Research on Minimum Ignition Energy Testing of Normal-Alkane Vapors and Its Dependence on Carbon Chain Length

Research on Minimum Ignition Energy Testing of Normal-Alkane Vapors and Its Dependence on Carbon Chain Length | 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 Research on Minimum Ignition Energy Testing of Normal-Alkane Vapors and Its Dependence on Carbon Chain Length Caizhi Xiong, Xuhong Jia, Boyang Xu, Yulong Zhu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7506516/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Minimum Ignition Energy (MIE) is a critical parameter for assessing the combustion and explosion risks of liquid fuels under specific conditions. However, systematic testing methods for long-chain alkanes remain underdeveloped. In this study, an experimental apparatus was developed based on American Society for Testing and Materials Standard ASTM E582-21 to measure the MIE of liquid fuel vapors. Significant improvements in ignition energy control precision were achieved by effectively mitigating vapor condensation. Furthermore, the relationship between MIE and carbon chain length in long-chain alkanes was investigated. System sensitivity parameters were calibrated using methane/air and propane/air mixtures, establishing optimal testing conditions as a 2.0 mm electrode gap and a 14.0 pF capacitance. The reliability of the system was validated through MIE measurements of C 5 –C 8 alkanes (n-pentane, n-hexane, n-heptane, and n-octane), yielding values of 0.197 mJ (at 3.4 vol%), 0.253 mJ (at 3.3 vol%), 0.303 mJ (at 3.0 vol%), and 0.323 mJ (at 2.8 vol%), respectively. These results show less than 5% deviation from literature values and a relative error below 8%. Extended measurements of C 9 –C 11 alkanes revealed MIE values of 0.523 mJ (at 2.8 vol%) for n-nonane, 0.857 mJ (at 2.5 vol%) for n-decane, and 1.127 mJ (at 2.0 vol%) for n-undecane. Notably, the results demonstrate a substantial increase in MIE with carbon chain length, showing a 471% rise from C 5 to C 11 . A nonlinear regression analysis confirmed a strong correlation between MIE and carbon chain length (R² = 0.98). Minimum ignition energy Liquid fuels Long-chain alkanes Sensitive conditions Volume fraction Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Introduction Minimum Ignition Energy (MIE) is defined as the minimum electrical spark energy required to initiate combustion or explosion in a mixture of flammable gas, volatile liquid vapor, or combustible dust cloud with air under specific test conditions. It is also referred to as the critical ignition energy or minimum spark ignition energy [1] . When liquid fuels leak and form highly volatile vapors, their MIE can reach values as low as millijoule levels; for instance, the MIE of ethanol vapor is approximately 0.72 mJ [2] . Such vapors are particularly susceptible to ignition from weak energy sources such as electrostatic sparks, resulting in frequent combustion and explosion accidents in industries including petrochemical processing and aviation fuel storage and transportation [3- 4] . Investigation of the MIE of liquid fuels supports the assessment of fire and explosion risks associated with specific ignition scenarios (e.g., arc discharge or friction). This research also contributes to the identification of causes underlying fuel-related fire and explosion incidents. Moreover, in environments where flammable liquid fuels are present, studies on MIE provide essential data and theoretical foundations for establishing safety standards and preventive measures, which are crucial for ensuring the safety of human life and property. Current research on the minimum ignition energy (MIE) of various combustible materials has addressed multiple dimensions, including influencing factors, measurement techniques, and theoretical modeling. Fernández-Tarrazo E et al. [5] employed the Navier–Stokes equations combined with detailed chemical kinetics to systematically evaluate the MIE of H₂/NH₃ mixtures in air under varying pressure conditions. Their study examined the effects of volume fraction, equivalence ratio, and pressure on MIE across the full concentration spectrum from pure hydrogen to pure ammonia, elucidating the theoretical basis for the sustainability of ultra-lean flames. Movileanu C et al. [6] investigated the spark ignition characteristics of propane/air mixtures and their blends with inert gases (Ar, N₂, He, CO₂) at initial pressures ranging from 0.5 to 1.5 bar. The introduction of inert gases was found to increase both the quenching distance (QD) and MIE, with CO₂ exhibiting the most pronounced effect. Using flange electrode technology, the authors determined a power-law relationship between QD and pressure and derived the overall activation energy via the correlation between QD and flame temperature. Ghosh A et al. [7] conducted high-pressure spark discharge experiments to measure the MIE of methane/air (equivalence ratio 1.0) and hydrogen/air (equivalence ratio 0.16) mixtures at temperatures as low as 200 K. Their results indicate a linear increase in MIE with decreasing temperature, with a more substantial rate of increase for hydrogen mixtures (–7.9 μJ/K) compared to methane (–3.4 μJ/K). These findings offer vital data for the design of low-temperature fuel storage systems. Zhang W et al. [8] performed simulations based on detailed chemical reaction mechanisms to analyze the effect of water vapor dilution on the ignition of methane, n-butane, and n-decane/air mixtures. The study demonstrated that MIE is inversely proportional to pressure and increases exponentially with the water vapor dilution ratio under various pressure conditions. A generalized empirical correlation among MIE, pressure, and dilution ratio was subsequently established. Yu-ichiro et al. [9] conducted experiments using a 2.35 L cylindrical stainless-steel explosion vessel thermostatically maintained at 30 °C in a water bath. A tungsten rod with a diameter of 1 mm and a sharp tip served as the discharge electrode, with an inter-electrode gap set to 2.5 mm. Spark discharges were generated using a direct current power supply capable of delivering up to 16 kV, coupled with a set of capacitors ranging from 10 to 1000 pF. Ebina et al. [10] ignited propane/air mixtures through Joule heating and melting of a thin Ni–Cr wire via electrical discharge. The energy dissipated during wire melting was measured experimentally and defined as the MIE of the propane/air mixture. Coronel et al. [11] developed a capacitive spark ignition system capable of delivering low energy (60 µJ to 1.8 mJ) within short durations (less than 50 ns), designed to simulate electrostatic discharge conditions typical of static ignition hazards. Cirrone et al. [12] proposed a predictive model for accurately estimating the MIE of hydrogen–air mixtures across arbitrary initial compositions and temperatures. By utilizing flame thickness rather than critical flame kernel radius, the model improves MIE prediction accuracy under lean combustion conditions. Wang et al. [13] developed a multivariate linear regression (MLR) model based on quantitative structure–property relationship (QSPR) principles to predict the MIE of chemical compounds. Standard test methods for the minimum ignition energy (MIE) of flammable substances—such as China National Standard GB/T 14288-1993, International Electrotechnical Commission Standard IEC 61241-2-3-1994, and European Standard EN 13281—are widely applicable to gases, dusts, and liquid mists [14- 16] . However, these standards are not designed for long-chain alkane liquid fuels with flash points exceeding 60 °C, such as n-decane and n-undecane. Moreover, they fail to account for measurement inaccuracies resulting from the condensation of high-boiling-point fuel vapors. Furthermore, conventional capacitive discharge methods exhibit significant energy fluctuations and limited adjustment precision [17] . While existing academic research on MIE has predominantly focused on gaseous and combustible dust systems [18] , there remains a notable scarcity of reliable MIE data for long-chain alkane liquid fuels beyond C 9 . In response to current research gaps and methodological limitations, this study introduces an experimental apparatus and testing methodology based on American Society for Testing and Materials Standard ASTM E582-21 for determining the minimum ignition energy (MIE) of alkane-based liquid fuels. The system sensitive parameters were calibrated using methane/air mixtures and propane/air mixture to ensure measurement reliability. Validation was performed with C 5 –C 8 alkanes (n-pentane, n-hexane, n-heptane, and n-octane), followed by MIE measurements of C 9 –C 11 alkanes (n-nonane, n-decane, and n-undecane). The study aims to systematically examine the dependence of MIE on carbon chain length, thereby providing theoretical and experimental support for the formulation of safety standards applicable to long-chain alkane fuels. 1 Apparatus and testing methodology 1.1 Experimental materials In this experiment, methane and propane were employed to calibrate the sensitive parameters of the experimental system. The minimum ignition energy (MIE) of n-pentane, n-hexane, n-heptane, and n-octane was measured and compared with published literature values to assess the reliability and accuracy of the apparatus. Furthermore, n-nonane, n-decane, and n-undecane were selected to determine the MIE of these higher-carbon-number alkanes. The specific results are summarized in Table 1 . Table 1 Experimental materials Test Sample Purity Manufacturer Methane, Propane 99.9% Guanghan Mingyuan Gas Co,Ltd. Dry Air 99.9% Chengdu Jinkexing Gas Co, Ltd. n -Pentane, n -Hexane, n -Heptane, n -Octane 99.5% Chengdu Jinshudu Scientific Supply Co,Ltd. n -Nonane, n -Decane, n -Undecane 99.2% Chengdu Kelong Chemical Co,Ltd. 1.2 Apparatus The minimum ignition energy (MIE) test system used in this study comprises several key components, including a reaction vessel, buffer tank, vacuum pump, ignition control system, and gas supply system. The apparatus was designed and built in compliance with the American Society for Testing and Materials standard ASTM E582-07. A schematic diagram of the experimental setup is presented in Fig. 1. Conventional spark discharge methods for determining the minimum ignition energy (MIE) of combustible materials suffer from limitations such as unstable energy release and insufficient energy adjustment accurac y[ 19 ] . The energy delivered via capacitive discharge is susceptible to voltage fluctuations, capacitance drift, and variations in circuit impedance, resulting in poor reproducibility of spark energy and compromised measurement precision. Moreover, energy adjustment—typically achieved by varying capacitance or voltage—is constrained by the finite resolution of component specifications (e.g., capacitance tolerance of ± 5%), thus hindering continuous fine-tuning and further diminishing measurement accuracy. To overcome these limitations, the present experimental system utilizes a DC constant-current source (adjustable within the range of 0–30 mA) to extend the discharge duration to 6 s, thereby minimizing the influence of voltage fluctuations and circuit impedance variations on the ignition energy and better simulating actual electrostatic discharge processes. By calibrating capacitance values—pre-selected at four levels: 5, 20, 80, and 320 pF—along with discharge voltage (1–20 kV) according to energy requirements, the system enables continuous fine-tuning of ignition energy with a precision of 0.001 mJ, significantly improving experimental accuracy. Furthermore, a two-stage temperature control system is incorporated, comprising a buffer tank heater capable of reaching 200°C and a pipeline heating zone rated up to 500°C, effectively eliminating measurement deviations caused by vapor condensation. The experimental system can be configured to deliver output voltages ranging from 1 to 20 kV. Capacitors are provided at four preset levels: 5, 20, 80, and 320 pF, enabling ignition energy outputs from 0.01 to 20.00 mJ. The electrodes, fabricated from 304 stainless steel, undergo passivation treatment to minimize variations in spark characteristics due to surface conditions. A high-precision electric needle valve is incorporated to accurately regulate the inflow and outflow of flammable gases, allowing control over fuel concentration with an accuracy of 0.01%. The entire setup is constructed from 304 stainless steel and includes spherical reaction vessels with volumes of 1.0 L or 5.0 L, along with a 20.0 L buffer tank, ensuring experimental stability and reproducibility. The core components of the system consist of the vapor distribution unit—connected to the buffer tank—and the combustible gas ignition control system, linked to the reaction vessel, as illustrated in Fig. 2. 