:}=\\frac{\\text{v}{\\text{t}}_{\\text{s}}}{{\\text{L}}_{\\text{c}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e13\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\:\\text{P}\\text{e}=\\frac{\\text{v}{\\text{L}}_{\\text{c}}}{{\\text{D}}_{\\text{a}\\text{x}}}\\:\\text{a}\\text{n}\\text{d}\\:{{\\alpha\\:}}_{\\text{i}}={\\text{K}}_{\\text{i},\\text{j}}{\\text{t}}_{\\text{s}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e14\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eDimensionless parameters for time (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\theta\\:}\\)\u003c/span\u003e\u003c/span\u003e) and column axial distance (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\chi\\:}\\)\u003c/span\u003e\u003c/span\u003e) are written as:\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$$\\:{\\theta\\:}=\\frac{\\text{t}}{{\\text{t}}_{\\text{s}}}\\:\\text{a}\\text{n}\\text{d}\\:{\\chi\\:}=\\frac{\\text{z}}{{\\text{L}}_{\\text{c}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e15\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:\\text{v}\\)\u003c/span\u003e \u003c/span\u003e is the interstitial velocity (m/s), calculated from the ratio of superficial velocity to bed porosity. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{t}}_{\\text{s}}\\:\\)\u003c/span\u003e\u003c/span\u003eis the switching time for TZ-SMB operation (s) or the operating time for adsorption-desorption in breakthrough curve experiment. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{L}}_{\\text{c}}\\:\\)\u003c/span\u003e\u003c/span\u003eis the length of the preparative C18 column (m). \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{D}}_{\\text{a}\\text{x}}\\)\u003c/span\u003e\u003c/span\u003e is the axial dispersion coefficient (m\u003csup\u003e2\u003c/sup\u003e/s). The P\u0026eacute;clet number (Pe) is a dimensionless number that represents the ratio of convective to dispersive mass transport rates. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{K}}_{\\text{i},\\text{j}}\\:\\)\u003c/span\u003e\u003c/span\u003eis the global mass-transfer coefficient (s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) calculated by Eq.\u0026nbsp;(\u003cspan refid=\"Equ9\" class=\"InternalRef\"\u003e16\u003c/span\u003e) [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e].\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ9\" name=\"EquationSource\"\u003e\n$$\\:\\frac{1}{{\\text{K}}_{\\text{i},\\text{j}}}=\\frac{1}{{\\text{k}}_{\\text{i}}}+\\frac{{\\text{R}}_{\\text{p}}}{3{\\text{k}}_{\\text{i},\\text{j}}^{\\text{f}}}{\\text{H}}_{\\text{i}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e16\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{H}}_{\\text{i}}\\:\\)\u003c/span\u003e\u003c/span\u003eis the linear adsorption isotherm of compound i. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{R}}_{\\text{p}}\\:\\)\u003c/span\u003e\u003c/span\u003eis the radius of solid adsorbent (cm). \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{k}}_{\\text{i}}\\:\\)\u003c/span\u003e\u003c/span\u003eis the linear driving force mass-transfer coefficient (s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) calculated from the correlation proposed by Wilson and Geankoplis, as shown below:\u003cdiv id=\"Equ10\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ10\" name=\"EquationSource\"\u003e\n$$\\:{\\text{k}}_{\\text{i}}=\\left(\\frac{{\\Omega\\:}{\\text{D}}_{\\text{e}\\text{f}\\text{f},\\text{i}}}{{\\text{R}}_{\\text{p}}^{2}}\\right)\\left(\\frac{1}{1-{{\\epsilon\\:}}_{\\text{p}}}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e17\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere\u003cdiv id=\"Equ11\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ11\" name=\"EquationSource\"\u003e\n$$\\:{\\text{D}}_{\\text{e}\\text{f}\\text{f},\\text{i}}=\\frac{{{\\epsilon\\:}}_{\\text{p}{\\text{D}}_{\\text{m},\\text{i}}}}{{\\tau\\:}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e18\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ12\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ12\" name=\"EquationSource\"\u003e\n$$\\:\\tau\\:=\\frac{{\\left(2-{{\\epsilon\\:}}_{\\text{p}}\\right)}^{2}}{{{\\epsilon\\:}}_{\\text{p}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e19\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above equations, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Omega\\:}\\)\u003c/span\u003e\u003c/span\u003e is the geometric factor. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{D}}_{\\text{e}\\text{f}\\text{f},\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e is the effective diffusivity (cm\u003csup\u003e2\u003c/sup\u003e/s). \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\tau\\:}\\)\u003c/span\u003e\u003c/span\u003e is the tortuosity factor. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{p}\\:\\)\u003c/span\u003e\u003c/span\u003eis the particle porosity. The liquid phase convective mass-transfer coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{k}}_{\\text{i},\\text{j}}^{\\text{f}}\\:\\)\u003c/span\u003e\u003c/span\u003e(cm/s), which is valid for 0.0015\u0026thinsp;\u0026lt;\u0026thinsp;Reynolds number\u0026thinsp;\u0026lt;\u0026thinsp;55, can be calculated from the correlation shown in Eq.\u0026nbsp;(\u003cspan refid=\"Equ13\" class=\"InternalRef\"\u003e20\u003c/span\u003e) [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e].\u003cdiv id=\"Equ13\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ13\" name=\"EquationSource\"\u003e\n$$\\:\\text{S}\\text{h}=\\left(\\frac{{\\text{k}}_{\\text{i},\\text{j}}^{\\text{f}}{\\text{d}}_{\\text{p}}}{{\\text{D}}_{\\text{m},\\text{i}}}\\right)=\\left(\\frac{1.09}{{{\\epsilon\\:}}_{\\text{b}}}\\right){\\left(\\frac{{{\\rho\\:}}_{\\text{f}}\\text{v}{{\\epsilon\\:}}_{\\text{b}}{\\text{d}}_{\\text{p}}}{{\\eta\\:}}\\right)}^{0.33}{\\left(\\frac{{\\eta\\:}}{{{\\rho\\:}}_{\\text{f}{\\text{D}}_{\\text{m},\\text{i}}}}\\right)}^{0.33}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e20\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eSh, is the dimensionless quantity called Sherwood number. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{d}}_{\\text{p}}\\:\\)\u003c/span\u003e\u003c/span\u003eis the diameter of solid adsorbent particles (cm). \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\rho\\:}}_{\\text{f}}\\)\u003c/span\u003e\u003c/span\u003e is the density of liquid solvent (kg/m\u003csup\u003e3\u003c/sup\u003e). \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\eta\\:}\\)\u003c/span\u003e\u003c/span\u003e is the viscosity of liquid solvent (kg/m\u0026sdot;s). The diffusivity of a solute adsorbed in the column, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{D}}_{\\text{m},\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e (m\u003csup\u003e2\u003c/sup\u003e/s), can be calculated from the correlation of Wike and Chang, as shown in Eq.\u0026nbsp;(\u003cspan refid=\"Equ14\" class=\"InternalRef\"\u003e21\u003c/span\u003e) [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e].\u003cdiv id=\"Equ14\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ14\" name=\"EquationSource\"\u003e\n$$\\:{\\text{D}}_{\\text{m},\\text{i}}=7.4\\times\\:{10}^{-8}\\frac{{\\left({\\upvarphi\\:}{\\text{M}}_{\\text{i}}\\right)}^{0.5}\\text{T}}{{\\eta\\:}{\\text{V}}_{\\text{m},\\text{i}}^{0.6}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e21\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\upvarphi\\:}\\)\u003c/span\u003e\u003c/span\u003e is the association solvent parameter [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{M}}_{\\text{i}}\\:\\)\u003c/span\u003e\u003c/span\u003eis the molecular weight of solvent (g/mol). T is the absolute temperature (K). \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{V}}_{\\text{m}.\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e is the molar volume of solute at its normal boiling point (mL/mol). The dimensionless initial and boundary conditions for solving Eqs.\u0026nbsp;(11) and (12) are shown in Eqs.\u0026nbsp;(22), (23) and (24).\u003c/p\u003e \u003cp\u003eInitial conditions: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:{\\text{C}}_{\\text{i}}\\left({\\chi\\:},0\\right)=0\\:\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\stackrel{-}{\\text{q}}}_{\\text{i}}\\:\\left({\\chi\\:},0\\right)=0\\)\u003c/span\u003e\u003c/span\u003e(22)\u003c/p\u003e \u003cp\u003eBoundary conditions:\u003c/p\u003e \u003cp\u003eAt column entrance: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{C}}_{\\text{i}}\\left(0,{\\theta\\:}\\right)={\\text{C}}_{\\text{i}}^{\\text{i}\\text{n}}+\\frac{1}{\\text{P}\\text{e}}\\frac{\\partial\\:{\\text{C}}_{\\text{i}}}{\\partial\\:{\\chi\\:}}\\)\u003c/span\u003e\u003c/span\u003e (23)\u003c/p\u003e \u003cp\u003eAt column exit: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{\\partial\\:{\\text{C}}_{\\text{i}}}{\\partial\\:{\\chi\\:}}\\left(1,{\\theta\\:}\\right)=0\\)\u003c/span\u003e\u003c/span\u003e (24)\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{C}}_{\\text{i}}^{\\text{i}\\text{n}}\\)\u003c/span\u003e\u003c/span\u003e is the initial feed concentration (g/L) of solute i fed to the column.