Enabling a Leidenfrost drop to perform Biellmann spin

Enabling a Leidenfrost drop to perform Biellmann spin | 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 Article Enabling a Leidenfrost drop to perform Biellmann spin Yao Lu, Shuai Huang, Minghao Li, Enze Liu, Kai Feng, Zeming Wang, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6246861/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 Leidenfrost phenomenon refers to the levitation of a liquid drop on a sufficiently hot surface and has been studied since its discovery in 1756. Extensive research has explored this effect across both liquids and solids, uncovering fascinating behaviours and intricate underlying mechanisms. However, most research on this phenomenon only focused on unrestricted drops, such as self-rotating motions, trampolining, and manipulating substrate morphology to control drop motions, few reports have explored the behaviour of a restricted Leidenfrost drop due to the significant challenge to manipulate a highly mobile levitating drop. Here we report a new phenomenon of a high-speed spinning Leidenfrost drop by confining both its vertical and horizontal movements. We term this phenomenon the Biellmann-Leidenfrost spin because it is reminiscent of the Biellmann spin in figure skating. This phenomenon originates from the vertical restriction on a Leidenfrost drop that initiates star-like oscillations, and is enhanced when the drop satisfies the double resonance conditions, enabling a maximum angular velocity of ~ 1700 r/min, and can be sustained by replenishing water. The Biellmann-Leidenfrost effect holds significant potential for converting waste heat into mechanical energy, for applications in energy conversion and conservation. Physical sciences/Materials science Physical sciences/Physics Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction When a liquid drop is placed on a substrate heated far above its boiling point, it can levitate over a cushion of its own vapour, this is a phenomenon known as the Leidenfrost effect 1 . Due to the absence of friction and the continuous escape of vapour from the Leidenfrost cushion, the drop exhibits remarkable mobility. At the same time, the vapour layer, with its poor heat conductivity, insulates the drop from the substrate, extending its lifetime to the order of a few minutes. These unique properties make Leidenfrost drops highly applicable in various fields, such as drop transport 2 , thermal engineering 3 , and cryopreservation 4 . Extending beyond liquids to solids, extensive research on the Leidenfrost effect has revealed intriguing transport behaviors and complex underlying physics 2,5-14 . A common approach to achieving directional motion involves exploiting the interaction between Leidenfrost drops and asymmetric substrates. This is often achieved using structured surfaces with features such as ratchets 2,6,15 , microtextures with geometric gradients 8 or curvatures 16 , and herringbone-like structures 17,18 , or by introducing temperature gradients that mimic a ratchet-like mechanism 19 . In these self-propelling systems, asymmetry serves as the primary driver of movement. Unidirectional self-transport is achieved by rectifying the vapour flow beneath the drop through asymmetric textures, imparting a well-defined velocity (typically around 10 cm/s). However, these asymmetric structural systems inherently limit the direction of drop motion. Moreover, directional transport of Leidenfrost drops has also been observed on flat solid surfaces due to spontaneous symmetry breaking of internal flows 14,20 . Furthermore, the inverse Leidenfrost effect where a liquid drop self-propels on a liquid surface such as in cryogenic baths 5,11,21,22 , occurs due to similar symmetry breaking within the vapour film that levitates the drop. However, these symmetry breaking effects are size-dependent, occurring only for drops within a specific size range. Beyond directional transport, Leidenfrost drops can also exhibit self-propulsion in the form of rotation. This is typically achieved by exploiting asymmetry to generate unbalanced vapour flows. For instance, a water drop that is partially adhered to a hot surface can undergo violent rotation 23 , but this phenomenon occurs randomly and remains difficult to control. Another approach involves designing wetting heterogeneity on the substrate to rectify vapour flow and induce drop spinning 24 . However, the long-term chemical stability of such substrates under high temperature remains a challenge. In this study, we investigate the dynamics of drops deposited on a hot substrate without any deliberate asymmetric patterns, confined by a cover plate on the top – a “restricted” Leidenfrost scenario distinct from those previously studied. Contrary to the symmetry breaking induced by surface topography in conventional unrestricted Leidenfrost drops, we demonstrate that, in the absence of such topographic asymmetry, spontaneous symmetry breaking can induce rapid spinning of liquid drops, achieving velocities on the order of 1000 r/min. We term