1.3Testing methodology During measurement of the minimum ignition energy (MIE) of liquid fuel vapors, the liquid fuel is first injected into the buffer tank through a feed port and evacuated to vacuum using a vacuum pump. The system is then heated above the fuel’s boiling point (up to 200°C) via a buffer tank heater to facilitate complete vaporization. To prevent condensation of the generated flammable vapors as they transit through the metal tubing into the reaction vessel—which could introduce errors in MIE measurements—a constant-temperature heating tape (capable of reaching 500°C) is applied to the surfaces of both the metal transfer line and the reaction vessel. This ensures that the temperature remains above the boiling point of the fuel throughout the experimental setup. During the gas mixing process, the reaction vessel is first evacuated to vacuum using a vacuum pump. The vapor of the liquid fuel under test and dry air from a gas cylinder are then introduced through inlet ports 1 and 2, respectively. The target concentration is set, and the inflow is precisely regulated via a high-precision electric needle valve. The system employs an automated partial-pressure-based gas mixing method. After mixing, the desired ignition energy (0.01–20.00 mJ) and voltage (approximately 8000 V) are set. The control program selects the appropriate capacitor bank according to the voltage and energy requirements, and adjusts the discharge voltage to achieve the target ignition energy, E 0 . An energy step size, ΔE (5–10% of the preset energy), is defined. Ignition is subsequently initiated, and the delivered energy is measured. Ignition success is determined by visual observation through the glass viewport on the reaction vessel. To minimize random variability in measurement outcomes, the Bruceton staircase method was employed to determine the ignition energy corresponding to a 50% probability of ignition. The energy level for each subsequent test was dynamically adjusted based on the result of the previous ignition trial, with an adaptive step size used to iteratively converge toward the threshold value. This approach significantly reduces the number of tests required while improving the accuracy of the estimated minimum ignition energy [ 20 ] . Specifically, after each trial, the energy was decreased by a step size ΔE following a successful ignition, and increased by ΔE following a failure. This procedure was repeated over 20–30 trials to determine the MIE with statistical significance. The minimum ignition energy was calculated using the Bruceton up-and-down method as follows [ 21 ] : $$\:\text{E}\text{=}{\text{E}}_{\text{min}}\text{+Δ}\text{E}\left(\frac{\sum\:_{\text{i}\text{=0}}^{\text{m}}\text{i}\text{⋅}{\text{n}}_{\text{i}}}{\text{N}}\text{−}\frac{\text{1}}{\text{2}}\right)$$ 1 Where E is the minimum ignition energy (mJ); E min denotes the lowest energy level (mJ); ΔE represents the energy step size (mJ); m is the number of energy levels; i is the energy level index; ni is the number of tests at that energy level; and N is the total number of valid tests. 2 Results and discussion 2.1 Determination of critical thresholds In addition to the intrinsic properties of the combustible material and external environmental conditions, system-specific parameters—such as capacitance and electrode gap distance—also significantly influence the minimum ignition energy (MIE) of combustible substances [ 22 ] . In this study, the minimum ignition energy (MIE) of combustible materials was measured using an electric spark ignition method. The value of the energy storage capacitor was found to influence the MIE outcome, while the electrode gap also contributed to measurement variability. Furthermore, as explosive limits differ across combustible materials, a sensitive volume fraction exists at which the most accurate MIE values can be obtained. Therefore, before conducting MIE measurements for liquid fuels, it is essential to identify the optimal system configuration—including the critical capacitance and electrode gap—under which measurements exhibit highest precision. 2.1.1 Determination of critical capacitance value The explosive limit range of propane is 2.0–9.5%, and the equivalent volume fraction is 4.0%. Using a fixed electrode gap of 2.0 mm, a propane/air mixture at this concentration (4.0%) was utilized in the experiments. The minimum ignition energy (MIE) of propane was subsequently determined using the Bruceton staircase method with a capacitance value of 14.0 pF, as described below. (1)An initial energy value E 0 = 0.30mJ was set, with an energy step size of ΔE = 0.02mJ(corresponding to 7% of E 0 ). A total of 24 tests were conducted under these conditions. The results are summarized in Table 2 . A total of 24 ignition tests were performed, resulting in 13 successful ignitions and 11 failed attempts. Measurements were conducted at four energy levels: 0.24 mJ (0 successes, 6 failures), 0.26 mJ (6 successes, 4 failures), 0.28 mJ (4 successes, 1 failure), and 0.30 mJ (3 successes, 0 failures). (2)The experimental data were organized in ascending order of energy level, with the lowest level set at 0.24 mJ. The sorted results are presented in Table 3 . Table 2 Measurement of propane MIE via Bruceton staircase method Test number Ignition energy(mJ) Results Adjustment 1 0.30 S reduce Δ E 2 0.28 F increase Δ E 3 0.30 S reduce Δ E 4 0.28 S reduce Δ E 5 0.26 F increase Δ E 6 0.28 S reduce Δ E 7 0.26 S reduce Δ E 8 0.24 F increase Δ E 9 0.26 S reduce Δ E 10 0.24 F increase Δ E ... ... ... ... 23 0.28 S reduce Δ E 24 0.26 F over S: success; F: fail Table 3 Energy Level Distribution Energy level (mJ) Level number i Total number of times ni Number of successful attempts Number of failed attempts i · ni 0.24 0 6 0 6 0 0.26 1 10 6 4 10 0.28 2 5 4 1 10 0.30 3 3 3 0 9 Total / 24 13 11 29 As summarized in Table 3 , the minimum energy level E min was 0.24 mJ, the energy step size ΔE was 0.02 mJ, the number of energy levels m = 4, and the total number of experiments N = 24. Using the Bruceton up-and-down method, the minimum ignition energy E of propane was calculated via Eq. ( 1 ) to be 0.254 mJ. Figure 3 presents the minimum ignition energy (MIE) values of propane, as determined by the Bruceton staircase method, across varying capacitance values. As shown in Fig. 3 , the minimum ignition energy (MIE) of propane exhibits an approximately U-shaped dependence on capacitance. With increasing capacitance, the MIE decreases progressively, reaching a minimum value of 0.254 mJ at 14.0 pF. Upon further increase in capacitance, the MIE rises markedly. According to the charging and discharging principles of spark discharge circuits, a larger storage capacitance enables greater energy accumulation and higher deliverable ignition energy. However, in practical testing, an excessively large capacitor prolongs the energy release duration, thereby reducing the instantaneous power density and potentially failing to ignite the combustible mixture effectively. Conversely, an insufficiently small capacitance may not meet the critical energy required for ignition, whereas an overly large capacitance can exceed practical needs and lead to overestimated MIE values [ 23 ] . Therefore, an optimal storage capacitance exists that minimizes the ignition energy required for a given combustible material—this value is referred to as the sensitive capacitance. As indicated in Fig. 3 , the measured ignition energy reaches a minimum at a capacitance of 14.0 pF, confirming that the sensitive capacitance under these experimental conditions is 14.0 pF. 2.1.2 Determination of critical optimal electrode gap The explosive limit range of methane is 5.0–15.0%, with an equivalent volume fraction of 9.5%. Experiments were conducted using a methane/air mixture at this concentration (9.5%) under standard conditions. A fixed capacitance of 14.0 pF was selected, and the minimum ignition energy (MIE) of methane was measured at varying electrode gap distances to investigate the influence of gap size on ignition energy. The results are presented in Fig. 4 . As shown in Fig. 4 , the minimum ignition energy (MIE) of methane decreases progressively with increasing electrode gap distance. The ignition energy reaches a minimum value of 0.274 mJ at a gap of 2.0 mm. Upon further increase of the gap, the MIE is observed to rise gradually. The electrode gap is a critical parameter influencing the minimum ignition energy (MIE) of combustible substances, as it directly affects the breakdown voltage, flame kernel development, and energy transfer efficiency [ 24 ] . An excessively small gap promotes dominant heat loss to the electrodes, dissipating thermal energy generated by the gas reaction and leaving only limited spark energy available for flame initiation. This restricts flame kernel growth and may lead to ignition failure or necessitate higher ignition energy. Conversely, an overly large gap weakens the electric field intensity, reducing electron and ion acceleration and thereby increasing the breakdown voltage required to initiate spark discharge. The elevated breakdown voltage in turn demands higher energy input to achieve ignition, resulting in an increased measured MIE [ 25 ] . Therefore, an optimal electrode gap exists that minimizes the ignition energy—denoted as the sensitive electrode gap. As shown in Fig. 4 , the smallest MIE was observed at a gap of 2.0 mm, indicating that the sensitive electrode gap under these experimental conditions is 2.0 mm. Based on the analysis of the results presented in Fig. 3 and Fig. 4 , the sensitive conditions for this test system were identified as a capacitance of 14.0 pF and an electrode gap of 2.0 mm. Under these optimized parameters, the minimum ignition energy (MIE) of other liquid fuels can be accurately and reliably determined. 2.2 Integrated system validation Within the flammability limits of liquid fuel vapors, the maximum energy release occurs during complete combustion with oxygen, i.e., when the volume fraction ratio matches the stoichiometric coefficient ratio in the chemical reaction equation. However, under practical conditions, the optimal volume fraction of the combustible substance often exceeds the theoretical stoichiometric value. This deviation arises due to factors such as impurities in the fuel and incomplete mixing [ 26 ] . Consequently, a slightly fuel-rich volume fraction—termed the sensitive volume fraction—exists at which the minimum ignition energy (MIE) is achieved. Take \(\:\text{CxHy}\) fuel as an example. The chemical equation for complete reaction with oxygen is $$\:\text{CxHy}\text{+}\left(\text{x}\text{+}\frac{\text{y}}{\text{4}}\right){\text{O}}_{\text{2}}\text{→}\text{xC}{\text{O}}_{\text{2}}\text{+}\frac{\text{y}}{\text{2}}{\text{H}}_{\text{2}}\text{O}$$ 2 The amount of O₂ required to burn 1 mol \(\:\text{CxHy}\) is \(\:\text{x}\text{+}\frac{\text{y}}{\text{4}}\) mol. The oxygen content in standard air is 20.95%. Therefore, the chemical equivalent volume fraction n (%) of the reaction in air is calculated as follows: $$\:\text{n}\text{=}\frac{\text{20.95}}{\text{0}\text{.2095}\text{+}\text{x}\text{+}\frac{\text{y}}{\text{4}}}\text{×100%}$$ 3 An electrode gap of 2.0 mm and a capacitance of 14.0 pF were employed. The minimum ignition energy (MIE) of four alkane fuel vapors—n-pentane, n-hexane, n-heptane, and n-octane—was measured across a range of volume fractions. The results are presented in Fig. 5 . Table 4 compares the stoichiometric volume fractions of these alkane fuel vapors, calculated using Eqs. ( 2 ) and ( 3 ), with the experimentally determined sensitive volume fractions. Table 4 Comparative analysis of alkane vapors (C 5 -C 8 ) volume fraction Alkane vapors explosion limit range(%) Equivalent volume fraction(%) Critical volume fraction(%) C 5 H 12 1.4 ~ 7.8 2.6 3.4 C 6 H 14 1.1 ~ 7.5 2.2 3.3 C 7 H 16 1.1 ~ 6.7 1.9 3.0 C 8 H18 1.8 ~ 6.5 1.7 2.8 As shown in Fig. 5 , the minimum ignition energy (MIE) generally exhibits a characteristic V-shaped dependence on the vapor concentration of the liquid fuels. Within the flammability