\u003c/p\u003e"},{"header":"2. Material and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Chemicals and Raw Materials\u003c/h2\u003e \u003cp\u003eMangosteen pericarps were sourced from a local market in Bangkok. Distilled deionized water (DDW) with a resistivity of 18.2 MΩ\u0026middot;cm was used as a solvent. HPLC-grade acetonitrile, methanol, and acetone were purchased from MERCK (Darmstadt, Germany). Alpha-mangostin (α-MG) and gamma-mangostin (γ-MG) standards, with a minimum purity of 98% (HPLC), were obtained from Sigma-Aldrich. Blue dextran (HPLC grade), used as a chromatographic marker, was also procured from Sigma-Aldrich.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Preparation of Xanthone Powder\u003c/h2\u003e \u003cp\u003eMangosteen pericarps were cleaned and dried in a hot air oven (Memmert, UF110) at 60\u0026deg;C for 48 hours to remove moisture. The dried pericarps were ground into a fine powder using a grinder and sieved to obtain particles smaller than 150 \u0026micro;m. A reflux extractor with a 500 mL working volume was used to extract the powdered pericarps. Pure acetonitrile was employed as the solvent, with a solid-to-liquid ratio of 1:8.24 (g/mL), and the extraction was conducted at 70\u0026deg;C for 120 min. The resulting extract was filtered through a 0.45 \u0026micro;m membrane filter to remove solid residues. The filtered extract was concentrated tenfold using a vacuum evaporator. Subsequently, deionized distilled water (DDW) was added in a 4:1 volume ratio to induce the precipitation of xanthones. The precipitated xanthones were collected and dried in a hot air oven at 60\u0026deg;C for 24 h.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3. The Single-Column Experiments\u003c/h2\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e2.3.1. Determination of External and Total Porosities of a Preparative C18 Column\u003c/h2\u003e \u003cp\u003eA C18 preparative column (Visper, USA) with dimensions of 10 x 250 mm and a particle size of 10 \u0026micro;m was used. The HPLC system described in Section \u003cspan refid=\"Sec14\" class=\"InternalRef\"\u003e2.6\u003c/span\u003e was employed for this experiment. The column temperature was maintained at 40\u0026deg;C, and a mobile phase consisting of 75% v/v acetonitrile was used. The pump flow rate was varied between 0.6 and 1.4 mL/min, with a wavelength of 330 nm and an injection volume of 50 \u0026micro;L.\u003c/p\u003e \u003cp\u003eTo determine the external bed porosity, a 0.76 mg/mL solution of blue dextran in DDW water was injected into the column. For the total bed porosity, pure acetone was injected instead of blue dextran. The retention times of both substances were recorded and used to calculate the respective bed porosities using Eq.\u0026nbsp;(\u003cspan refid=\"Equ15\" class=\"InternalRef\"\u003e25\u003c/span\u003e).\u003cdiv id=\"Equ15\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ15\" name=\"EquationSource\"\u003e\n$$\\:{\\text{t}}_{\\text{r}}={\\epsilon\\:}\\frac{{\\text{L}}_{\\text{c}}}{\\text{u}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e25\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{t}}_{\\text{r}}\\)\u003c/span\u003e\u003c/span\u003e​ is the retention time of blue dextran or acetone (min), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}\\)\u003c/span\u003e\u003c/span\u003e represents the external bed porosity (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\epsilon\\:}}_{\\text{b}}\\)\u003c/span\u003e\u003c/span\u003e​) or total bed porosity (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\epsilon\\:}}_{\\text{T}}\\)\u003c/span\u003e\u003c/span\u003e​). \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{L}}_{\\text{c}}\\)\u003c/span\u003e\u003c/span\u003e​ is the column length (m), and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{u}\\)\u003c/span\u003e\u003c/span\u003e is the superficial velocity (m/min), calculated by dividing the flow rate (mL/min) by the cross-sectional area of the column (m\u003csup\u003e2\u003c/sup\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e2.3.2. Pulse Injection Experiment in a Preparative C18-Column\u003c/h2\u003e \u003cp\u003eTo determine the linear adsorption isotherms of α-MG and γ-MG, a pulse injection experiment was conducted using the chromatographic setup illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. This setup comprised a gradient dual-piston pump (Waters, USA), a preparative C18 column (Visper, USA) with dimensions of 10 x 250 mm and a particle size of 10 \u0026micro;m, and a convection oven. The column temperature was maintained at 40\u0026deg;C, and the mobile phase flow rate was varied between 4 and 7 mL/min with a composition ranging from 65\u0026ndash;75% v/v acetonitrile.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA feed solution, prepared by extracting DMP with pure acetonitrile and diluting with DDW to match the mobile phase composition, was introduced into the column using an isocratic pump (Knauer, Germany) at a flow rate of 1 mL/min for 30 seconds. The injection was controlled by a multi-position valve (VICI-Valco, USA). The product stream was split into two: one directed to a UV detector (Variant 7250, USA) for signal detection at 320 nm, and the other routed to a multi-position valve for periodic fractionation. The volumetric ratio between the two streams was regulated using an isocratic pump (Knauer, Germany) and a needle valve.\u003c/p\u003e \u003cp\u003eThe retention times (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{t}}_{\\text{r},\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e) of α-MG and γ-MG were recorded and used to calculate the linear adsorption isotherms (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{H}}_{\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e) using Eq.\u0026nbsp;(\u003cspan refid=\"Equ16\" class=\"InternalRef\"\u003e26\u003c/span\u003e) and the selectivity of separation (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{}_{\\text{i},\\text{j}}\\)\u003c/span\u003e\u003c/span\u003e) using Eq.\u0026nbsp;(\u003cspan refid=\"Equ17\" class=\"InternalRef\"\u003e27\u003c/span\u003e).\u003cdiv id=\"Equ16\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ16\" name=\"EquationSource\"\u003e\n$$\\:{\\text{t}}_{\\text{r},\\text{i}}=\\left[1+\\left(\\frac{1-{{\\epsilon\\:}}_{\\text{b}}}{{{\\epsilon\\:}}_{\\text{b}}}\\right){\\text{H}}_{\\text{i}}\\right]\\left(\\frac{{{\\epsilon\\:}}_{\\text{b}}{\\text{V}}_{\\text{c}}}{\\text{Q}}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e26\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ17\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ17\" name=\"EquationSource\"\u003e\n$$\\:{}_{\\text{i},\\text{j}}=\\frac{{\\text{H}}_{\\text{j}}}{{\\text{H}}_{\\text{i}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e27\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{Q}\\)\u003c/span\u003e\u003c/span\u003e is the mobile phase flow rate (mL/min) and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{V}}_{\\text{c}}\\)\u003c/span\u003e\u003c/span\u003e is the column volume (mL).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e2.3.3. Breakthrough Curve Experiment in a Preparative C18 Column\u003c/h2\u003e \u003cp\u003eThe chromatographic system described in Section \u003cspan refid=\"Sec7\" class=\"InternalRef\"\u003e2.3.2\u003c/span\u003e was employed for adsorption-desorption experiments. A preparative C18 column, maintained at 40\u0026deg;C, was used. Feed solutions containing 1, 3, and 5 g/L of xanthone powder dissolved in 75% v/v acetonitrile were prepared. During the adsorption phase, a 75% acetonitrile solution was delivered to the column at a flow rate of 5 mL/min. This solution was mixed with the feed solution, delivered at 1 mL/min, resulting in a total flow rate of 6 mL/min. The adsorption phase continued for 40 min until column saturation. Subsequently, the system switched to the desorption phase, where a 75% acetonitrile solution was introduced at a flow rate of 6 mL/min for 40 min to elute all adsorbed components. Effluent samples were collected every minute during both adsorption and desorption phases and analyzed using HPLC (described in Section \u003cspan refid=\"Sec14\" class=\"InternalRef\"\u003e2.6\u003c/span\u003e) to quantify α-MG and γ-MG concentrations.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e2.3.4. Computational Simulation of Breakthrough Curve\u003c/h2\u003e \u003cp\u003eThe concentration-time profiles of α-MG and γ-MG at the column's exit, obtained from adsorption-desorption experiments, were modeled using the mathematical approaches outlined in section \u003cspan refid=\"Sec1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, as expressed in Eqs.