this phenomenon the “Biellmann-Leidenfrost effect”. Through both experimental and theoretical analyses, we show that the Biellmann-Leidenfrost spin is initiated by an asymmetric vapour flow acting on a petal of a star-shaped drop. This spinning motion is sustained and further accelerated due to star oscillations under double resonance conditions. We find that this phenomenon is robust across a wide range of drop sizes and cover plate shapes. Finally, we demonstrate that with a continuous supply of water, the spin can be precisely controlled and maintained indefinitely. This discovery challenges conventional understanding in two crucial aspects: first, it demonstrates that sustained motion can emerge in completely symmetric Leidenfrost systems; second, it reveals a previously unrecognized coupling between confinement, external disturbance, and the intrinsic properties such as resonant excitation of the drop itself. These findings open new possibilities for controlled fluid manipulation in high-temperature environments while providing fresh insights into non-equilibrium hydrodynamic systems. To confine the levitation of the Leidenfrost drop, we placed a copper plate (~0.21 g) onto a water drop (initial volume of ~350 µL, dyed red to aid visualisation), which was on a hot substrate (500 ℃) as shown in Supplementary Movie S1. The water drop shows a high-speed spin by adding water of room temperature. To study this high-speed spinning phenomenon, a bottom hole (diameter of 5.0 mm; depth of 0.3 mm) was fabricated on an aluminium substrate to restrict the horizontal movements of the Leidenfrost drop (Fig. 1a, b). Fig. 1c shows the evaporation of a 200 µL water drop on a 500 ℃ hot substrate, displaying a conventional Leidenfrost effect and it took 105 s for the drop to fully evaporate (Supplementary Movie S2). However, when a cover plate (coloured with red, yellow and blue to aid visualisation) was applied on the top of the 200 µL water drop, it performed a high-speed spin with a maximum angular velocity ( ω max ) of ~835 r/min, on the 500 ℃ substrate, i.e. the Biellmann-Leidenfrost spin (Fig. 1d and Supplementary Movie S2). Under the same condition, it took only 59 s for the Biellmann-Leidenfrost drop to evaporate, indicating that this spin significantly favours the evaporation process of a Leidenfrost drop. To study the trace of the Biellmann-Leidenfrost drop, we monitored the distribution of its mass centre during evaporation (Fig. 1e). At the initial stage, there was a scattered distribution of the mass centre, indicating that the Biellmann-Leidenfrost drop vibrates significantly within the confinement of the bottom hole. The spinning motion gradually stabilized as the increase of the angular velocity to its maximum at ~40.1 s. From 40.1 s to 54.3 s, the mass centre became scattered again and the angular velocity deceased until the water drop fully evaporated at 59 s. To determine if there is any contact between the spinning drop and the substrate, we used a circular needle to restrict the position of the spinning Biellmann-Leidenfrost drop on the plateau, and a stable air cushion was observed with a thickness of ~100 μm 25,26 , indicating that there is no direct contact between the spinning Biellmann-Leidenfrost drop and the substrate (Fig. 1f and Supplementary Movie S3). In contrast, no spinning was observed for the drop without a cover plate 14 . The spinning behaviour of the Biellmann-Leidenfrost drop is conceptually different from numerous previous studies on controlling a Leidenfrost drop through morphology manipulation of the substrate 8,16,23,24,27 , because the substrate morphology has negligible influence on the Biellmann-Leidenfrost phenomenon. Fig. 1g and Fig. S1 shows a super depth-of-field image and scanning electron microscopy (SEM) images of the bottom hole. The depth of the groove structures was ~0.16 μm, which is significantly smaller than the vapour layer with a thickness of ~100 μm. Therefore, the impact of the groove structures on the drop spin can be ignored. To further understand the influence of the surface structures of the bottom hole on the Biellmann-Leidenfrost spin, we fabricated three bottom holes with the same parameters, i.e., diameter of 5 mm and depth of 0.3 mm, and counted the number of spins in each direction, either clockwise or anticlockwise. We performed 50 experiments using each bottom hole as shown in Fig. S2, and we found that the direction of spin was random, with no singularity in each direction. Although there was a tendency for a preferential spin direction within each bottom hole, the surface structure of the bottom hole is not a decisive factor that influences the spin direction because the drop spun in both clockwise and anticlockwise directions. This is fundamentally different from the previous research on the Leidenfrost effect, where the morphology of the substrate typically dictates drop behaviour 8,16,23,24,27 . To study the key factor that influences the direction of the Biellmann-Leidenfrost spin, we used a needle to inject air in the Biellmann-Leidenfrost