limits, MIE decreases with increasing volume fraction and reaches a relatively low value near the stoichiometric concentration. Subsequently, as the volume fraction continues to rise, the MIE increases accordingly. According to the critical flame nucleus theory, the critical radius ( r c ) denotes the minimum flame size required to achieve self-sustaining combustion [ 27 ] . When the mixture ratio of alkane vapor to oxygen approaches the stoichiometric proportion, the chemical reaction rate reaches its maximum, leading to the smallest r c and thus the minimum ignition energy (MIE). At low alkane vapor concentrations, the reduced fuel availability decreases the reaction rate, necessitating a larger r c to accumulate sufficient thermal energy, which consequently increases the MIE. Conversely, under fuel-rich conditions where oxygen is limited, incomplete chemical reactions reduce the temperature gradient between the flame and the ambient environment. This also demands an increase in r c to compensate for enhanced heat losses, resulting in a rebound in MIE. Based on the comparative analysis summarized in Table 4 , the volume fractions corresponding to the minimum ignition energy for all four alkane vapors are slightly higher than their respective stoichiometric values. Consequently, the sensitive volume fractions for n-pentane, n-hexane, n-heptane, and n-octane are determined to be 3.4%, 3.3%, 3.0%, and 2.8%, respectively. The experimentally determined sensitive volume fraction is consistently slightly higher than the chemically equivalent volume fraction. This deviation arises from two primary factors: firstly, practical fuels contain trace impurities (e.g., water or antioxidants), which consume reactive free radicals and thereby reduce combustion efficiency, necessitating a slightly elevated concentration to achieve sustained ignition; secondly, during the injection of alkane vapor into the reaction vessel, imperfect mixing results in local concentration gradients. Regions with higher fuel concentration thereby favor the attainment of ignition conditions. The minimum ignition energy (MIE) of four alkane fuel vapors was determined using the Bruceton staircase method within this experimental system. The results were compared with existing literature data to validate the reliability and accuracy of both the apparatus and the methodology. A comparative summary of the experimentally obtained MIE values and those reported in the literature is provided in Table 5 [ 28 ] . Table 5 Comparative analysis of MIE for alkane vapors(C 5 -C 8 ) Alkane vapors Experimentally Determined MIE(mJ) Literature-Reported MIE(mJ) Relative Error (%) C 5 H 12 0.197 0.194 2.5 C 6 H 14 0.253 0.248 2.0 C 7 H 16 0.303 0.282 7.4 C 8 H18 0.323 0.314 2.7 As summarized in Table 5 , the minimum ignition energy (MIE) values obtained in this study for the vapors of n-pentane, n-hexane, n-heptane, and n-octane are 0.197 mJ, 0.253 mJ, 0.303 mJ, and 0.323 mJ, respectively. These values are consistently slightly higher than those reported for pure gaseous alkanes. This discrepancy can be attributed to the presence of aerosolized liquid droplets during the vaporization process, which consume a portion of the spark energy upon entering the reaction vessel, thereby increasing the ignition difficulty and resulting in an elevated MIE [ 29 ] . Overall, the experimental results demonstrate close agreement with literature values, exhibiting deviations below 5% and relative errors within 8%. This confirms that the experimental system developed in this study offers high accuracy and reliability for determining the minimum ignition energy (MIE) of alkane-based liquid fuels. Consequently, the apparatus is suitable for further investigation into the variation patterns of MIE with respect to key influencing factors. 2.3 Minimum Ignitation Energy of Alkane Vapors(C 9 -C 11 ) Following validation of the system and methodology, the minimum ignition energy (MIE) of long-chain alkanes (C9–C11) was measured to investigate the dependence of MIE on carbon chain length. The findings provide theoretical and experimental support for establishing safety standards for high-boiling-point long-chain alkane fuels. Under the optimized experimental conditions, the electrode gap was set to 2.0 mm, capacitance to 14.0 pF, initial temperature to 25°C, relative humidity to 45%, and initial pressure to 0.1 MPa. The minimum ignition energy (MIE) of n-nonane, n-decane, and n-undecane was measured across various volume fractions within their flammability limits. The results are presented in Fig. 6 and summarized in Table 6. Table 7 Experimental results for alkane vapors(C 9 -C 11 ) Alkane vapors explosion limit range(%) MIE(mJ) Critical volume fraction(%) C 9 H 20 0.7 ~ 5.6 0.523 2.8 C 10 H 22 0.8 ~ 5.4 0.857 2.5 C 11 H 24 0.6 ~ 6.5 1.127 2.0 As indicated in Fig. 6 and Table 6, the experimentally determined MIE values for n-nonane, n-decane, and n-undecane were 0.523 mJ, 0.857 mJ, and 1.127 mJ, respectively, with corresponding sensitive volume fractions of 2.8%, 2.5%, and 2.0%. The relationship between the minimum ignition energy (MIE) of alkane vapors and the carbon chain length was further investigated; the corresponding results are presented in Fig. 7 . As shown in Fig. 7 , the minimum ignition energy (MIE) of long-chain alkane vapors exhibits a gradual increase with carbon chain length. The growth trend is relatively moderate from C 5 to C 8 , but becomes markedly steeper beyond C 8 . Owing to the measurement range limitation of the experimental system (< 20 mJ), the MIE of alkanes with longer carbon chains (e.g., n-dodecane and n-tridecane) could not be accurately determined; it is inferred that their values would be substantially higher. Overall, the MIE increased by 471% from C 5 to C 11 , with a particularly sharp rise of 115% observed from C 9 to C 11 . The strong dependence of MIE on carbon chain length is further supported by nonlinear fitting, yielding a coefficient of determination (R²) of 0.98, which indicates a highly significant correlation. The observed increase in MIE with carbon chain length in alkanes can be attributed to systematic changes in their physicochemical properties. Increasing molecular weight leads to an exponential decrease in saturated vapor pressure—for instance, at 20°C, the vapor pressure drops from 14.5 kPa for n-pentane to merely 0.04 kPa for n-heptane, with even lower values for longer-chain alkanes [ 30 ] . This reduction significantly decreases the number density of fuel molecules in the vapor phase and raises the local concentration gradient required to form a combustible mixture. Moreover, enhanced van der Waals interactions in longer-chain alkanes result in a sharp decline in the gas-phase diffusion coefficient, which considerably delays fuel–oxidizer mixing and reduces mixing efficiency within the ignition kernel [ 31 ] . Furthermore, cracking of long-chain alkanes generates more stable free radicals, diminishing the reactivity of chain-branching reactions and necessitating higher energy input to sustain combustion [ 32 ] . To our knowledge, this study presents the first systematic determination of the minimum ignition energy (MIE) for C 9 –C 11 n-alkanes, thereby addressing a significant gap in the foundational safety parameters of high-boiling-point long-chain alkane fuels. Experimental results demonstrate an exponential increase in MIE with carbon chain length, evidencing a 471% rise from C 5 to C 11 . Although long-chain alkanes are frequently perceived as lower fire risks owing to their high flash points, their vapor MIE values at critical concentrations—such as 1.127 mJ for n-undecane at 2.0 vol%—remain well below the typical human electrostatic discharge threshold (10 mJ), underscoring a persistent ignition hazard in industrial environments. These findings offer critical insights for enhancing safety protocols in the storage and transportation of aviation kerosene and diesel components. A carbon-number-dependent model enables the precise determination of inerting concentrations—for example, through the introduction of nitrogen to suppress ignition—and supports the selection of appropriate explosion-proof electrical equipment. Furthermore, the strong correlation between MIE and carbon chain length (R² = 0.98) advances the mechanistic understanding of how molecular structure influences combustion chain reactions, providing a foundation for predictive models of ignition behavior in multi-component fuels. 3 Conclusion In this study, methane and propane were utilized as calibration gases to determine the optimal experimental parameters, namely the sensitive capacitance and sensitive electrode gap. The sensitive volume fractions and corresponding minimum ignition energy (MIE) values of four alkane vapors were measured within their flammability limits. Comparison with literature data showed minor deviations and low relative errors, confirming the high reliability and reproducibility of the experimental system and methodology in determining the MIE of alkane-based liquid fuels. This approach offers an effective tool for industrial safety design and combustion mechanism research. Furthermore, the MIE values of n-nonane, n-decane, and n-undecane were obtained, demonstrating a significant increase in MIE with carbon chain length. This study not only establishes a high-precision testing method for MIE determination but also reveals a strong carbon-number dependence of MIE in long-chain alkanes, providing critical experimental support for the development of fuel safety standards and improved fire risk assessment. Using methane and propane as calibration gases, the sensitive capacitance and sensitive electrode gap of the experimental system were determined to be 14.0 pF and 2.0 mm, respectively. Within the flammability limits, the MIE values of n-pentane, n-hexane, n-heptane, and n-octane were determined as 0.197 mJ, 0.253 mJ, 0.303 mJ, and 0.323 mJ, respectively, using the present experimental system. Compared to literature values, these results show deviations of less than 5% and relative errors below 8%, demonstrating the high reliability of both the experimental setup and testing methodology for MIE measurement of liquid fuels. The measured minimum ignition energy (MIE) values for the long-chain alkanes n-nonane, n-decane, and n-undecane were 0.523 mJ (at 2.8 vol%), 0.857 mJ (at 2.5 vol%), and 1.127 mJ (at 2.0 vol%), respectively. A significant increase in MIE with carbon chain length was observed, showing a 471% rise from C 5 to C 11 alkanes. The strong correlation between MIE and carbon number is further supported by a nonlinear fit yielding R² = 0.98. Declarations Author Contribution X.C:Wrote the main manuscript text；J.X:Writing-editing, Methodology, Funding ;X.B:Prepared figure 1, and provided experimental guidance；Z.Y:Reviewed the manuscript. References C. Popa, S. Nan, M. Paraian, et al. 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Geneva,Swiss: international Electrotechnical Commission,1994: 13-15. Comite Europeen de Normalisation. 