\u0026nbsp;(11)-(24). These models were employed to fine-tune the experimental breakthrough curve data across various concentration levels, enabling the determination of adsorption parameters for each compound, such as the linear adsorption isotherm constant, the global mass-transfer coefficient, and P\u0026eacute;clet number. The initial guesses for the linear isotherm were derived from the results of the pulse injection experiment described in section \u003cspan refid=\"Sec7\" class=\"InternalRef\"\u003e2.3.2\u003c/span\u003e, while the values for the global mass-transfer coefficient were calculated using Eqs.\u0026nbsp;(\u003cspan refid=\"Equ9\" class=\"InternalRef\"\u003e16\u003c/span\u003e)-(\u003cspan refid=\"Equ14\" class=\"InternalRef\"\u003e21\u003c/span\u003e). All equations were numerically solved using the finite element method in MATLAB\u0026reg; version 2021b and FLEXPDE\u0026reg; version 6.5, running on the Windows\u0026reg; 10 operating system. The effectiveness of the fine-tuning process was assessed by calculating r-squared.\u003c/p\u003e \u003cp\u003eThe concentration-time profiles of α-MG and γ-MG at the column outlet, obtained from adsorption-desorption experiments, were modeled using the mathematical framework described in Section \u003cspan refid=\"Sec1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (see Eqs.\u0026nbsp;(11)-(24)). These models were employed to fit the experimental breakthrough curve data at various concentration levels, enabling the determination of adsorption parameters for each compound, including the linear adsorption isotherm constant, global mass-transfer coefficient, and P\u0026eacute;clet number. Initial estimates for the linear isotherm parameters were derived from the pulse injection experiments described in Section \u003cspan refid=\"Sec7\" class=\"InternalRef\"\u003e2.3.2\u003c/span\u003e, while the global mass-transfer coefficients were calculated using Eqs.\u0026nbsp;(\u003cspan refid=\"Equ9\" class=\"InternalRef\"\u003e16\u003c/span\u003e)-(\u003cspan refid=\"Equ14\" class=\"InternalRef\"\u003e21\u003c/span\u003e). All equations were numerically solved using the finite element method in MATLAB\u0026reg; version 2021b and FLEXPDE\u0026reg; version 6.5, running on Windows\u0026reg; 10. The goodness-of-fit of the models was assessed by calculating the coefficient of determination (R\u0026sup2;).\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e2.4. Three-Zone Simulated Moving Bed (TZ-SMB)\u003c/h2\u003e \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e \u003ch2\u003e2.4.1. Simulation of TZ-SMB System\u003c/h2\u003e \u003cp\u003eThe five operating parameters of the TZ-SMB system, namely the flow rates of desorbent (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Q}}_{\\text{D}}\\)\u003c/span\u003e\u003c/span\u003e), feed (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Q}}_{\\text{F}}\\)\u003c/span\u003e\u003c/span\u003e), extract (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Q}}_{\\text{E}}\\)\u003c/span\u003e\u003c/span\u003e), and raffinate (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Q}}_{\\text{R}}\\)\u003c/span\u003e\u003c/span\u003e), and the switching time (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{t}}_{\\text{s}}\\)\u003c/span\u003e\u003c/span\u003e), were determined using separation triangle theory, as detailed in Section 3.3. Each operating condition within the separation triangle was used to simulate the concentration profiles of α-MG and γ-MG along the column length in each zone of the TZ-SMB. The mathematical models for a single column, Eqs.\u0026nbsp;(11)-(24), and the material balance equations for the TZ-SMB, Eqs.\u0026nbsp;(1)-(4), were applied, using the previously determined adsorption parameters from single-column experiments. The system of equations was solved numerically using MATLAB\u0026reg; version 2021b and FLEXPDE\u0026reg; version 6.5 on a Windows\u0026reg; 10 operating system.\u003c/p\u003e \u003cp\u003eIn the simulated TZ-SMB system, the inlet and outlet ports were periodically shifted to mimic countercurrent flow between the solid and liquid phases. This was computationally achieved by setting the final state of each column as the initial state of the subsequent column at the end of each switching period. Separation performance was evaluated using Equations (5)-(\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e10\u003c/span\u003e), based on data obtained during the cyclic steady state.\u003c/p\u003e \u003cp\u003eFor the TZ-SMB simulations, a feed solution containing α-MG and γ-MG at initial concentrations of 0.30 g/L and 0.05 g/L, respectively, was used. Three preparative C18 columns with dimensions of 10 x 250 mm were employed. The system temperature was maintained at 40\u0026deg;C, and the desorbent flow rate was set to 5 mL/min. The switching time was fixed at 20 min. The optimal operating condition for the TZ-SMB was defined as the one that maximized productivity while ensuring that the relative purities of γ-MG in the raffinate product and α-MG in the extract product were both at least 98%.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003e2.4.2. Experiment of TZ-SMB system\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates the three-zone simulated moving bed (TZ-SMB) system employed in this study. The system comprises three HPLC pumps (Shimadzu, Japan) delivering the mobile phase (desorbent), feed solution (xanthone solution), and extract product. The flow rates of the extract product were regulated using a metering valve, while the raffinate product flow rate was uncontrolled and determined by mass balance. Four six-port valves (VICI Valco Instruments) equipped with a control module governed the periodic port switching within the TZ-SMB. Three preparative C18 columns (10 \u0026times; 250 mm, 10 \u0026micro;m particle size, Visper, USA) were housed in a temperature-controlled convection oven at 40\u0026deg;C and interconnected with check valves to direct flow. The feed solution for the TZ-SMB (liquid extract of xanthone) was prepared by dissolving dried xanthone powder in 75% v/v acetonitrile solution to achieve a concentration of 0.5 g/L. During TZ-SMB operation, the following flow rates were maintained: desorbent 5.00 mL/min, feed solution 0.929 mL/min, extract product 2.292 mL/min, and raffinate product 3.637 mL/min, with a switching time of 20 min. The experiment was conducted for 48 switches (16 cycles). Throughout this period, the extract and raffinate products were continuously collected and analyzed by HPLC to determine α-MG and γ-MG concentrations. The separation performance, including % relative purity and production capacity of bioactive compounds, was evaluated using Eqs.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e6\u003c/span\u003e), (\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e8\u003c/span\u003e) and (9), respectively.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e2.5. Determination of HPLC Purity of Alpha-Mangostin in the Products\u003c/h2\u003e \u003cp\u003eTo compare the purity of α-mangostin in xanthone powder (prepared as described in Section \u003cspan refid=\"Sec4\" class=\"InternalRef\"\u003e2.2\u003c/span\u003e) and the dried α-mangostin fraction from the TZ-SMB extract product, both samples were analyzed by HPLC. The TZ-SMB extract product was concentrated by vacuum evaporation to obtain dried α-mangostin. The HPLC purity of α-mangostin in both the xanthone powder and the dried α-mangostin fraction was determined using a weighing method. A 5 mg sample of each was dissolved in 5 mL of acetonitrile to create a 1 g/L stock solution. Dilutions of this stock solution were prepared to obtain concentrations ranging from 0.1 to 0.5 g/L. A calibration curve was constructed using these solutions, and the calibration factor (slope) was determined. The % purity of α-mangostin in each sample was calculated by dividing the calibration factor of the sample by the calibration factor of an α-mangostin HPLC standard.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e2.6. Analytical Method\u003c/h2\u003e \u003cp\u003eHPLC analysis was performed on a C18 ACE Excel 5 column (25 cm \u0026times; 4.6 mm, 5 \u0026micro;m particle size) maintained at 20\u0026deg;C with a detection wavelength of 320 nm. Liquid samples were filtered through a 0.45 \u0026micro;m syringe filter and stored in 2 mL vials. A 10 \u0026micro;L injection volume and a mobile phase flow rate of 1 mL/min were employed. The mobile phase consisted of a gradient mixture of distilled deionized water (A) and acetonitrile (B). The initial composition was 15% A and 85% B, linearly increasing to 30% A and 70% B over 20 min. The solvent composition was then further adjusted to 10% A and 90% B at 22 min and held constant until the end of the analysis at 35 min. Separate calibration curves were generated for α-MG and γ-MG using standards dissolved in 80% methanol. The α-MG standard concentrations ranged from 0.06 to 0.53 mg/mL, while the γ-MG standard concentrations ranged from 0.05 to 0.51 mg/mL.