drop, in clockwise and anticlockwise directions, respectively; and repeated this process for 50 times in each direction, to initiate the spin (Fig. S3 and Supplementary Movie S4). A glass cover plate was used to aid the visualisation of this experiment. Remarkably, the spin direction of the drop 100% follows the direction of the injected bubbles, indicating that the direction of the Biellmann-Leidenfrost spin is decided by the direction of the initial driving force. Although the direction of the initial driving force can be well controlled using injected bubbles, it remains random under the influence of the surface structures of the bottom hole. To quantify the spin velocity, we utilized an aluminium foil cover plate onto which a paper sheet was stuck. The top surface of the paper was marked to aid in velocity measurements. Additionally, we placed a polystyrene sphere in the drop to observe if there is any slip between the drop and the cover plate, and found that under the optimal condition of the spin stability, there is no displacement between the sphere and the marker during drop spinning (Supplementary Movie S5), indicating a non-slip condition between the drop and the cover plate. Therefore, we measure the spin velocity of a Biellmann-Leidenfrost drop by taking the spin velocity of the cover plate through detecting the marker, details on reading the angular velocity of the spinning drop are in Methods . Moreover, wettability of the cover plate is a key factor that enables the Biellmann-Leidenfrost spin. The wettability of the paper and aluminium layers was manipulated to test the stability of the spin (Fig. S4). When superhydrophobic treatment was applied to the upper paper layer with a water contact angle of 158°±1.2°, and the bottom aluminium layer was untreated with a water contact angle of 89°±2.6°, the spin achieved the best stability. Furthermore, the Biellmann-Leidenfrost drop spin can also be achieved by other shapes of cover plates such as triangles, crosses, circles, rectangles and squares (Fig. S5). To facilitate the visualisation and characterisation of the Biellmann-Leidenfrost phenomenon, we used circular cover plates throughout this paper unless otherwise specified. We now explain the underlying physics behind the spectacular spinning behaviours of the drop. In the literature, numerous studies on the Leidenfrost phenomenon were focused on unrestricted water drops 14,28-31 , where vertical vibrations of the vapour film beneath the Leidenfrost drop trigger Faraday waves 32-34 . In contrast, we found that the restriction imposed by the cover plate on the top of the drop is the key factor enabling the high-speed spinning motion of the Biellmann-Leidenfrost drop by restricting the Faraday waves (Fig. 1h). When both the equatorial and polar hemiperimeters of the drop are integer multiples of their corresponding wavelengths, the drop satisfies the double resonance condition and acts as a resonant cavity, leading to the formation of a classic Leidenfrost star 28,30 . However, in the Biellmann-Leidenfrost phenomenon, the Faraday wave at the top of the drop is suppressed by the cover plate, resulting in an energy transfer from the Faraday wave to other forms of kinetic energy, including horizontal translation and spin. Since the levitation is restricted by gravity and horizontal translation is confined by the bottom hole, the energy from the restricted Faraday wave was converted to the kinetic energy of spinning of the Leidenfrost drop due to the vertical restriction of the cover plate (see Supplementary Note 3 for analysis). Faraday waves are always present, which triggers the spin when the drop is placed on a hot surface. Fig. 2a and Supplementary Movie S6 illustrate the time dependence of the angular velocity ω throughout the lifespan of a spinning Biellmann-Leidenfrost drop. Upon depositing the drop on the substrate and covering it with a plate, a vigorous fluctuation was observed and ω stabilized at a characteristic angular velocity ω 0 (150 r/min). Subsequently, the drop underwent a significant acceleration process, reaching a maximum spinning velocity ω max (720 r/min) after ~20 s. The drop then experienced a sudden deceleration, coming to a halt. The initial fluctuation stage could be viewed as the process through which the drop transitions from a static to a spinning state. Although the continuous input of energy from the Faraday wave may sustain the spin of the drops, it does not explain the sudden appearance of a significant acceleration stage. Our findings suggest that, the star oscillation emerges almost simultaneously with the acceleration stage (Fig. S6). Fig. 2b, c shows an exemplary image and an illustration of a drop with a cover plate, while Fig 2d, e shows drops without a cover plate. In a sense, the star oscillation breaks the symmetry of round drops. For a spinning drop (Fig. 2c), the reaction forces of the vapour flow exerted to a petal is asymmetric due to environmental disturbances when drops have a star shape, unlike the symmetric reaction forces experienced