2002 Potentially explosive atmosphere,explosion prevention and protection,determination of minimum ignition energy of dust/air mixtures: EN 13821[S]. London: Comite Europeen de Normalisation,2002:5-14. D. Yu, Z. Chen. Premixed flame ignition: Theoretical development[J]. Progress in Energy and Combustion Science,2024,104101174-101174. B. Su, H. Dong, Z. Luo, et al. Research progress on explosion dynamics characteristics and mechanism of hybrid mixtures[J]. CIESC Journal,(2024),75(6): 2109-2122. Z. Zhang, P. Cai. Study on Affecting Factors of Minimum Ignition Energy (MIE) and Analysis on Its Calculation Error[J]. China Safety Science Journal, 2004, 14(5): 88-91. D. Christensen, P. Novik, E. Unneberg. Estimating sensitivity with the Bruceton method: Setting the record straight[J]. Propellants, Explosives, Pyrotechnics,2024,49(7): e202400022. C. Kershaw. A comparison of estimators of the ED50 in up-and-down experiments[J]. Journal of Statistical Computation & Simulation, 1987, 27(2): 175-184. C. Li, Z. Ma, Z. Dong, et al. Theoretical study on electric spark ignition sensitivity of methane / air mixture[J]. Journal of Safety and Environment,2022,22(4): 1913-1918. T. Charles, P. Vassilios, F. Samer, et al. On the minimum ignition energy and its transition in the localised forced ignition of turbulent homogeneous mixtures [J]. Combustion and Flame,2019,201:104-117. A. Dorval, K. Geraud, F. Valensi,et al. Statistical analysis of pulsed spark discharges in water: Effects of gap distance, electrode material, and voltage polarity on discharge characteristics[J]. Journal of Vacuum Science & Technology A-Vacuum Surfaces and Films, 2022, 40(4):17. F. Wu, S. Liu, D. Wang. Influence of needle electrode curvature radius on breakdown characteristics of micro-gap discharge in air[J]. Journal of Xi'an University of Science and Technology,2023,43(5): 1015-1024. B. Wang, X. Liu, C. Xie. Effect of temperature on minimum ignition energy (MIE) of hydrocarbon combustible gas[J]. Journal of Safety and Environment, 2016,16(2): 90-93. J.H. Kim, K. Van, K.D. Lee, et al. Laminar flame speed, Markstein length, and cellular instability for spherically propagating methane/ethylene–air premixed flames[J]. Combustion and Flame,2020,214464-474. J. Moorhouse, A. Williams, T.E. Maddison. An investigation of the minimum ignition energies of some C 1 to C 7 hydrocarbons[J]. Combustion and flame,1974,23(2): 203-213. W. Zhang, X. Gou, Z. Chen. Effects of water vapor dilution on the minimum ignition energy of methane, n-butane and n-decane at normal and reduced pressures[J]. Fuel, 2017, 187: 111-116. S.H. Mazloumi, A. Haghtalab, A. Karimi. Extension of a square-well equation of state for chain-like molecules using perturbed hard chain theory[J]. Fluid Phase Equilibria, 2023:565. T. Hori, T. Kamino, Y. Yoshimoto, et al. Mutual influence of molecular diffusion in gas and surface phases[J]. Physical Review E, 2018, 97(1): 013101. H. Wang, S. Gong, L. Wang, et al. High pressure pyrolysis mechanism and kinetics of a strained-caged hydrocarbon fuel quadricyclane[J]. Fuel, 2019, 239: 935-945. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7506516","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":512050072,"identity":"09a45963-b62d-443b-be78-20e89ac3bcf9","order_by":0,"name":"Caizhi Xiong","email":"","orcid":"","institution":"Civil Aviation Flight University of China","correspondingAuthor":false,"prefix":"","firstName":"Caizhi","middleName":"","lastName":"Xiong","suffix":""},{"id":512050073,"identity":"2d405cb5-4398-4a7d-8169-89a53b8139ce","order_by":1,"name":"Xuhong Jia","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA10lEQVRIiWNgGAWjYBACxmYQ0QAkmJkPPkioqCFFC3tbssGDM8eItQqkheeMmeTDFmbCqpnbmZ9J8+6wyZOPSDCrSGxgY+Bv704g4DA2Y2PeM2nFhjcS0m4k7pBhkDhzdgMBLQyGj3nbDidunJFw7EbiGTYGA4lcQlrYPxyGaElsK0hsYyZGCw/Elvk8h9kYiNVSbDi3LS1xA3sbs0TCmWM8BP1i2H98m8TbNpvE+c38Hz/+qKiR42/vJaClAcowOAChefAqBwF5OKMBj6pRMApGwSgY2QAAVhhLNiivIX8AAAAASUVORK5CYII=","orcid":"","institution":"Civil Aviation Flight University of China","correspondingAuthor":true,"prefix":"","firstName":"Xuhong","middleName":"","lastName":"Jia","suffix":""},{"id":512050074,"identity":"fad998e4-a0fe-487b-b21a-a9bacbb95769","order_by":2,"name":"Boyang Xu","email":"","orcid":"","institution":"Civil Aviation Flight University of China","correspondingAuthor":false,"prefix":"","firstName":"Boyang","middleName":"","lastName":"Xu","suffix":""},{"id":512050075,"identity":"da1b59a4-aabb-4f15-81ef-a776aec8a215","order_by":3,"name":"Yulong Zhu","email":"","orcid":"","institution":"Civil Aviation Flight University of China","correspondingAuthor":false,"prefix":"","firstName":"Yulong","middleName":"","lastName":"Zhu","suffix":""}],"badges":[],"createdAt":"2025-09-01 09:08:57","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7506516/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7506516/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":90904937,"identity":"2ddb222c-044f-4b8e-ba1a-9ef664643aa0","added_by":"auto","created_at":"2025-09-09 12:56:37","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":45666,"visible":true,"origin":"","legend":"\u003cp\u003eSimplified diagram of the MIE test apparatus\u003c/p\u003e\n\u003cp\u003e1-Vapor-generation subsystem,2-Ignition control module.3-Reaction vessel,4-Buffer tanks,5-Vacuum pump,6-Electric needle valve,7-Metal electrodes,8-High-voltage wires,9-Power cord,10-Heating wires\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7506516/v1/4fddfe224cf0e4ecb96cb686.jpg"},{"id":90904923,"identity":"aae2c0d9-dc97-46c1-8208-21e1cc9372ea","added_by":"auto","created_at":"2025-09-09 12:56:37","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":79472,"visible":true,"origin":"","legend":"\u003cp\u003ePhysical diagram of the MIE test apparatus\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7506516/v1/9716261b36b1f91cab0e1086.jpg"},{"id":90905396,"identity":"4c8d4017-7af0-4e44-bc82-66e2c9f4b47e","added_by":"auto","created_at":"2025-09-09 13:04:37","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":47780,"visible":true,"origin":"","legend":"\u003cp\u003eInfluence of capacitance on MIE\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7506516/v1/5b0ea6e94aa1e6cb0ae8ad69.jpg"},{"id":90905399,"identity":"39be843b-feab-4865-89b3-69be4fda6e66","added_by":"auto","created_at":"2025-09-09 13:04:37","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":45908,"visible":true,"origin":"","legend":"\u003cp\u003eInfluence of electrode gap on MIE\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7506516/v1/914b9cb6b34fdd4c539cfcbd.jpg"},{"id":90905397,"identity":"77651b45-ecad-4df5-aff8-d89dca460811","added_by":"auto","created_at":"2025-09-09 13:04:37","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":114654,"visible":true,"origin":"","legend":"\u003cp\u003eMIE of alkane vapors (C\u003csub\u003e5\u003c/sub\u003e-C\u003csub\u003e8\u003c/sub\u003e) at four different volume fractions\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7506516/v1/03375f3ca84562017bd427a9.jpg"},{"id":90904925,"identity":"43a80602-87bf-4312-be35-18befb74a7ed","added_by":"auto","created_at":"2025-09-09 12:56:37","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":61096,"visible":true,"origin":"","legend":"\u003cp\u003eMIE of higher alkane vapors (C\u003csub\u003e9\u003c/sub\u003e-C\u003csub\u003e11\u003c/sub\u003e) at different volume fractions\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7506516/v1/7f7d15740fd12b216f974319.jpg"},{"id":90904934,"identity":"f16adc33-00d6-488f-bfd5-f48b8dea3319","added_by":"auto","created_at":"2025-09-09 12:56:37","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":48261,"visible":true,"origin":"","legend":"\u003cp\u003eVariation pattern of (MIE) in alkane vapors (C\u003csub\u003e5\u003c/sub\u003e–C\u003csub\u003e11\u003c/sub\u003e) with carbon chain length\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7506516/v1/1bcfce8ea9fda1e2cc691376.jpg"},{"id":94474399,"identity":"9204c05b-72d0-41db-985c-8f527d00cfbc","added_by":"auto","created_at":"2025-10-27 15:48:53","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1323160,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7506516/v1/17306397-383c-47ad-a794-5da2bb0d76f3.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Research on Minimum Ignition Energy Testing of Normal-Alkane Vapors and Its Dependence on Carbon Chain Length","fulltext":[{"header":"Introduction","content":"\u003cp\u003eMinimum Ignition Energy (MIE) is defined as the minimum electrical spark energy required to initiate combustion or explosion in a mixture of flammable gas, volatile liquid vapor, or combustible dust cloud with air under specific test conditions. It is also referred to as the critical ignition energy or minimum spark ignition energy\u003csup\u003e[1]\u003c/sup\u003e. When liquid fuels leak and form highly volatile vapors, their MIE can reach values as low as millijoule levels; for instance, the MIE of ethanol vapor is approximately 0.72 mJ\u003csup\u003e[2]\u003c/sup\u003e. Such vapors are particularly susceptible to ignition from weak energy sources such as electrostatic sparks, resulting in frequent combustion and explosion accidents in industries including petrochemical processing and aviation fuel storage and transportation\u003csup\u003e[3-\u003c/sup\u003e\u003csup\u003e4]\u003c/sup\u003e. Investigation of the MIE of liquid fuels supports the assessment of fire and explosion risks associated with specific ignition scenarios (e.g., arc discharge or friction). This research also contributes to the identification of causes underlying fuel-related fire and explosion incidents. Moreover, in environments where flammable liquid fuels are present, studies on MIE provide essential data and theoretical foundations for establishing safety standards and preventive measures, which are crucial for ensuring the safety of human life and property.\u003c/p\u003e\n\u003cp\u003eCurrent research on the minimum ignition energy (MIE) of various combustible materials has addressed multiple dimensions, including influencing factors, measurement techniques, and theoretical modeling. Fern\u0026aacute;ndez-Tarrazo E et al.\u003csup\u003e[5]\u003c/sup\u003eemployed the Navier\u0026ndash;Stokes equations combined with detailed chemical kinetics to systematically evaluate the MIE of H₂/NH₃ mixtures in air under varying pressure conditions. Their study examined the effects of volume fraction, equivalence ratio, and pressure on MIE across the full concentration spectrum from pure hydrogen to pure ammonia, elucidating the theoretical basis for the sustainability of ultra-lean flames. Movileanu C et al.\u003csup\u003e[6]\u003c/sup\u003einvestigated the spark ignition characteristics of propane/air mixtures and their blends with inert gases (Ar, N₂, He, CO₂) at initial pressures ranging from 0.5 to 1.5 bar. The introduction of inert gases was found to increase both the quenching distance (QD) and MIE, with CO₂ exhibiting the most pronounced effect. Using flange electrode technology, the authors determined a power-law relationship between QD and pressure and derived the overall activation energy via the correlation between QD and flame temperature. Ghosh A et al.\u003csup\u003e[7]\u003c/sup\u003econducted high-pressure spark discharge experiments to measure the MIE of methane/air (equivalence ratio 1.0) and hydrogen/air (equivalence ratio 0.16) mixtures at temperatures as low as 200 K. Their results indicate a linear increase in MIE with decreasing temperature, with a more substantial rate of increase for hydrogen mixtures (\u0026ndash;7.9 \u0026mu;J/K) compared to methane (\u0026ndash;3.4 \u0026mu;J/K). These findings offer vital data for the design of low-temperature fuel storage systems. Zhang W et al.\u003csup\u003e[8]\u003c/sup\u003eperformed simulations based on detailed chemical reaction mechanisms to analyze the effect of water vapor dilution on the ignition of methane, n-butane, and n-decane/air mixtures. The study demonstrated that MIE is inversely proportional to pressure and increases exponentially with the water vapor dilution ratio under various pressure conditions. A generalized empirical correlation among MIE, pressure, and dilution ratio was subsequently established.\u003c/p\u003e\n\u003cp\u003eYu-ichiro et al.\u003csup\u003e[9]\u003c/sup\u003econducted experiments using a 2.35 L cylindrical stainless-steel explosion vessel thermostatically maintained at 30 \u0026deg;C in a water bath. A tungsten rod with a diameter of 1 mm and a sharp tip served as the discharge electrode, with an inter-electrode gap set to 2.5 mm. Spark discharges were generated using a direct current power supply capable of delivering up to 16 kV, coupled with a set of capacitors ranging from 10 to 1000 pF. Ebina et al.\u003csup\u003e[10]\u003c/sup\u003eignited propane/air mixtures through Joule heating and melting of a thin Ni\u0026ndash;Cr wire via electrical discharge. The energy dissipated during wire melting was measured experimentally and defined as the MIE of the propane/air mixture. Coronel et al.\u003csup\u003e[11]\u003c/sup\u003edeveloped a capacitive spark ignition system capable of delivering low energy (60 \u0026micro;J to 1.8 mJ) within short durations (less than 50 ns), designed to simulate electrostatic discharge conditions typical of static ignition hazards. Cirrone et al.\u003csup\u003e[12]\u003c/sup\u003eproposed a predictive model for accurately estimating the MIE of hydrogen\u0026ndash;air mixtures across arbitrary initial compositions and temperatures. By utilizing flame thickness rather than critical flame kernel radius, the model improves MIE prediction accuracy under lean combustion conditions. Wang et al.\u003csup\u003e[13]\u003c/sup\u003edeveloped a multivariate linear regression (MLR) model based on quantitative structure\u0026ndash;property relationship (QSPR) principles to predict the MIE of chemical compounds.