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Result and Discussions","content":"\u003cp\u003eThis work was divided into three primary areas of investigation. First, xanthone powder was prepared using extraction and precipitation methods. This powder served as the feedstock for subsequent separations in both single-column and TZ-SMB systems. Second, adsorption parameters were determined through pulse injection and breakthrough curve experiments conducted on a single preparative C18 chromatographic column. Third, the TZ-SMB system was designed and simulated using the experimentally determined adsorption parameters for the series of preparative C18 columns. The efficacy of this system was experimentally validated through the continuous separation of α-mangostin and γ-mangostin.\u003c/p\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Preparation of Xanthone Powder\u003c/h2\u003e \u003cp\u003eXanthone, a mixture containing α-mangostin (α-MG), γ-mangostin (γ-MG), and other minor compounds, was extracted from dried mangosteen pericarps using a solid-liquid extraction method. Due to the extremely low water solubility of α-MG and γ-MG (approximately 2.03 \u0026times; 10⁻⁴ mg/L for α-MG [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]), a solvent with a lower polarity index than water (polarity index\u0026thinsp;=\u0026thinsp;1) was required. While low-polarity solvents like hexane could be considered, their toxicity precluded their use. Considering the molecular structure of α-MG and γ-MG, which primarily consists of a xanthone backbone with hydroxyl, methoxy, and prenyl functional groups, solvents with moderate polarity were deemed suitable. Ethanol (polarity index\u0026thinsp;=\u0026thinsp;0.654) and acetonitrile (polarity index\u0026thinsp;=\u0026thinsp;0.46) were identified as promising candidates. Acetonitrile was selected due to its lower viscosity (0.334 cP) compared to ethanol (1.1 cP), which facilitates mass transfer of bioactive compounds from the solid matrix into the solvent. Additionally, acetonitrile is more cost-effective than ethanol, especially in regions with alcohol taxes like Thailand.\u003c/p\u003e \u003cp\u003eThe HPLC chromatogram of the liquid extract (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) and the corresponding yields of α-MG and γ-MG, based on the dried weight of mangosteen pericarp, are presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The predominant peak in the chromatogram corresponds to α-MG, indicating a higher yield compared to γ-MG, as confirmed by the quantitative data in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The obtained yields of α-MG (21.10 mg/g DMP) and γ-MG (2.48 mg/g DMP) are comparable to those reported in the literature using ethanol and microwave-assisted extraction (27.03 mg/g for α-MG and 5.56 mg/g for γ-MG [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe yields of α-MG and γ-MG, reported based on the weights of DMP and dried xanthone.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBioactive compounds\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYield (mg/ g DMP)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYield (mg/ g xanthone)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAlpha-mangostin (α-MG)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e21.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e205.81\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGamma-mangostin (γ-MG)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e36.82\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo obtain xanthone powder, the liquid extract was concentrated by evaporation to remove excess solvent. The resulting concentrated liquid extract, primarily composed of acetonitrile, was then subjected to a precipitation process. Given the low water solubility of both α-MG and γ-MG, the addition of excess water induced the precipitation of insoluble xanthones, effectively separating them from polar, water-soluble impurities.\u003c/p\u003e \u003cp\u003eThe precipitated solid was isolated from the supernatant and dried to yield xanthone powder. This powder was subsequently dissolved in acetonitrile and analyzed by HPLC to confirm the presence of α-MG and γ-MG. The chromatogram in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e10\u003c/span\u003ea and the corresponding yields in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e indicate that the composition of the xanthone powder closely resembled that of the initial liquid extract.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe obtained xanthone powder served as the feedstock for both batch single-column and continuous TZ-SMB separation processes. Based on the chromatogram in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e10\u003c/span\u003ea, α-MG and γ-MG were identified as the major and minor components, respectively. To accurately determine the purity of α-MG in the xanthone powder, calibration curves were constructed for both the sample and a commercial α-MG standard (HPLC grade) using various concentrations in acetonitrile (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e5\u003c/span\u003e). The ratio of the slopes of these calibration curves provides the true HPLC purity of the xanthone powder, which was found to be 71.56%. To further enhance the purity of α-MG to at least 98%, the implementation of a TZ-SMB system was explored.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Separation of Alpha-Mangostin and Gamma-Mangostin in a Single Preparative C18 Chromatographic Column.\u003c/h2\u003e \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e \u003ch2\u003e3.2.1. Determination of Bed and Total Porosities of a Preparative C18 Column\u003c/h2\u003e \u003cp\u003eThe external bed porosity was determined using blue dextran, a high molecular weight substance (approximately 2000 Da). Due to its large size, blue dextran can only permeate the external pores of the column, undergoing size exclusion. Total bed porosity was estimated using acetone, which can access both external and internal pores of the C18 adsorbent.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e6\u003c/span\u003e illustrates the retention times of blue dextran and acetone plotted against the ratio of superficial velocity to column length. The slopes of these graphs represent the external (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{b}\\)\u003c/span\u003e\u003c/span\u003e) and total (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{T}\\)\u003c/span\u003e\u003c/span\u003e) porosities, respectively. The calculated values were \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{b}\\)\u003c/span\u003e\u003c/span\u003e = 0.3238 and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{T}\\)\u003c/span\u003e\u003c/span\u003e = 0.6717. The external porosity of 0.3238 is consistent with the typical range for nearly spherical adsorbent particles (around 0.4). The total porosity, which accounts for both external and internal pore volumes, is naturally higher than the external porosity. Particle porosity (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{p}\\)\u003c/span\u003e\u003c/span\u003e) was calculated using Eq.\u0026nbsp;(\u003cspan refid=\"Equ18\" class=\"InternalRef\"\u003e28\u003c/span\u003e), yielding a value of 0.5145.\u003c/p\u003e \u003cp\u003e \u003cdiv id=\"Equ18\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ18\" name=\"EquationSource\"\u003e\n$$\\:{\\epsilon\\:}_{T}={\\epsilon\\:}_{b}+\\left(1-{\\epsilon\\:}_{b}\\right){\\epsilon\\:}_{p}\\:\\:$$\u003c/div\u003e \u003cdiv class=\"EquationNumber\"\u003e28\u003c/div\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section3\"\u003e \u003ch2\u003e3.2.2. Determination of Linear Isotherm Parameters Using Pulse Injection Method\u003c/h2\u003e \u003cp\u003eLinear adsorption isotherms for α-mangostin and γ-mangostin were calculated using Eq.\u0026nbsp;\u003cspan refid=\"Equ16\" class=\"InternalRef\"\u003e26\u003c/span\u003e at various acetonitrile concentrations in the mobile phase, considering the predetermined external bed porosity. As shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, a decrease in acetonitrile concentration led to a corresponding increase in the linear adsorption isotherm values for both compounds. This phenomenon can be attributed to the increased polarity of the mobile phase with a higher water content. Due to their low water solubility and non-polar nature, α-mangostin and γ-mangostin exhibit stronger retention or adsorption on the C18 phase in a more polar environment, resulting in increased retention times as the acetonitrile concentration decreases.\u003c/p\u003e \u003cp\u003eFurthermore, the linear isotherm of α-mangostin was consistently higher than that of γ-mangostin across all mobile phase compositions, indicating stronger retention of α-mangostin compared to γ-mangostin. Consequently, in the continuous separation using a three-zone simulated moving bed, α-mangostin was designated as the extract product, while γ-mangostin was considered the raffinate product.