by round drops. This asymmetry provides the driving torque accounting for the drop spin. Fig. 2c, e provides comparisons with and without the cover plate, respectively. Ultimately, as the drop shrank and the plate-water-air three-phase contact line pinned, the star-oscillations disappeared, the drop dramatically lost momentum and halted its spinning due to the dominant drag torque. These observations indicate that the three stages of behaviour correspond to three distinct mechanisms, for which we developed a mathematical model for clarification below. Fig. 2f shows the origin of the driving torque during the initial stage, detailed force analysis can be found in Supplementary Note 4 . Fig. 2g illustrates the results of the temporal evolution of the angular velocity of the drop under a cover plate with a radius R (2 mm ≤ R ≤ 5 mm) during evaporation. The results indicate that within this range of R , a smaller size of the cover plate corresponds to a higher maximum angular velocity that a Biellmann-Leidenfrost drop can achieve. , we explore the underlying physics of the drop throughout the spinning process. In the initial stage, a vigorous fluctuation is observed, and we attribute the driving torque to the deviation of the vapour flow (between the drop and the substrate) from the radial direction. The driving torque can be derived by integrating the shear force of the vapour over the entire contact area, resulting in T dri ~ η v U || * r 3 / δ (see Supplementary Note 4 ). Meanwhile, the drop must overcome the drag torque resulting from the liquid viscosity to transition from a static state to a spinning state, yielding T drag ~ η w r 4 ω 0 / h . Here, η v and η w represent the viscosity of vapour and water, respectively. The variables r and h represent the maximum radius and the height of the spinning drop with a characteristic angular velocity ω 0 in this stage. U || * = φ U || represent the velocity of the vapour flow deviated from the radius direction U || , with φ being a coefficient estimated as φ = tan 1° ≈ 0.02. This also indicates that even a slight deviation of the vapour flow could trigger a significant spinning of the drop. Moreover, U || = [( k Δ T ρ w gh )/(6 ρ v L η v )] 1/2 and the vapour film thickness δ = [3 k Δ T η v /(2 L ρ v ρ w gh )] 1/4 r 1/2 are derived based on the classical theory 25 . Here, k , L and g represent the vapour thermal conductivity, latent heat of water, and gravitational acceleration, respectively. Additionally, ρ v and ρ w represent the mass densities of vapour and water, respectively. The temperature difference between the substrate T s and water T w is defined as Δ T = T s – T w . A combination of T dri and T drag leads to ω 0 ~ [ k Δ T η v /( L ρ v )]) 1/4 ( ρ w gh ) 3/4 η w –1 hr –3/2 . At this point, we consider the value of r when the first stage ends and denoted it as r 0 , which is slightly larger than R . Subsequently, the drop begins to accelerate with a smoother spin while evaporating more rapidly than a typical Leidenfrost drop, indicating a significantly stronger vapour release. Due to the disturbance, the vapour flow evaporated from the drop exhibits an asymmetric behaviour (Fig. 2c). Base on the conservation of momentum, we derive the driving torque exerted on the petals during this stage, T dri = d L m /d t = (Δ M /Δ t ) r 2 ω ~ ρ v δ U || r 3 ω , with L m being angular momentum, and Δ M being the decrease in drop mass over a time span Δ t . In this scenario, the formation of an air boundary layer on the cover plate contributes a dominant torque to resulting from the viscous force of the air on the top of the cover plate, and we obtain T drag ~ ( η a ρ a ) 1/2 r 4 ω 3/2 , with η a and ρ a representing the dynamic viscosity and mass density of air, respectively. As a consequence, we formulate the kinetic equation of the spinning drop considering the drop with mass M (including the mass of the cover plate), Iα = T dri – T drag , with I = Mr 2 /2 and α being the moment of inertia of the spinning drop and the angular acceleration, respectively. Finally, as the drop radius r approaches R , star-like oscillations are significantly dampened due to the pinning of the three-phase contact line, resulting a notable decrease in driving torque. Furthermore, a noticeable oscillation of the entire drop re-emerges, leading us to attribute the drag torque to the viscous force within the vapour layer between the drop and the substrate. As a result, we derive T drag = η v r 4 ω / δ , and the corresponding dynamic equation becomes Iα = – T drag . Fig. 3a shows comparisons between our experimental and theoretical results for the relations ω 0 vs. r 0 and ω max vs. R . In the former, the theoretical curve for the relation between ω 0 and r 0 are derived from the above analyses, while in the latter, the theoretical predictions of ω max are numerical results based on the dynamic equation Iα = T dri – T drag over a duration of 20 s. Moreover, the comparisons between the experimental and theoretical results of ω max and T s are shown in Fig. 3b. All the experimental