\u003c/p\u003e\n\u003cp\u003eStandard test methods for the minimum ignition energy (MIE) of flammable substances\u0026mdash;such as China National Standard GB/T 14288-1993, International Electrotechnical Commission Standard IEC 61241-2-3-1994, and European Standard EN 13281\u0026mdash;are widely applicable to gases, dusts, and liquid mists\u003csup\u003e[14-\u003c/sup\u003e\u003csup\u003e16]\u003c/sup\u003e. However, these standards are not designed for long-chain alkane liquid fuels with flash points exceeding 60 \u0026deg;C, such as n-decane and n-undecane. Moreover, they fail to account for measurement inaccuracies resulting from the condensation of high-boiling-point fuel vapors. Furthermore, conventional capacitive discharge methods exhibit significant energy fluctuations and limited adjustment precision\u003csup\u003e[17]\u003c/sup\u003e. While existing academic research on MIE has predominantly focused on gaseous and combustible dust systems\u003csup\u003e[18]\u003c/sup\u003e, there remains a notable scarcity of reliable MIE data for long-chain alkane liquid fuels beyond C\u003csub\u003e9\u003c/sub\u003e.\u003c/p\u003e\n\u003cp\u003eIn response to current research gaps and methodological limitations, this study introduces an experimental apparatus and testing methodology based on American Society for Testing and Materials Standard ASTM E582-21 for determining the minimum ignition energy (MIE) of alkane-based liquid fuels. The system sensitive parameters were calibrated using methane/air mixtures and propane/air mixture to ensure measurement reliability. Validation was performed with C\u003csub\u003e5\u003c/sub\u003e\u0026ndash;C\u003csub\u003e8\u003c/sub\u003e alkanes (n-pentane, n-hexane, n-heptane, and n-octane), followed by MIE measurements of C\u003csub\u003e9\u003c/sub\u003e\u0026ndash;C\u003csub\u003e11\u003c/sub\u003e alkanes (n-nonane, n-decane, and n-undecane). The study aims to systematically examine the dependence of MIE on carbon chain length, thereby providing theoretical and experimental support for the formulation of safety standards applicable to long-chain alkane fuels.\u003c/p\u003e"},{"header":"1 Apparatus and testing methodology","content":"\u003cdiv id=\"Sec2\" class=\"Section2\"\u003e\u003ch2\u003e1.1 Experimental materials\u003c/h2\u003e\u003cp\u003eIn this experiment, methane and propane were employed to calibrate the sensitive parameters of the experimental system. The minimum ignition energy (MIE) of n-pentane, n-hexane, n-heptane, and n-octane was measured and compared with published literature values to assess the reliability and accuracy of the apparatus. Furthermore, n-nonane, n-decane, and n-undecane were selected to determine the MIE of these higher-carbon-number alkanes. The specific results are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\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\u003eExperimental materials\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=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTest Sample\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePurity\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eManufacturer\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMethane, Propane\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e99.9%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eGuanghan Mingyuan Gas Co,Ltd.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDry Air\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e99.9%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eChengdu Jinkexing Gas Co, Ltd.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003en\u003c/em\u003e-Pentane, \u003cem\u003en\u003c/em\u003e-Hexane, \u003cem\u003en\u003c/em\u003e-Heptane, \u003cem\u003en\u003c/em\u003e-Octane\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e99.5%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eChengdu Jinshudu Scientific Supply Co,Ltd.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003en\u003c/em\u003e-Nonane, \u003cem\u003en\u003c/em\u003e-Decane, \u003cem\u003en\u003c/em\u003e-Undecane\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e99.2%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eChengdu Kelong Chemical Co,Ltd.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e1.2 Apparatus\u003c/h2\u003e\u003cp\u003eThe minimum ignition energy (MIE) test system used in this study comprises several key components, including a reaction vessel, buffer tank, vacuum pump, ignition control system, and gas supply system. The apparatus was designed and built in compliance with the American Society for Testing and Materials standard ASTM E582-07. A schematic diagram of the experimental setup is presented in Fig.\u0026nbsp;1.\u003c/p\u003e\n\u003cp\u003eConventional spark discharge methods for determining the minimum ignition energy (MIE) of combustible materials suffer from limitations such as unstable energy release and insufficient energy adjustment accurac\u003csup\u003ey[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/sup\u003e. The energy delivered via capacitive discharge is susceptible to voltage fluctuations, capacitance drift, and variations in circuit impedance, resulting in poor reproducibility of spark energy and compromised measurement precision. Moreover, energy adjustment\u0026mdash;typically achieved by varying capacitance or voltage\u0026mdash;is constrained by the finite resolution of component specifications (e.g., capacitance tolerance of \u0026plusmn;\u0026thinsp;5%), thus hindering continuous fine-tuning and further diminishing measurement accuracy.\u003c/p\u003e\u003cp\u003eTo overcome these limitations, the present experimental system utilizes a DC constant-current source (adjustable within the range of 0\u0026ndash;30 mA) to extend the discharge duration to 6 s, thereby minimizing the influence of voltage fluctuations and circuit impedance variations on the ignition energy and better simulating actual electrostatic discharge processes. By calibrating capacitance values\u0026mdash;pre-selected at four levels: 5, 20, 80, and 320 pF\u0026mdash;along with discharge voltage (1\u0026ndash;20 kV) according to energy requirements, the system enables continuous fine-tuning of ignition energy with a precision of 0.001 mJ, significantly improving experimental accuracy. Furthermore, a two-stage temperature control system is incorporated, comprising a buffer tank heater capable of reaching 200\u0026deg;C and a pipeline heating zone rated up to 500\u0026deg;C, effectively eliminating measurement deviations caused by vapor condensation.\u003c/p\u003e\u003cp\u003eThe experimental system can be configured to deliver output voltages ranging from 1 to 20 kV. Capacitors are provided at four preset levels: 5, 20, 80, and 320 pF, enabling ignition energy outputs from 0.01 to 20.00 mJ. The electrodes, fabricated from 304 stainless steel, undergo passivation treatment to minimize variations in spark characteristics due to surface conditions. A high-precision electric needle valve is incorporated to accurately regulate the inflow and outflow of flammable gases, allowing control over fuel concentration with an accuracy of 0.01%. The entire setup is constructed from 304 stainless steel and includes spherical reaction vessels with volumes of 1.0 L or 5.0 L, along with a 20.0 L buffer tank, ensuring experimental stability and reproducibility. The core components of the system consist of the vapor distribution unit\u0026mdash;connected to the buffer tank\u0026mdash;and the combustible gas ignition control system, linked to the reaction vessel, as illustrated in Fig.\u0026nbsp;2.\u003c/p\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e1.3Testing methodology\u003c/h2\u003e\u003cp\u003eDuring measurement of the minimum ignition energy (MIE) of liquid fuel vapors, the liquid fuel is first injected into the buffer tank through a feed port and evacuated to vacuum using a vacuum pump. The system is then heated above the fuel\u0026rsquo;s boiling point (up to 200\u0026deg;C) via a buffer tank heater to facilitate complete vaporization. To prevent condensation of the generated flammable vapors as they transit through the metal tubing into the reaction vessel\u0026mdash;which could introduce errors in MIE measurements\u0026mdash;a constant-temperature heating tape (capable of reaching 500\u0026deg;C) is applied to the surfaces of both the metal transfer line and the reaction vessel. This ensures that the temperature remains above the boiling point of the fuel throughout the experimental setup.\u003c/p\u003e\u003cp\u003eDuring the gas mixing process, the reaction vessel is first evacuated to vacuum using a vacuum pump. The vapor of the liquid fuel under test and dry air from a gas cylinder are then introduced through inlet ports 1 and 2, respectively. The target concentration is set, and the inflow is precisely regulated via a high-precision electric needle valve. The system employs an automated partial-pressure-based gas mixing method. After mixing, the desired ignition energy (0.01\u0026ndash;20.00 mJ) and voltage (approximately 8000 V) are set. The control program selects the appropriate capacitor bank according to the voltage and energy requirements, and adjusts the discharge voltage to achieve the target ignition energy, \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e. An energy step size, \u003cem\u003eΔE\u003c/em\u003e (5\u0026ndash;10% of the preset energy), is defined. Ignition is subsequently initiated, and the delivered energy is measured. Ignition success is determined by visual observation through the glass viewport on the reaction vessel.\u003c/p\u003e\u003cp\u003eTo minimize random variability in measurement outcomes, the Bruceton staircase method was employed to determine the ignition energy corresponding to a 50% probability of ignition. The energy level for each subsequent test was dynamically adjusted based on the result of the previous ignition trial, with an adaptive step size used to iteratively converge toward the threshold value. This approach significantly reduces the number of tests required while improving the accuracy of the estimated minimum ignition energy\u003csup\u003e[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]\u003c/sup\u003e. Specifically, after each trial, the energy was decreased by a step size \u003cem\u003eΔE\u003c/em\u003e following a successful ignition, and increased by \u003cem\u003eΔE\u003c/em\u003e following a failure. This procedure was repeated over 20\u0026ndash;30 trials to determine the MIE with statistical significance.\u003c/p\u003e\u003cp\u003eThe minimum ignition energy was calculated using the Bruceton up-and-down method as follows\u003csup\u003e[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]\u003c/sup\u003e:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\text{E}\\text{=}{\\text{E}}_{\\text{min}}\\text{+\u0026Delta;}\\text{E}\\left(\\frac{\\sum\\:_{\\text{i}\\text{=0}}^{\\text{m}}\\text{i}\\text{\u0026sdot;}{\\text{n}}_{\\text{i}}}{\\text{N}}\\text{\u0026minus;}\\frac{\\text{1}}{\\text{2}}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere \u003cem\u003eE\u003c/em\u003e is the minimum ignition energy (mJ); \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003emin\u003c/em\u003e\u003c/sub\u003e denotes the lowest energy level (mJ); \u003cem\u003eΔE\u003c/em\u003e represents the energy step size (mJ); \u003cem\u003em\u003c/em\u003e is the number of energy levels; \u003cem\u003ei\u003c/em\u003e is the energy level index; \u003cem\u003eni\u003c/em\u003e is the number of tests at that energy level; and \u003cem\u003eN\u003c/em\u003e is the total number of valid tests.\u003c/p\u003e\u003c/div\u003e"},{"header":"2 Results and discussion","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e2.1 Determination of critical thresholds\u003c/h2\u003e\u003cp\u003eIn addition to the intrinsic properties of the combustible material and external environmental conditions, system-specific parameters\u0026mdash;such as capacitance and electrode gap distance\u0026mdash;also significantly influence the minimum ignition energy (MIE) of combustible substances\u003csup\u003e[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eIn this study, the minimum ignition energy (MIE) of combustible materials was measured using an electric spark ignition method. The value of the energy storage capacitor was found to influence the MIE outcome, while the electrode gap also contributed to measurement variability. Furthermore, as explosive limits differ across combustible materials, a sensitive volume fraction exists at which the most accurate MIE values can be obtained. Therefore, before conducting MIE measurements for liquid fuels, it is essential to identify the optimal system configuration\u0026mdash;including the critical capacitance and electrode gap\u0026mdash;under which measurements exhibit highest precision.