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe linear adsorption isotherms of α-MG and γ-MG in a preparative C18 column\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAcetonitrile\u003c/p\u003e \u003cp\u003econcentration (%v/v)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLinear adsorption isotherm\u003c/p\u003e \u003cp\u003eof alpha-mangostin, H\u003csub\u003eα\u0026minus;MG\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLinear adsorption isotherm\u003c/p\u003e \u003cp\u003eof gamma-mangostin, H\u003csub\u003eγ\u0026minus;MG\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSelectivity\u003c/p\u003e \u003cp\u003e(H\u003csub\u003eα\u0026minus;MG\u003c/sub\u003e / H\u003csub\u003eγ\u0026minus;MG\u003c/sub\u003e)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.55\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.58\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e12.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e7.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.58\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe selectivity of the separation on the preparative C18 column, calculated as the ratio of the linear isotherm of α-mangostin to that of γ-mangostin (Eq.\u0026nbsp;(\u003cspan refid=\"Equ17\" class=\"InternalRef\"\u003e27\u003c/span\u003e)), was approximately 1.6 across all mobile phase concentrations. This selectivity value, greater than unity, indicated the feasibility of the separation. Considering these results, an acetonitrile concentration of 75% v/v was selected for subsequent experiments. While this concentration resulted in the lowest linear adsorption isotherms, it offered a suitable balance between selectivity, resolution, and retention time, which are crucial factors for efficient TZ-SMB operation. Shorter retention times enable the system to reach cyclic steady-state operation more rapidly. The chosen conditions, 75% v/v acetonitrile and a flow rate of 6 mL/min, were employed for the breakthrough curve experiments described in the following section.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section3\"\u003e \u003ch2\u003e3.2.3. Breakthrough Curve Experiments of Alpha-mangostin and Gamma-Mangostin\u003c/h2\u003e \u003cp\u003eXanthone solutions prepared at initial concentrations of 1, 3, and 5 g/L in 75% v/v acetonitrile were used as feed for adsorption and desorption experiments. The concentration profiles of γ-mangostin and α-mangostin during adsorption are depicted in Figs.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e7\u003c/span\u003ea and \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e7\u003c/span\u003ec. Initially, neither compound was detected in the effluent, as both were fully adsorbed onto the column. Subsequently, γ-mangostin appeared at 7 min, followed by α-mangostin at 12 min. The concentrations of both compounds gradually increased until reaching a plateau, indicating saturation of the column. The sharp S-shaped breakthrough curves suggest minimal mass transfer resistance during the adsorption process. The 5-min time gap between the breakthrough of α-mangostin and γ-mangostin highlights the successful separation, attributable to the differing adsorption affinities of the two compounds. γ-Mangostin, being less retained, eluted earlier, while α-mangostin, the more strongly retained compound, eluted later.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eDuring the desorption process, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e7\u003c/span\u003eb and \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e7\u003c/span\u003ed, the concentrations of both compounds decreased over time, eventually reaching zero, indicating complete elution. The less retained γ-mangostin was eluted first, followed by the more retained α-mangostin. The time gap between the two compounds persisted during desorption, further emphasizing their distinct adsorption behaviors.\u003c/p\u003e \u003cp\u003eThe simulated concentration profiles for all initial xanthone concentrations are overlaid as lines in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e7\u003c/span\u003ea-\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e7\u003c/span\u003ef. The fitted parameters obtained from the breakthrough curve experiments are presented in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Model validation was performed using an initial xanthone concentration of 2 g/L, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e7\u003c/span\u003ee and \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e7\u003c/span\u003ef. The good agreement between the experimental data and the model predictions, as indicated by the R-squared values in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, confirms the accuracy of the model.\u003c/p\u003e \u003cp\u003eThe adsorption parameters obtained from the single preparative C18 column were subsequently used in the design and simulation of the TZ-SMB system, as detailed in the next section.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe fitted adsorption parameters from the breakthrough curve experiments and the column parameters for a single preparative C18 column\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAdsorption Parameters\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUnit\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAlpha-mangostin\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGamma-mangostin\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLinear adsorption isotherm (H\u003csub\u003ei\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGlobal mass-transfer coefficient (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{K}}_{\\text{i},\\text{j}}\\)\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003es\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e73.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e90.65\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eP\u0026eacute;clet number (Pe)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eColumn Parameters\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExternal bed porosity (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{b}\\)\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003e0.3238\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTotal porosity (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{T}\\)\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003e0.6717\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParticle porosity (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{p}\\)\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003e0.5145\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eColumn length\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003emm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003e250\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eColumn diameter\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003emm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe R-squared values for the simulation of breakthrough curve experiments\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eXanthone\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eAlpha-mangostin\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eGamma-Mangostin\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003econcentration\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAdsorption\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDesorption\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAdsorption\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDesorption\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(g/L)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eR-squared\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR-squared\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eR-squared\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eR-squared\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9976\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9989\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9993\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9965\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9956\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9803\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9972\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9812\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9873\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9644\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9753\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9216\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9856\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9573\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9930\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9592\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003e3.3. Design and Simulation of the Separation of Alpha-Mangostin and Gamma-Mangostin in a Three-Zone Simulated Moving Bed System\u003c/em\u003e \u003c/p\u003e \u003cp\u003eThe triangle theory [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e] was employed to determine the optimal operating parameters of the TZ-SMB system, including switching time and flow rates for the desorbent, feed (liquid extract), extract product, and raffinate product. This theory assumes instantaneous equilibrium between the liquid and solid phases (adsorbent) and neglects the effects of mass transfer resistance. To achieve complete separation, each of the three zones in the TZ-SMB must fulfill specific functions:\u003c/p\u003e \u003cp\u003eZone I: Both α-mangostin and γ-mangostin are designed to elute completely, with the extract product predominantly consisting of α-mangostin. The flow rate ratio, as defined by Eq.