results are based on direct measurements from experiments with errors. When T s is sufficiently high, Fig. 3b shows that ω max no longer increases with T s , a trend similar to that observed in conventional Leidenfrost drops transported on asymmetric ratchet 35,36 and microstructured 37 surfaces. This phenomenon can be attributed to the thickening of the vapour film beneath the drop, which suppresses asymmetric environmental disturbances from the substrate, leading to increased symmetry in the system and a weakened driving force. To understand the influence of the mass of the cover plate m p on ω max , we added layers of aluminum foil to adjust m p . Fig. 3c shows the relation between ω max and m p for the cover plates with radii of R = 3.0 mm, 4.0 mm and 5.0 mm, respectively. In this context, ω max is derived by considering the dynamic equation of the drop, but with m p updated (see Supplementary Note 4 ). The theoretical results in Fig. 3a, 3b, and 3c agree well with the experimental data, although ω max exhibits fluctuations (error bars). These fluctuations arise due to the uncertainty of the resonance state and other random influences caused by the violent shakes, e.g., the variation of the geometrical centre (Fig. S9, Supplementary Note 5 ), even when the experiments are repeated under identical conditions. Throughout the entire spinning process, the shape of the drop evolves due to evaporation. Fig. 3d and Supplementary Note 6 demonstrate the relation between the drop height h and radius r . The drop height h and radius r are defined as follows: in the side view of the drop, we approximate the maximum width of the drop as its diameter (2 r ), and the maximum height of the drop as its height ( h ). The red dashed curve represents the theoretical solution for h vs. r of a two-dimensional static drop obtained from the Young-Laplace equation 38,39 , which serves as the upper bound for the height of the Biellmann-Leidenfrost drop. The constraining effect of the upper cover plate is more pronounced as r decreases. The drop height h and drop radius r did not decrease in the same manner over time t , particularly when the drop radius r was similar to the cover plate radius R . The three-phase contact line would pin at the edge of the cover plate due to the hydrophilicity of its bottom side, impeding the reduction of the drop radius. Consequently, over a relatively long period, the drop radius r remained nearly constant, facilitating the generation and maintenance of the resonance conditions. Under these circumstances, the drop would persist until it reached the appropriate size to satisfy the resonance conditions 25 , thereby enhancing the Biellmann-Leidenfrost spin (see Supplementary Note 7 ). Fig. 3e illustrates typical Biellmann-Leidenfrost drop shapes at various stages. When the drop radius satisfies r < R (the vertical lines in Fig. 3d) due to the pinning of the solid-liquid-gas three-phase contact line, the spin abruptly halts. The Biellmann-Leidenfrost phenomenon may find applications in thermal engineering 3,40,41 . For example, Fig. 4a shows the persistence of vision effect of a spinning Biellmann-Leidenfrost drop under a cover plate of 3 mm in radius at a substrate of 500 ℃. There are eight motions of the Biellmann’s spin in figure skating on the cover plate, forming a series of actions due to the drop spin at an angular velocity of 225 r/min (Supplementary Movie S7). The Biellmann-Leidenfrost drop provided a stable display at a high temperature, and may be used for in-situ monitoring the temperature of a hot object by detecting the spin velocity. To support a sustainable Biellmann-Leidenfrost drop spin, we explored the conditions that enable this phenomenon. The acceleration of Biellmann-Leidenfrost spin is closely related to the star oscillation under double resonance conditions 28 . Fig. 4b shows the analyses of the resonance mode n and m of spinning Leidenfrost drops. The solid curves represent the equatorial resonance mode n = π r/λ , where π r denotes the equatorial hemiperimeter of the drop and λ ≈ [2π σ LV /( ρ w f 3 )] 1/3 denotes the forcing wavelength caused by Faraday instability 32-34 , with σ LV and f representing the liquid-vapour interfacial tension and the frequency of the capillary wave, respectively. Additionally, the dotted and dashed lines represent the boundaries of the polar resonance mode m = (2 r + h ) /λ , where (2 r + h ) denotes the polar hemiperimeter of the drop. Specifically, in the upper panel of Fig. 4b, we consider the condition of subharmonic resonance, i.e., f = f v /2, with f v being the vibration frequency of the vapour film beneath the drop. The dotted and dashed blue curves represent the lower and upper bounds of h in the mode m . The red areas satisfy the subharmonic resonance conditions, which is the most common situation in the Faraday instability. Furthermore, employing a similar approach, we also illustrate the condition of harmonic resonance (green areas) in the lower panel of Fig. 4b, where f = f v /2 is satisfied. The dotted and dashed green curves