\u003c/p\u003e\u003cdiv id=\"Sec8\" class=\"Section3\"\u003e\u003ch2\u003e2.1.1 Determination of critical capacitance value\u003c/h2\u003e\u003cp\u003eThe explosive limit range of propane is 2.0\u0026ndash;9.5%, and the equivalent volume fraction is 4.0%. Using a fixed electrode gap of 2.0 mm, a propane/air mixture at this concentration (4.0%) was utilized in the experiments. The minimum ignition energy (MIE) of propane was subsequently determined using the Bruceton staircase method with a capacitance value of 14.0 pF, as described below.\u003c/p\u003e\u003cp\u003e(1)An initial energy value \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.30mJ was set, with an energy step size of \u003cem\u003eΔE\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.02mJ(corresponding to 7% of \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e). A total of 24 tests were conducted under these conditions. The results are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eA total of 24 ignition tests were performed, resulting in 13 successful ignitions and 11 failed attempts. Measurements were conducted at four energy levels: 0.24 mJ (0 successes, 6 failures), 0.26 mJ (6 successes, 4 failures), 0.28 mJ (4 successes, 1 failure), and 0.30 mJ (3 successes, 0 failures).\u003c/p\u003e\u003cp\u003e(2)The experimental data were organized in ascending order of energy level, with the lowest level set at 0.24 mJ. The sorted results are presented in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\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\u003eMeasurement of propane MIE via Bruceton staircase method\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=\"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\u003eTest number\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIgnition energy(mJ)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eResults\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eAdjustment\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=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eS\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003ereduce Δ\u003cem\u003eE\u003c/em\u003e\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=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.28\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eF\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eincrease Δ\u003cem\u003eE\u003c/em\u003e\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=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eS\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003ereduce Δ\u003cem\u003eE\u003c/em\u003e\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=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.28\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eS\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003ereduce Δ\u003cem\u003eE\u003c/em\u003e\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=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.26\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eF\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eincrease Δ\u003cem\u003eE\u003c/em\u003e\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=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.28\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eS\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003ereduce Δ\u003cem\u003eE\u003c/em\u003e\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=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.26\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eS\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003ereduce Δ\u003cem\u003eE\u003c/em\u003e\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=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.24\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eF\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eincrease Δ\u003cem\u003eE\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.26\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eS\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003ereduce Δ\u003cem\u003eE\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.24\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eF\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eincrease Δ\u003cem\u003eE\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e...\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e...\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e...\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e...\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e23\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.28\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eS\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003ereduce Δ\u003cem\u003eE\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e24\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.26\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eF\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eover\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"4\"\u003eS: success; F: fail\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\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\u003eEnergy Level Distribution\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\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=\"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\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEnergy level\u003c/p\u003e\u003cp\u003e(mJ)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLevel number\u003c/p\u003e\u003cp\u003e\u003cem\u003ei\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eTotal number of times \u003cem\u003eni\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eNumber of successful attempts\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eNumber of failed attempts\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cem\u003ei\u003c/em\u003e\u0026middot;\u003cem\u003eni\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.24\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.26\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e10\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.28\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e10\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e9\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTotal\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e/\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e24\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e29\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\u003eAs summarized in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, the minimum energy level \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003emin\u003c/em\u003e\u003c/sub\u003e was 0.24 mJ, the energy step size \u003cem\u003eΔE\u003c/em\u003e was 0.02 mJ, the number of energy levels \u003cem\u003em\u003c/em\u003e\u0026thinsp;=\u0026thinsp;4, and the total number of experiments \u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;24. Using the Bruceton up-and-down method, the minimum ignition energy \u003cem\u003eE\u003c/em\u003e of propane was calculated via Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) to be 0.254 mJ.\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e3\u003c/span\u003e presents the minimum ignition energy (MIE) values of propane, as determined by the Bruceton staircase method, across varying capacitance values.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e3\u003c/span\u003e, the minimum ignition energy (MIE) of propane exhibits an approximately U-shaped dependence on capacitance. With increasing capacitance, the MIE decreases progressively, reaching a minimum value of 0.254 mJ at 14.0 pF. Upon further increase in capacitance, the MIE rises markedly.\u003c/p\u003e\u003cp\u003eAccording to the charging and discharging principles of spark discharge circuits, a larger storage capacitance enables greater energy accumulation and higher deliverable ignition energy. However, in practical testing, an excessively large capacitor prolongs the energy release duration, thereby reducing the instantaneous power density and potentially failing to ignite the combustible mixture effectively. Conversely, an insufficiently small capacitance may not meet the critical energy required for ignition, whereas an overly large capacitance can exceed practical needs and lead to overestimated MIE values \u003csup\u003e[\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]\u003c/sup\u003e. Therefore, an optimal storage capacitance exists that minimizes the ignition energy required for a given combustible material\u0026mdash;this value is referred to as the sensitive capacitance. As indicated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e3\u003c/span\u003e, the measured ignition energy reaches a minimum at a capacitance of 14.0 pF, confirming that the sensitive capacitance under these experimental conditions is 14.0 pF.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section3\"\u003e\u003ch2\u003e2.1.2 Determination of critical optimal electrode gap\u003c/h2\u003e\u003cp\u003eThe explosive limit range of methane is 5.0\u0026ndash;15.0%, with an equivalent volume fraction of 9.5%. Experiments were conducted using a methane/air mixture at this concentration (9.5%) under standard conditions. A fixed capacitance of 14.0 pF was selected, and the minimum ignition energy (MIE) of methane was measured at varying electrode gap distances to investigate the influence of gap size on ignition energy. The results are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the minimum ignition energy (MIE) of methane decreases progressively with increasing electrode gap distance. The ignition energy reaches a minimum value of 0.274 mJ at a gap of 2.0 mm. Upon further increase of the gap, the MIE is observed to rise gradually.\u003c/p\u003e\u003cp\u003eThe electrode gap is a critical parameter influencing the minimum ignition energy (MIE) of combustible substances, as it directly affects the breakdown voltage, flame kernel development, and energy transfer efficiency\u003csup\u003e[\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]\u003c/sup\u003e. An excessively small gap promotes dominant heat loss to the electrodes, dissipating thermal energy generated by the gas reaction and leaving only limited spark energy available for flame initiation. This restricts flame kernel growth and may lead to ignition failure or necessitate higher ignition energy. Conversely, an overly large gap weakens the electric field intensity, reducing electron and ion acceleration and thereby increasing the breakdown voltage required to initiate spark discharge. The elevated breakdown voltage in turn demands higher energy input to achieve ignition, resulting in an increased measured MIE\u003csup\u003e[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]\u003c/sup\u003e. Therefore, an optimal electrode gap exists that minimizes the ignition energy\u0026mdash;denoted as the sensitive electrode gap. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the smallest MIE was observed at a gap of 2.0 mm, indicating that the sensitive electrode gap under these experimental conditions is 2.0 mm.\u003c/p\u003e\u003cp\u003eBased on the analysis of the results presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e3\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the sensitive conditions for this test system were identified as a capacitance of 14.0 pF and an electrode gap of 2.0 mm. Under these optimized parameters, the minimum ignition energy (MIE) of other liquid fuels can be accurately and reliably determined.