\u0026nbsp;(\u003cspan refid=\"Equ19\" class=\"InternalRef\"\u003e32\u003c/span\u003e), must exceed the linear adsorption isotherms of both compounds.\u003c/p\u003e \u003cp\u003eZone II: This zone facilitates the adsorption of α-mangostin while promoting the complete desorption of γ-mangostin.\u003c/p\u003e \u003cp\u003eZone III: α-mangostin adsorption is maintained to prevent its premature elution, while γ-mangostin undergoes desorption, allowing the raffinate product, primarily composed of γ-mangostin, to exit from this zone.\u003c/p\u003e \u003cp\u003eZones II and III are collectively referred to as the separation zones. The flow rate ratios in these two zones must fall between the linear adsorption isotherm values of γ-mangostin and α-mangostin.\u003c/p\u003e \u003cp\u003eBased on the above description, the equations representing the triangle separation region are as follows:\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eZone I: m\u003csub\u003eI\u003c/sub\u003e \u0026gt; H\u003csub\u003eα\u0026minus;MG\u003c/sub\u003e (29)\u003c/p\u003e\u003cp\u003eZone II: H\u003csub\u003eγ\u0026minus;MG\u003c/sub\u003e \u0026lt; m\u003csub\u003eII\u003c/sub\u003e \u0026lt; H\u003csub\u003eα\u0026minus;MG\u003c/sub\u003e (30)\u003c/p\u003e\u003cp\u003eZone III: H\u003csub\u003eγ\u0026minus;MG\u003c/sub\u003e \u0026lt; m\u003csub\u003eIII\u003c/sub\u003e \u0026lt; H\u003csub\u003eα\u0026minus;MG\u003c/sub\u003e (31)\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe flow rate ratio (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{m}}_{\\text{j}}\\)\u003c/span\u003e\u003c/span\u003e) in each zone j of TZ-SMB is defined as:\u003cdiv id=\"Equ19\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ19\" name=\"EquationSource\"\u003e\n$$\\:{\\text{m}}_{\\text{j}}=\\frac{{\\text{Q}}_{\\text{j}}{\\text{t}}_{\\text{s}}-{{\\epsilon\\:}}_{\\text{b}}{\\text{V}}_{\\text{C}}}{\\left(1-{{\\epsilon\\:}}_{\\text{b}}\\right){\\text{V}}_{\\text{C}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e32\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Q}}_{\\text{j}}\\)\u003c/span\u003e\u003c/span\u003e is the volumetric flow rate in zone j of TZ-SMB (mL/min).\u003c/p\u003e \u003cp\u003eThe initial step involved determining the optimal flow rate ratio for Zone I (m\u003csub\u003eI\u003c/sub\u003e). A flow rate of 5 mL/min (Q\u003csub\u003eI\u003c/sub\u003e or Q\u003csub\u003eD\u003c/sub\u003e) and a switching time (t\u003csub\u003es\u003c/sub\u003e) of 20 minutes were selected based on the breakthrough curve experiments. This flow rate ensured complete elution of all bioactive compounds within the 20-min switching time while minimizing pressure drop across the column. The corresponding flow rate ratio, calculated using Eq.\u0026nbsp;(\u003cspan refid=\"Equ19\" class=\"InternalRef\"\u003e32\u003c/span\u003e), was 7.053.\u003c/p\u003e \u003cp\u003eTo construct the separation triangle defined by Eqs.\u0026nbsp;(29), (30), and (31), the coordinates (m\u003csub\u003eII\u003c/sub\u003e, m\u003csub\u003eIII\u003c/sub\u003e) were varied within the triangular region, as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e8\u003c/span\u003e. A total of 22 simulation conditions, derived from Eqs.\u0026nbsp;(\u003cspan refid=\"Equ19\" class=\"InternalRef\"\u003e32\u003c/span\u003e) and (1)-(4), were generated and listed in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe simulated results of TZ-SMB for the separation of α-MG and γ-MG\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"13\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eRun\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eQ\u003csub\u003eD\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eQ\u003csub\u003eF\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eQ\u003csub\u003eE\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eQ\u003csub\u003eR\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:⟨{\\text{C}}_{\\text{A}\\text{M}}^{\\text{E}}⟩\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:⟨{\\text{C}}_{\\text{G}\\text{M}}^{\\text{R}}⟩\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{P}{\\text{U}}_{\\text{E}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{P}{\\text{U}}_{\\text{R}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003ePd\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{C}\\text{a}\\text{p}}_{\\text{A}\\text{M}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{C}\\text{a}\\text{p}}_{\\text{G}\\text{M}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c13\"\u003e \u003cp\u003eSC\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(mL/min)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(mL/min)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(mL/min)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(mL/min)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(mg/mL)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(mg/mL)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e%\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003e%\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003emg/mL\u0026sdot;h\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003emg/h\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003emg/h\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c13\"\u003e \u003cp\u003e(mL/mg)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.664\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.425\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.239\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.082\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e99.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e99.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e11.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e21.52\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.664\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.359\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.305\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.084\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e99.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e99.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e11.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e21.52\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.664\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.292\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.372\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.087\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e99.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e99.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e11.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e21.52\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.664\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.226\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.438\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.089\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e100.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e99.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e11.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e21.52\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.664\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.159\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.504\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.092\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e100.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e99.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e11.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e21.52\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.664\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.093\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.571\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.095\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e100.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e99.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e11.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e21.52\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.664\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.027\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.637\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.098\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e100.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e98.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e11.