represent the lower and upper bounds of h in the mode m (more details in Supplementary Notes 7-9 ). Combining the upper and lower panels of Fig. 4b, it becomes evident that all areas within r = 2-6 mm satisfy the resonance conditions, indicating that a Biellmann-Leidenfrost drop spin could be achieved by confining the drop radius within this range. To facilitate the practical applications (e.g., in-situ temperature monitoring), water could be continuously replenished to sustain the Biellmann-Leidenfrost drop by dynamically meeting the double resonance conditions. Previous research and our work suggest that there is not a systematic match between modes n and m , and the empirical condition for observing a star mode satisfies Δ r / r ~ 10% 28 . Due to evaporation, the drop radius shrank at a rate of v = |d r /d t | ≈ 30 μm/s; to preserve its original resonance conditions, additional water should be supplemented in a time span of Δ r / v = (Δ r / r )( r / v ), which is in a few seconds. During the evaporation, the evaporation rate can be calculated by ∂ M /∂ t = − k Δ TA /( Lδ ), where A = πr 2 is the contact area between the drop and the hot substrate 42 . Taking typical values for the different parameters ( k ≈ 0.05 W/(m⸱K), Δ T ≈ 400 K, L ≈ 2.26 ´ 10 6 J/kg, r ≈ 2 mm and δ ≈ 100 μm), we find that ∂ M /∂ t is on the order of 1.0 mg/s. 25 To maintain a balanced evaporation rate, we added small droplets with a radius of ~ 0.9 mm for every 3 s, to replenish the evaporating drop. This allowed for a continuous Biellmann-Leidenfrost spin over a significantly extended period, with an angular velocity of ~800-1200 r/min for over 350 s (Fig. 4c and Supplementary Movie S8). In this way, we could in-situ monitor the condition of a hot surface. In summary, we discover a new phenomenon of a water drop with a Biellmann-spin behaviour, by confining the vertical movement of a Leidenfrost drop. This finding challenges the prevailing paradigm that spatially asymmetric textures are required for liquid control. Through both experimental and theoretical analysis, we found that the driving torque of the Biellmann-Leidenfrost spin is initiated by an asymmetric vapour flow acting on a petal of a star-shaped drop, and is sustained and accelerated due to star oscillation under double resonance conditions. The selection of the spin is influenced by initial perturbations, with each petal functioning like a propeller, generating a propulsion force through dynamic symmetry breaking. An intriguing question that arises is how other types of Biellmann-spin behaviour manifest work in broader systems, such as on curved solid surface, on liquid baths, or on an air cushion blown from below. Our findings significantly enhance the fundamental understanding of self-propulsion of liquids and the dynamics of liquid-solid interfaces, with promise far-reaching implications for fluid dynamics, surface science, spontaneous symmetry breaking in dynamical systems, as well as for broad applications in liquid metal, energy conversion and harvesting, and heat transfer manipulation. Methods Fabrication and characterisation of the bottom hole The bottom hole that was used to confine the horizontal movement of the Biellmann-Leidenfrost drop was machined with a diameter of 5 mm and a depth of 0.3 mm using a 1500 W water-cooled CNC engraving machine (YD3040, Shenzhen Yidiao Technology Co., Ltd, China). The formation of the groove structures in the bottom hole was due to the nature of the machining technique and was not intentionally designed to guide the direction of drop spin. The substrate was heated to 500°C for the experiments throughout this paper unless otherwise specified. An optical drop analyser (JC2000D4F, Zhongchen, China) was used to observe the vapour layer generated by the Biellmann-Leidenfrost drops on the surface of the hole. The macroscopic morphology of the hole was observed using an ultra-depth 3D microscope (VHX-6000, Keenes, Japan). Scanning electron microscopy (SEM, SUPRA 55 SAPPHIRE, Germany) was used to examine the microscopic morphology of the bottom of the hole. Fabrication of the cover plate The cover plate consisted of aluminium foil with a paper sheet on the upper surface. The thickness of the cover plate was 0.15 mm and its density was 0.24 g/cm 3 . The superhydrophobic treatment on the upper cover plate was achieved using a commercially available superhydrophobic coating (Never Wet Multi Purpose Kit, Rust Oleum 274232, USA). The method of reading the angular velocity of the spinning drop As illustrated in (a), by employing a high-speed colour camera (100 fps), we captured the entire process of the drop from the top view. To achieve better recognition of the cover plate boundary, we added a small amount of red ink into the drops without affecting their physical properties. Specifically, we first read the boundary of the cover plate, and then measured the angular velocity of the drop by marking a pointer on the cover plate. As shown in Fig. S4a, the cover plate remained synchronized with the spinning drop, enabling us to