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e2.2 Integrated system validation\u003c/h2\u003e\u003cp\u003eWithin the flammability limits of liquid fuel vapors, the maximum energy release occurs during complete combustion with oxygen, i.e., when the volume fraction ratio matches the stoichiometric coefficient ratio in the chemical reaction equation. However, under practical conditions, the optimal volume fraction of the combustible substance often exceeds the theoretical stoichiometric value. This deviation arises due to factors such as impurities in the fuel and incomplete mixing\u003csup\u003e[\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]\u003c/sup\u003e. Consequently, a slightly fuel-rich volume fraction\u0026mdash;termed the sensitive volume fraction\u0026mdash;exists at which the minimum ignition energy (MIE) is achieved.\u003c/p\u003e\u003cp\u003eTake \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{CxHy}\\)\u003c/span\u003e\u003c/span\u003e fuel as an example. The chemical equation for complete reaction with oxygen is\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\text{CxHy}\\text{+}\\left(\\text{x}\\text{+}\\frac{\\text{y}}{\\text{4}}\\right){\\text{O}}_{\\text{2}}\\text{\u0026rarr;}\\text{xC}{\\text{O}}_{\\text{2}}\\text{+}\\frac{\\text{y}}{\\text{2}}{\\text{H}}_{\\text{2}}\\text{O}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe amount of O₂ required to burn 1 mol \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{CxHy}\\)\u003c/span\u003e\u003c/span\u003e is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{x}\\text{+}\\frac{\\text{y}}{\\text{4}}\\)\u003c/span\u003e\u003c/span\u003e mol. The oxygen content in standard air is 20.95%. Therefore, the chemical equivalent volume fraction \u003cem\u003en\u003c/em\u003e (%) of the reaction in air is calculated as follows:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:\\text{n}\\text{=}\\frac{\\text{20.95}}{\\text{0}\\text{.2095}\\text{+}\\text{x}\\text{+}\\frac{\\text{y}}{\\text{4}}}\\text{\u0026times;100%}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eAn electrode gap of 2.0 mm and a capacitance of 14.0 pF were employed. The minimum ignition energy (MIE) of four alkane fuel vapors\u0026mdash;n-pentane, n-hexane, n-heptane, and n-octane\u0026mdash;was measured across a range of volume fractions. The results are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e5\u003c/span\u003e. Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e compares the stoichiometric volume fractions of these alkane fuel vapors, calculated using Eqs.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) and (\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), with the experimentally determined sensitive volume fractions.\u003c/p\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\u003eComparative analysis of alkane vapors (C\u003csub\u003e5\u003c/sub\u003e-C\u003csub\u003e8\u003c/sub\u003e) volume fraction\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\u003eAlkane vapors\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eexplosion limit range(%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eEquivalent volume fraction(%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eCritical volume fraction(%)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eC\u003csub\u003e5\u003c/sub\u003eH\u003csub\u003e12\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.4\u0026thinsp;~\u0026thinsp;7.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e3.4\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eC\u003csub\u003e6\u003c/sub\u003eH\u003csub\u003e14\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.1\u0026thinsp;~\u0026thinsp;7.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e3.3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eC\u003csub\u003e7\u003c/sub\u003eH\u003csub\u003e16\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.1\u0026thinsp;~\u0026thinsp;6.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e3.0\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eC\u003csub\u003e8\u003c/sub\u003eH18\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.8\u0026thinsp;~\u0026thinsp;6.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.8\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\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e5\u003c/span\u003e, the minimum ignition energy (MIE) generally exhibits a characteristic V-shaped dependence on the vapor concentration of the liquid fuels. Within the flammability limits, MIE decreases with increasing volume fraction and reaches a relatively low value near the stoichiometric concentration. Subsequently, as the volume fraction continues to rise, the MIE increases accordingly. According to the critical flame nucleus theory, the critical radius (\u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e) denotes the minimum flame size required to achieve self-sustaining combustion\u003csup\u003e[\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]\u003c/sup\u003e. When the mixture ratio of alkane vapor to oxygen approaches the stoichiometric proportion, the chemical reaction rate reaches its maximum, leading to the smallest \u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e and thus the minimum ignition energy (MIE). At low alkane vapor concentrations, the reduced fuel availability decreases the reaction rate, necessitating a larger \u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e to accumulate sufficient thermal energy, which consequently increases the MIE. Conversely, under fuel-rich conditions where oxygen is limited, incomplete chemical reactions reduce the temperature gradient between the flame and the ambient environment. This also demands an increase in \u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e to compensate for enhanced heat losses, resulting in a rebound in MIE.\u003c/p\u003e\u003cp\u003eBased on the comparative analysis summarized in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the volume fractions corresponding to the minimum ignition energy for all four alkane vapors are slightly higher than their respective stoichiometric values. Consequently, the sensitive volume fractions for n-pentane, n-hexane, n-heptane, and n-octane are determined to be 3.4%, 3.3%, 3.0%, and 2.8%, respectively. The experimentally determined sensitive volume fraction is consistently slightly higher than the chemically equivalent volume fraction. This deviation arises from two primary factors: firstly, practical fuels contain trace impurities (e.g., water or antioxidants), which consume reactive free radicals and thereby reduce combustion efficiency, necessitating a slightly elevated concentration to achieve sustained ignition; secondly, during the injection of alkane vapor into the reaction vessel, imperfect mixing results in local concentration gradients. Regions with higher fuel concentration thereby favor the attainment of ignition conditions.\u003c/p\u003e\u003cp\u003eThe minimum ignition energy (MIE) of four alkane fuel vapors was determined using the Bruceton staircase method within this experimental system. The results were compared with existing literature data to validate the reliability and accuracy of both the apparatus and the methodology. A comparative summary of the experimentally obtained MIE values and those reported in the literature is provided in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e\u003csup\u003e[\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]\u003c/sup\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\u003eComparative analysis of MIE for alkane vapors(C\u003csub\u003e5\u003c/sub\u003e-C\u003csub\u003e8\u003c/sub\u003e)\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\u003eAlkane vapors\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eExperimentally Determined MIE(mJ)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eLiterature-Reported MIE(mJ)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eRelative Error\u003c/p\u003e\u003cp\u003e(%)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eC\u003csub\u003e5\u003c/sub\u003eH\u003csub\u003e12\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.197\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.194\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.5\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eC\u003csub\u003e6\u003c/sub\u003eH\u003csub\u003e14\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.253\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.248\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.0\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eC\u003csub\u003e7\u003c/sub\u003eH\u003csub\u003e16\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.303\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.282\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e7.4\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eC\u003csub\u003e8\u003c/sub\u003eH18\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.323\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.314\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.7\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\u003eAs summarized in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, the minimum ignition energy (MIE) values obtained in this study for the vapors of n-pentane, n-hexane, n-heptane, and n-octane are 0.197 mJ, 0.253 mJ, 0.303 mJ, and 0.323 mJ, respectively. These values are consistently slightly higher than those reported for pure gaseous alkanes. This discrepancy can be attributed to the presence of aerosolized liquid droplets during the vaporization process, which consume a portion of the spark energy upon entering the reaction vessel, thereby increasing the ignition difficulty and resulting in an elevated MIE\u003csup\u003e[\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eOverall, the experimental results demonstrate close agreement with literature values, exhibiting deviations below 5% and relative errors within 8%. This confirms that the experimental system developed in this study offers high accuracy and reliability for determining the minimum ignition energy (MIE) of alkane-based liquid fuels. Consequently, the apparatus is suitable for further investigation into the variation patterns of MIE with respect to key influencing factors.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e2.3 Minimum Ignitation Energy of Alkane Vapors(C\u003csub\u003e9\u003c/sub\u003e-C\u003csub\u003e11\u003c/sub\u003e)\u003c/h2\u003e\u003cp\u003eFollowing validation of the system and methodology, the minimum ignition energy (MIE) of long-chain alkanes (C9\u0026ndash;C11) was measured to investigate the dependence of MIE on carbon chain length. The findings provide theoretical and experimental support for establishing safety standards for high-boiling-point long-chain alkane fuels.\u003c/p\u003e\u003cp\u003eUnder the optimized experimental conditions, the electrode gap was set to 2.0 mm, capacitance to 14.0 pF, initial temperature to 25\u0026deg;C, relative humidity to 45%, and initial pressure to 0.1 MPa. The minimum ignition energy (MIE) of n-nonane, n-decane, and n-undecane was measured across various volume fractions within their flammability limits. The results are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e6\u003c/span\u003e and summarized in Table\u0026nbsp;6.\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 7\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eExperimental results for alkane vapors(C\u003csub\u003e9\u003c/sub\u003e-C\u003csub\u003e11\u003c/sub\u003e)\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\u003eAlkane vapors\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eexplosion limit range(%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMIE(mJ)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eCritical volume fraction(%)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eC\u003csub\u003e9\u003c/sub\u003eH\u003csub\u003e20\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.7\u0026thinsp;~\u0026thinsp;5.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.523\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.8\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eC\u003csub\u003e10\u003c/sub\u003eH\u003csub\u003e22\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.8\u0026thinsp;~\u0026thinsp;5.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.857\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.5\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eC\u003csub\u003e11\u003c/sub\u003eH\u003csub\u003e24\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.6\u0026thinsp;~\u0026thinsp;6.