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e21.52\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.797\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.425\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.372\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e 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\u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.929\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.226\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.704\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.124\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e100.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e96.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e16.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e2.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e15.37\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.929\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.159\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.770\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.012\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e100.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e94.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e16.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e2.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e15.37\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.062\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.425\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.637\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.131\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e99.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e98.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e19.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e3.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e13.45\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.062\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.359\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.704\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.134\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e99.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e96.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e18.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e3.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e13.45\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.062\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.292\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.770\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.137\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e99.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e94.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e18.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e3.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e13.45\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.062\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.226\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.836\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e100.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e90.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e18.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e3.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e13.45\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTheoretically, complete separation (100% purity) is achievable within the boundaries of the separation triangle. The simulated performance parameters at cyclic steady-state, including average concentrations, relative purities, production capacities, productivity, and solvent consumption ratio, were calculated using Eqs.\u0026nbsp;(5)-(\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e10\u003c/span\u003e) and presented in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. In Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e8\u003c/span\u003e, operating conditions resulting in relative purities exceeding 98% for both extract and raffinate products are denoted by green squares, while those with lower purities are indicated by red squares. It is noteworthy that some operating conditions within the separation triangle failed to achieve the desired purities due to mass transfer resistance within the system. The optimal condition, yielding the highest productivity while meeting the purity criteria, is represented by a yellow triangle (condition #19 in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAt the optimal condition 19, the simulated results were as follows: the extract product exhibited a relative purity of 99.95% for α-mangostin, with a production capacity of 19.04 mg/h. The raffinate product demonstrated a relative purity of 98.41% for γ-mangostin, with a production capacity of 3.17 mg/h. The system achieved a productivity of 0.56 mg/mL\u0026middot;h and a solvent consumption ratio of 13.45 mL/mg. The corresponding flow rates for desorbent, feed, extract, and raffinate were 5.00, 1.062, 2.425, and 3.637 mL/min, respectively.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec21\" class=\"Section2\"\u003e \u003ch2\u003e3.4. Experimental Demonstration of TZ-SMB for the separation of α-MG and γ-MG\u003c/h2\u003e \u003cp\u003eCondition #16 from Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e was selected for the experimental demonstration of the TZ-SMB system. Although it offered a lower productivity compared to the optimal condition, it guaranteed the purity of both α-mangostin and γ-mangostin in the extract and raffinate products, as it resided within the green zone of at least 98% purity. Additionally, this condition provided a buffer against potential flow rate fluctuations in the real experimental system. Figure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e9\u003c/span\u003ea and \u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e9\u003c/span\u003eb illustrate the total capacities (mg/h) of α-mangostin and γ-mangostin in the extract and raffinate products, respectively, over the switching time. As calculated using Eqs.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e8\u003c/span\u003e) and (\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e9\u003c/span\u003e), all capacities increased over time and reached a plateau upon achieving cyclic steady-state. Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e presents a comparison of the separation parameters obtained from both experimental and simulation results for the TZ-SMB system, revealing a strong agreement between the predicted and experimental values.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSeparation parameters from the experimental and simulation results of the TZ-SMB system\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSeparation\u003c/p\u003e \u003cp\u003eparameters\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUnit\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eExperimental\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSimulation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e% Diff\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:⟨{\\text{C}}_{\\text{A}\\text{M}}^{\\text{E}}⟩\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003emg/mL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.1811\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1482\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e18.18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:⟨{\\text{C}}_{\\text{G}\\text{M}}^{\\text{R}}⟩\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003emg/mL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0138\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.85\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePu\u003csub\u003eE\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e100.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e99.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePu\u003csub\u003eR\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e98.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e98.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.66\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{C}\\text{a}\\text{p}}_{\\text{A}\\text{M}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003emg/h\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e23.73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e20.