calculate the angular velocity frame-by-frame by employing a custom-made MATLAB code. The average values of the angular velocity are presented in (b) and (c), obtained by averaging the angular velocity in 0.01 s and 0.1 s, respectively. Upon examination, it is evident that by utilizing a larger time interval of 0.1 s, the error associated with this method can be minimized. (c) supports the notion that the outcome remains highly credible. In this regard, when plotting the relation between ω and t (i.e., Fig. 2 f) or determining the maximum ω (i.e., Fig. 3 a, b, c), we employed a time interval of 0.1 s. Nevertheless, for the purpose of better elucidation, the time interval used in Fig. 2 a has been adjusted to 1.0 s. Declarations Acknowledgements This work was partially supported by the National Natural Science Foundation of China (NSFC, Grant No. 52275420, U23A20632, 12172189), the National Key R&D Program of China (2002YFB3403304). Y. Lu acknowledges the Royal Society Research Grant (RGS∖R1∖201071) for financial support. We thank Professor Julia Yeomens in the Department of Physics, University of Oxford, for constructive advice on building the mathematical model. Author contributions S.H., Y.L. and C.L. conceptualised this work, and K.F., Y.L. and C.L. supervised this work. S.H., M.L., Y.L designed the experiments. M.L., Z.W. performed the experiments. C.L., E.L. developed the mathematical model and performed theoretical analyses. S.H., Y.L., C.L., M.L., E.L. drafted the initial manuscript and all authors discussed the results and commented on the paper. S.H., M.L., E.L. contributed equally. Competing interests The authors declare no competing interests. References Leidenfrost, J. G. De aquae communis nonnullis qualitatibus tractatus . (Ovenius, 1756). Linke, H., Alemán, B. J., Melling, L. D., Taormina, M. J., Francis, M. J., Dow-Hygelund, C. C., Narayanan, V., Taylor, R. P. & Stout, A. Self-propelled Leidenfrost droplets. Physical Review Letters 96 , 154502 (2006). Wells, G. 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Nature Physics 12 , 606-612 (2016). Waitukaitis, S. R., Zuiderwijk, A., Souslov, A., Coulais, C. & Van Hecke, M. Coupling the Leidenfrost effect and elastic deformations to power sustained bouncing. Nature Physics 13 , 1095-1099 (2017). Waitukaitis, S., Harth, K. & Van Hecke, M. From bouncing to floating: the Leidenfrost effect with hydrogel spheres. Physical Review Letters 121 , 048001 (2018). Gauthier, A., van Der Meer, D., Snoeijer, J. H. & Lajoinie, G. Capillary orbits. Nature Communications 10 , 3947 (2019). Liu, D., Nguyen, T.-B., Nguyen, N.-V. & Tran, T. Sailing droplets in superheated granular layer. Physical Review Letters 125 , 168002 (2020). Graeber, G., Regulagadda, K., Hodel, P., Küttel, C., Landolf, D., Schutzius, T. M. & Poulikakos, D. Leidenfrost droplet trampolining. Nature Communications 12 , 1727 (2021). Bouillant, A., Mouterde, T., Bourrianne, P., Lagarde, A., Clanet, C. & Quéré, D. Leidenfrost wheels. Nature Physics 14 , 1188-1192 (2018). Dupeux, G., Le Merrer, M., Lagubeau, G., Clanet, C., Hardt, S. & Quéré, D. Viscous mechanism for Leidenfrost propulsion on a ratchet. Europhysics Letters 96 , 58001 (2011). Liu, C., Lu, C., Yuan, Z., Lv, C. & Liu, Y. Steerable drops on heated concentric microgroove arrays. Nature Communications 13 , 3141 (2022). Soto, D., Lagubeau, G., Clanet, C. & Quéré, D. Surfing on a herringbone. Physical Review Fluids 1 , 013902 (2016). Dodd, L. E., Agrawal, P., Parnell, M. T., Geraldi, N. R., Xu, B. B., Wells, G. G., Stuart-Cole, S., Newton, M. I., McHale, G. & Wood, D. Low-friction self-centering droplet propulsion and transport using a leidenfrost herringbone-ratchet structure. Physical Review Applied 11 , 034063 (2019). Bouillant, A., Lafoux, B., Clanet, C. & Quéré, D. Thermophobic leidenfrost. Soft Matter 17 , 8805-8809 (2021). Brandão, R. & Schnitzer, O. Spontaneous dynamics of two-dimensional Leidenfrost wheels. Physical Review Fluids 5 , 091601 (2020). Gauthier, A., Diddens, C., Proville, R., Lohse, D. & van Der Meer, D. Self-propulsion of inverse Leidenfrost drops on a cryogenic bath. Proceedings of the National Academy of Sciences 116 , 1174-1179 (2019). Sobac, B., Maquet, L., Duchesne, A., Machrafi, H., Rednikov, A., Dauby, P., Colinet, P. & Dorbolo, S. Self-induced flows enhance the levitation of Leidenfrost drops on liquid baths. Physical Review Fluids 5 , 062701 (2020). Yang, J., Li, Y., Wang, D., Fan, Y., Ma, Y., Yu, F., Guo, J., Chen, L., Wang, Z. & Deng, X. A standing Leidenfrost drop with Sufi whirling. Proceedings of the National Academy of Sciences 120 , e2305567120 (2023). Li, A., Li, H., Lyu, S., Zhao, Z., Xue, L., Li, Z., Li, K., Li, M., Sun, C. & Song, Y. Tailoring vapor film beneath a Leidenfrost drop. Nature Communications 14 , 2646 (2023). Biance, A.