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.127\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.0\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\u003eAs indicated in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e6\u003c/span\u003e and Table\u0026nbsp;6, the experimentally determined MIE values for n-nonane, n-decane, and n-undecane were 0.523 mJ, 0.857 mJ, and 1.127 mJ, respectively, with corresponding sensitive volume fractions of 2.8%, 2.5%, and 2.0%.\u003c/p\u003e\u003cp\u003eThe relationship between the minimum ignition energy (MIE) of alkane vapors and the carbon chain length was further investigated; the corresponding results are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e7\u003c/span\u003e, the minimum ignition energy (MIE) of long-chain alkane vapors exhibits a gradual increase with carbon chain length. The growth trend is relatively moderate from C\u003csub\u003e5\u003c/sub\u003eto C\u003csub\u003e8\u003c/sub\u003e, but becomes markedly steeper beyond C\u003csub\u003e8\u003c/sub\u003e. Owing to the measurement range limitation of the experimental system (\u0026lt;\u0026thinsp;20 mJ), the MIE of alkanes with longer carbon chains (e.g., n-dodecane and n-tridecane) could not be accurately determined; it is inferred that their values would be substantially higher. Overall, the MIE increased by 471% from C\u003csub\u003e5\u003c/sub\u003e to C\u003csub\u003e11\u003c/sub\u003e, with a particularly sharp rise of 115% observed from C\u003csub\u003e9\u003c/sub\u003e to C\u003csub\u003e11\u003c/sub\u003e. The strong dependence of MIE on carbon chain length is further supported by nonlinear fitting, yielding a coefficient of determination (R\u0026sup2;) of 0.98, which indicates a highly significant correlation.\u003c/p\u003e\u003cp\u003eThe observed increase in MIE with carbon chain length in alkanes can be attributed to systematic changes in their physicochemical properties. Increasing molecular weight leads to an exponential decrease in saturated vapor pressure\u0026mdash;for instance, at 20\u0026deg;C, the vapor pressure drops from 14.5 kPa for n-pentane to merely 0.04 kPa for n-heptane, with even lower values for longer-chain alkanes\u003csup\u003e[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]\u003c/sup\u003e. This reduction significantly decreases the number density of fuel molecules in the vapor phase and raises the local concentration gradient required to form a combustible mixture. Moreover, enhanced van der Waals interactions in longer-chain alkanes result in a sharp decline in the gas-phase diffusion coefficient, which considerably delays fuel\u0026ndash;oxidizer mixing and reduces mixing efficiency within the ignition kernel\u003csup\u003e[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]\u003c/sup\u003e. Furthermore, cracking of long-chain alkanes generates more stable free radicals, diminishing the reactivity of chain-branching reactions and necessitating higher energy input to sustain combustion\u003csup\u003e[\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eTo our knowledge, this study presents the first systematic determination of the minimum ignition energy (MIE) for C\u003csub\u003e9\u003c/sub\u003e\u0026ndash;C\u003csub\u003e11\u003c/sub\u003e n-alkanes, thereby addressing a significant gap in the foundational safety parameters of high-boiling-point long-chain alkane fuels. Experimental results demonstrate an exponential increase in MIE with carbon chain length, evidencing a 471% rise from C\u003csub\u003e5\u003c/sub\u003e to C\u003csub\u003e11\u003c/sub\u003e. Although long-chain alkanes are frequently perceived as lower fire risks owing to their high flash points, their vapor MIE values at critical concentrations\u0026mdash;such as 1.127 mJ for n-undecane at 2.0 vol%\u0026mdash;remain well below the typical human electrostatic discharge threshold (10 mJ), underscoring a persistent ignition hazard in industrial environments.\u003c/p\u003e\u003cp\u003eThese findings offer critical insights for enhancing safety protocols in the storage and transportation of aviation kerosene and diesel components. A carbon-number-dependent model enables the precise determination of inerting concentrations\u0026mdash;for example, through the introduction of nitrogen to suppress ignition\u0026mdash;and supports the selection of appropriate explosion-proof electrical equipment. Furthermore, the strong correlation between MIE and carbon chain length (R\u0026sup2; = 0.98) advances the mechanistic understanding of how molecular structure influences combustion chain reactions, providing a foundation for predictive models of ignition behavior in multi-component fuels.\u003c/p\u003e\u003c/div\u003e"},{"header":"3 Conclusion","content":"\u003cp\u003eIn this study, methane and propane were utilized as calibration gases to determine the optimal experimental parameters, namely the sensitive capacitance and sensitive electrode gap. The sensitive volume fractions and corresponding minimum ignition energy (MIE) values of four alkane vapors were measured within their flammability limits. Comparison with literature data showed minor deviations and low relative errors, confirming the high reliability and reproducibility of the experimental system and methodology in determining the MIE of alkane-based liquid fuels. This approach offers an effective tool for industrial safety design and combustion mechanism research. Furthermore, the MIE values of n-nonane, n-decane, and n-undecane were obtained, demonstrating a significant increase in MIE with carbon chain length. This study not only establishes a high-precision testing method for MIE determination but also reveals a strong carbon-number dependence of MIE in long-chain alkanes, providing critical experimental support for the development of fuel safety standards and improved fire risk assessment.\u003c/p\u003e\u003cp\u003eUsing methane and propane as calibration gases, the sensitive capacitance and sensitive electrode gap of the experimental system were determined to be 14.0 pF and 2.0 mm, respectively.\u003c/p\u003e\u003cp\u003eWithin the flammability limits, the MIE values of n-pentane, n-hexane, n-heptane, and n-octane were determined as 0.197 mJ, 0.253 mJ, 0.303 mJ, and 0.323 mJ, respectively, using the present experimental system. Compared to literature values, these results show deviations of less than 5% and relative errors below 8%, demonstrating the high reliability of both the experimental setup and testing methodology for MIE measurement of liquid fuels.\u003c/p\u003e\u003cp\u003eThe measured minimum ignition energy (MIE) values for the long-chain alkanes n-nonane, n-decane, and n-undecane were 0.523 mJ (at 2.8 vol%), 0.857 mJ (at 2.5 vol%), and 1.127 mJ (at 2.0 vol%), respectively. A significant increase in MIE with carbon chain length was observed, showing a 471% rise from C\u003csub\u003e5\u003c/sub\u003e to C\u003csub\u003e11\u003c/sub\u003e alkanes. The strong correlation between MIE and carbon number is further supported by a nonlinear fit yielding R\u0026sup2; = 0.98.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eX.C:Wrote the main manuscript text；J.X:Writing-editing, Methodology, Funding ;X.B:Prepared figure 1, and provided experimental guidance；Z.Y:Reviewed the manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eC. Popa, S. Nan, M. Paraian, et al. Aspects of laboratory tests for the determination of the minimum ignition energy of the fuel/dust mixture[C]//MATEC Web of Conferences. EDP Sciences,2021,342: 04004.\u003c/li\u003e\n\u003cli\u003eY. Wang, J. Ding, S. Yang, et al. Study on the test method of minimum ignition energy of vapor under the gas-liquid coexistence condition with trace liquid[J]. Fire Safety Science,2023,32(2): 77-84.\u003c/li\u003e\n\u003cli\u003eBaalisampang T, Abbassi R, Garaniya V, et al. 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Makarov, C. Proust, et al. Minimum ignition energy of hydrogen-air mixtures at ambient and cryogenic temperatures[J]. International journal of hydrogen energy,2023,48(43): 16530-16544.\u003c/li\u003e\n\u003cli\u003eB. Wang, L. Zhou, K. Xu, et al. Fast prediction of minimum ignition energy from molecular structure using simple QSPR model[J].Journal of Loss Prevention in the Process Industries,2017,50,290-294.\u003c/li\u003e\n\u003cli\u003eNational Technical Committee on Fire Safety of Standardization Administration of China. Determination of minimum ignition energy of combustible gases and flammable liquid vapors: GB/T 14288-1993[S]. China Standards Press, 1993.\u003c/li\u003e\n\u003cli\u003eInternational Electrotechnical Commission. Electrical apparatus for use in the presence of combustible dust: Part 2 test methods,section 3 method of determining minimum ignition energy of dust/air mixtures: IEC 61241-2-3-1994[S]. Geneva,Swiss: international Electrotechnical Commission,1994: 13-15.\u003c/li\u003e\n\u003cli\u003eComite Europeen de Normalisation. 2002 Potentially explosive atmosphere,explosion prevention and protection,determination of minimum ignition energy of dust/air mixtures: EN 13821[S]. London: Comite Europeen de Normalisation,2002:5-14.\u003c/li\u003e\n\u003cli\u003eD. Yu, Z. Chen. Premixed flame ignition: Theoretical development[J]. Progress in Energy and Combustion Science,2024,104101174-101174.\u003c/li\u003e\n\u003cli\u003eB. Su, H. Dong, Z. Luo, et al. Research progress on explosion dynamics characteristics and mechanism of hybrid mixtures[J]. CIESC Journal,(2024),75(6): 2109-2122.\u003c/li\u003e\n\u003cli\u003eZ. Zhang, P. Cai. Study on Affecting Factors of Minimum Ignition Energy (MIE) and Analysis on Its Calculation Error[J]. China Safety Science Journal, 2004, 14(5): 88-91.\u003c/li\u003e\n\u003cli\u003eD. Christensen, P. Novik, E. Unneberg. 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Fuel, 2019, 239: 935-945.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Minimum ignition energy, Liquid fuels, Long-chain alkanes, Sensitive conditions, Volume fraction","lastPublishedDoi":"10.21203/rs.3.rs-7506516/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7506516/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eMinimum Ignition Energy (MIE) is a critical parameter for assessing the combustion and explosion risks of liquid fuels under specific conditions. However, systematic testing methods for long-chain alkanes remain underdeveloped. In this study, an experimental apparatus was developed based on American Society for Testing and Materials Standard ASTM E582-21 to measure the MIE of liquid fuel vapors. Significant improvements in ignition energy control precision were achieved by effectively mitigating vapor condensation. Furthermore, the relationship between MIE and carbon chain length in long-chain alkanes was investigated. System sensitivity parameters were calibrated using methane/air and propane/air mixtures, establishing optimal testing conditions as a 2.0 mm electrode gap and a 14.0 pF capacitance. The reliability of the system was validated through MIE measurements of C\u003csub\u003e5\u003c/sub\u003e\u0026ndash;C\u003csub\u003e8\u003c/sub\u003e alkanes (n-pentane, n-hexane, n-heptane, and n-octane), yielding values of 0.197 mJ (at 3.4 vol%), 0.253 mJ (at 3.3 vol%), 0.303 mJ (at 3.0 vol%), and 0.323 mJ (at 2.8 vol%), respectively. These results show less than 5% deviation from literature values and a relative error below 8%. Extended measurements of C\u003csub\u003e9\u003c/sub\u003e\u0026ndash;C\u003csub\u003e11\u003c/sub\u003e alkanes revealed MIE values of 0.523 mJ (at 2.8 vol%) for n-nonane, 0.857 mJ (at 2.5 vol%) for n-decane, and 1.127 mJ (at 2.0 vol%) for n-undecane. Notably, the results demonstrate a substantial increase in MIE with carbon chain length, showing a 471% rise from C\u003csub\u003e5\u003c/sub\u003e to C\u003csub\u003e11\u003c/sub\u003e. A nonlinear regression analysis confirmed a strong correlation between MIE and carbon chain length (R\u0026sup2; = 0.98).\u003c/p\u003e","manuscriptTitle":"Research on Minimum Ignition Energy Testing of Normal-Alkane Vapors and Its Dependence on Carbon Chain Length","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-09 12:56:32","doi":"10.21203/rs.3.rs-7506516/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"abac1110-b694-45d6-ac0b-2d01f6499634","owner":[],"postedDate":"September 9th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-10-27T14:33:23+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-09 12:56:32","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7506516","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7506516","identity":"rs-7506516","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}