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e14.12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{C}\\text{a}\\text{p}}_{\\text{G}\\text{M}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003emg/h\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4.70\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe chromatograms of the feed, extract product, and raffinate product from the TZ-SMB system are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e10\u003c/span\u003ea, \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e10\u003c/span\u003eb, and \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e10\u003c/span\u003ec, respectively. The extract product was predominantly composed of α-mangostin, aligning with the experimental relative purity of 100%. Similarly, the raffinate product primarily consisted of γ-mangostin, as indicated by the experimental relative purity of 98.79%. The true purity of α-mangostin in the extract product was calculated from Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e5\u003c/span\u003e, using the slope of the calibration curve to determine the ratio of the extract product to the HPLC standard. The calculated true purity was 99.4%. Figure\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003eb depicts the appearance of the extract product after evaporation, revealing a yellowish dried powder similar to the xanthone powder shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003ea. The significant improvement achieved using the TZ-SMB system, increasing the HPLC purity of α-mangostin from 71.56\u0026ndash;99.4%, renders it suitable for pharmaceutical applications. This work successfully demonstrated the application of a continuous separation system to enhance the purity of α-mangostin derived from mangosteen pericarp waste.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eThis work successfully demonstrated the application of a three-zone simulated moving bed (TZ-SMB) system for the continuous separation of α-mangostin and γ-mangostin from a liquid extract derived from mangosteen pericarps. Initially, xanthone powder was prepared through solvent extraction and anti-solvent precipitation, yielding an α-mangostin purity of 71.56% as determined by HPLC. This xanthone powder served as the feedstock for a single preparative C18 chromatographic column, enabling the determination of adsorption parameters, including linear adsorption isotherms, mass transfer coefficients, and P\u0026eacute;clet numbers, through breakthrough curve experiments for both bioactive compounds. Pulse injection experiments confirmed that a mobile phase composed of 75% v/v acetonitrile effectively separated the two compounds. Subsequently, the design and simulation of the TZ-SMB system, leveraging triangle theory and the experimentally determined adsorption parameters, identified optimal operating conditions. With a switching time of 20 min and flow rates of 5.00, 1.062, 2.425, and 3.637 mL/min for desorbent, feed, extract, and raffinate, respectively, the system achieved a maximum productivity of 0.56 mg/mL\u0026middot;h while maintaining relative purities exceeding 98% for both bioactive compounds in the extract and raffinate products. Experimental validation of the TZ-SMB system, employing flow rates of 5.00, 0.929, 2.292, and 3.637 mL/min for the respective streams, yielded impressive results. The experimental relative purities of α-mangostin in the extract product and γ-mangostin in the raffinate product reached 100% and 98.79%, respectively. Gravimetric analysis of the dried extract product from the TZ-SMB system, coupled with HPLC analysis, revealed an α-mangostin purity of 99.4%. This study underscores the potential of TZ-SMB as a powerful separation technology for the purification of bioactive compounds derived from agricultural sources.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eDeclaration of competing interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eData will be made available on request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work received financial support from the National Research Council of Thailand (NRCT), grant number N42A650272.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eBCG Model, in, The National Science and Technology Development Agency (NSTDA), 2021.\u003c/li\u003e\n\u003cli\u003eA.F. 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Harriott, Unit Operations of Chemical Engineering 7ed., McGraw Hill, 2004.\u003c/li\u003e\n\u003cli\u003eN. Wathoni, A. Rusdin, K. Motoyama, I.M. Joni, R. Lesmana, M. Muchtaridi, Nanoparticle Drug Delivery Systems for alpha-Mangostin, Nanotechnol. Sci. Appl. 13 (2020) 23-36, https://doi.org/10.2147/NSA.S243017.\u003c/li\u003e\n\u003cli\u003eC. Reichardt, T. Welton, Solvents and Solvent Effects in Organic Chemistry, Wiley‐VCH Verlag GmbH \u0026amp; Co. KGaA, 2011.\u003c/li\u003e\n\u003cli\u003eL. Fang, Y. Liu, H. Zhuang, W. Liu, X. Wang, L. Huang, Combined microwave-assisted extraction and high-speed counter-current chromatography for separation and purification of xanthones from Garcinia mangostana, J. Chromatogr. B. 879 (2011) 3023-3027, https://doi.org/10.1016/j.jchromb.2011.08.040.\u003c/li\u003e\n\u003cli\u003eJ.P.S. Aniceto, I.S. Azenha, F.M.J. Domingues, A. Mendes, C.M. 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Technol. 192 (2018) 401-411, https://doi.org/10.1016/j.seppur.2017.10.016.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"waste-and-biomass-valorization","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"wave","sideBox":"Learn more about [Waste and Biomass Valorization](http://link.springer.com/journal/12649)","snPcode":"12649","submissionUrl":"https://submission.nature.com/new-submission/12649/3","title":"Waste and Biomass Valorization","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"alpha-mangostin, gamma-mangostin, xanthone, mangosteen pericarps, simulated moving bed","lastPublishedDoi":"10.21203/rs.3.rs-6102236/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6102236/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Mangosteen pericarps, a rich source of bioactive xanthones, particularly α-mangostin and γ-mangostin, were the focus of this study. The primary objective was to design and experimentally implement a continuous separation process using a three-zone simulated moving bed (TZ-SMB) system to isolate and purify these valuable compounds. Xanthone powder, extracted from mangosteen pericarps using acetonitrile and purified by anti-solvent precipitation, served as feedstock. This powder, with an initial α-mangostin purity of 71.56%, was subjected to separation on a single C18 preparative column to determine crucial adsorption parameters, including linear adsorption isotherms and mass transfer coefficients. A mobile phase consisting of 75% v/v acetonitrile was found to effectively separate α-mangostin and γ-mangostin. Subsequently, computational simulations based on triangle theory were employed to optimize TZ-SMB operating parameters. The optimal conditions involved a 20-min switching time and flow rates of 5.00, 1.062, 2.425, and 3.637 mL/min for the mobile phase, feed, extract, and raffinate, respectively. Under these conditions, the system achieved a maximum productivity of 0.56 mg/mL·h while maintaining high purities for both α-mangostin and γ-mangostin in the respective products. Experimental validation of the TZ-SMB system, using slightly adjusted flow rates, resulted in an α-mangostin purity of 100% in the extract product and a γ-mangostin purity of 98.79% in the raffinate product. The dried extract product exhibited an α-mangostin purity of 99.4% (HPLC grade). This research highlights the potential of TZ-SMB as a promising technology for the efficient and scalable purification of bioactive compounds from natural sources.","manuscriptTitle":"Continuous separation of alpha-mangostin and gamma-mangostin fractions from xanthone extracted from mangosteen pericarps using a preparative three-zone simulated moving bed system","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-03-31 11:47:51","doi":"10.21203/rs.3.rs-6102236/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2025-03-26T09:03:15+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-03-22T06:23:07+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"Waste and Biomass Valorization","date":"2025-03-16T14:42:57+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-02-25T13:20:15+00:00","index":"","fulltext":""},{"type":"submitted","content":"Waste and Biomass Valorization","date":"2025-02-25T02:06:47+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"waste-and-biomass-valorization","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"wave","sideBox":"Learn more about [Waste and Biomass Valorization](http://link.springer.com/journal/12649)","snPcode":"12649","submissionUrl":"https://submission.nature.com/new-submission/12649/3","title":"Waste and Biomass Valorization","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"a30019d8-059e-4e81-9066-4d340539bb7f","owner":[],"postedDate":"March 31st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-07-07T16:09:22+00:00","versionOfRecord":{"articleIdentity":"rs-6102236","link":"https://doi.org/10.1007/s12649-025-03185-4","journal":{"identity":"waste-and-biomass-valorization","isVorOnly":false,"title":"Waste and Biomass Valorization"},"publishedOn":"2025-07-03 15:58:55","publishedOnDateReadable":"July 3rd, 2025"},"versionCreatedAt":"2025-03-31 11:47:51","video":"","vorDoi":"10.1007/s12649-025-03185-4","vorDoiUrl":"https://doi.org/10.1007/s12649-025-03185-4","workflowStages":[]},"version":"v1","identity":"rs-6102236","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6102236","identity":"rs-6102236","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}