-L., Clanet, C. & Quéré, D. Leidenfrost drops. Physics of Fluids 15 , 1632-1637 (2003). Burton, J. C., Sharpe, A. L., Van Der Veen, R. C. A., Franco, A. & Nagel, S. R. Geometry of the vapor layer under a Leidenfrost drop. Physical Review Letters 109 , 074301 (2012). Jiang, M., Wang, Y., Liu, F., Du, H., Li, Y., Zhang, H., To, S., Wang, S., Pan, C., Yu, J., Quéré, D. & Wang, Z. Inhibiting the Leidenfrost effect above 1,000 °C for sustained thermal cooling. Nature 601 , 568-572 (2022). Bouillant, A., Cohen, C., Clanet, C. & Quéré, D. Self-excitation of Leidenfrost drops and consequences on their stability. Proceedings of the National Academy of Sciences 118 , e2021691118 (2021). Yim, E., Bouillant, A., Quéré, D. & Gallaire, F. Leidenfrost flows: instabilities and symmetry breakings. Flow 2 , E18 (2022). Brunet, P. & Snoeijer, J. H. Star-drops formed by periodic excitation and on an air cushion–a short review. The European Physical Journal Special Topics 192 , 207-226 (2011). Ma, X., Liétor-Santos, J.-J. & Burton, J. C. Star-shaped oscillations of Leidenfrost drops. Physical Review Fluids 2 , 031602 (2017). Faraday, M. On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Proceedings of the Royal Society of London Series I 3 , 49-51 (1831). Douady, S. Experimental study of the Faraday instability. Journal of Fluid Mechanics 221 , 383-409 (1990). Kumar, K. & Tuckerman, L. S. Parametric instability of the interface between two fluids. Journal of Fluid Mechanics 279 , 49-68 (1994). Ok, J. T., Lopez-Ona, E., Nikitopoulos, D. E., Wong, H. & Park, S. Propulsion of droplets on micro-and sub-micron ratchet surfaces in the Leidenfrost temperature regime. Microfluidics and Nanofluidics 10 , 1045-1054 (2011). Marin, A. G., Arnaldo del Cerro, D., Römer, G. R. B. E., Pathiraj, B. & Lohse, D. Capillary droplets on Leidenfrost micro-ratchets. Physics of Fluids 24 (2012). Kruse, C., Somanas, I., Anderson, T., Wilson, C., Zuhlke, C., Alexander, D., Gogos, G. & Ndao, S. Self-propelled droplets on heated surfaces with angled self-assembled micro/nanostructures. Microfluidics and Nanofluidics 18 , 1417-1424 (2015). Lv, C. & Shi, S. Wetting states of two-dimensional drops under gravity. Physical Review E 98 , 042802 (2018). Landau, L. D. & Lifshitz, E. M. Fluid Mechanics, 2nd ed. , 242–243 (Pergamon Press, Oxford, 1987). Agrawal, P., Wells, G. G., Ledesma-Aguilar, R., McHale, G., Buchoux, A., Stokes, A. & Sefiane, K. Leidenfrost heat engine: sustained rotation of levitating rotors on turbine-inspired substrates. Applied Energy 240 , 399-408 (2019). Agrawal, P., Wells, G. G., Ledesma-Aguilar, R., McHale, G. & Sefiane, K. Beyond Leidenfrost levitation: a thin-film boiling engine for controlled power generation. Applied Energy 287 , 116556 (2021). Bird, R. B., Stewart, W. E. & Lightfoot, E. N. Transport Phenomena, 2nd Editon . (John Wiley & Sons, Inc., 2007). Additional Declarations There is NO Competing Interest. Supplementary Files SINC1.docx Supplementary Information Video1.mp4 Supplementary Video 1 Video2.mp4 Supplementary Video 2 Video3.mp4 Supplementary Video 3 Video4.mp4 Supplementary Video 4 Video5.mp4 Supplementary Video 5 Video6.mp4 Supplementary Video 6 Video7.mp4 Supplementary Video 7 Video8.mp4 Supplementary Video 8 ExtendedDataFig.docx 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-6246861","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":477368312,"identity":"b4e5c0d2-3f0d-457a-9083-786b296f6ac2","order_by":0,"name":"Yao Lu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwklEQVRIiWNgGAWjYLCCBww2QJK5AcyRIEpLAkMakGQkTcthErQYHD98gCGx7bzs2hmJDQw/ahgSZzYQ0nImLQGo5bbxthuJDYw9xxgSZxO05UCOAUhLIkgLA28DQ+I8glrOvwFpOQfWwviXKC03wLYcAGthBtlC0GGSN54lHEg4l2y87czDhsMyxySMCXqf73zywQcfyuxktx1PPvjwTY2N7IwDBLQoABWA1IAj5QBRESkPdQYjIeeMglEwCkbBCAYAqatJFPP+W64AAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0001-9566-4122","institution":"Queen Mary University of London","correspondingAuthor":true,"prefix":"","firstName":"Yao","middleName":"","lastName":"Lu","suffix":""},{"id":477368313,"identity":"9be36320-c595-4806-ac81-c399ddf7939b","order_by":1,"name":"Shuai Huang","email":"","orcid":"","institution":"College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, P. R. China","correspondingAuthor":false,"prefix":"","firstName":"Shuai","middleName":"","lastName":"Huang","suffix":""},{"id":477368314,"identity":"94244ef9-fcc2-49be-aac7-55cd31187cdf","order_by":2,"name":"Minghao Li","email":"","orcid":"","institution":"College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, P. R. China","correspondingAuthor":false,"prefix":"","firstName":"Minghao","middleName":"","lastName":"Li","suffix":""},{"id":477368315,"identity":"ed5aa07f-bae3-4eeb-bf2d-48aa3f62da31","order_by":3,"name":"Enze Liu","email":"","orcid":"","institution":"Department of Engineering Mechanics and Center for Nano and Micro Mechanics, AML, Tsinghua University, Beijing, 100084, P. R. China","correspondingAuthor":false,"prefix":"","firstName":"Enze","middleName":"","lastName":"Liu","suffix":""},{"id":477368316,"identity":"83318ca2-24e7-49c8-8aa5-2535719460a6","order_by":4,"name":"Kai Feng","email":"","orcid":"","institution":"College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, P. R. China","correspondingAuthor":false,"prefix":"","firstName":"Kai","middleName":"","lastName":"Feng","suffix":""},{"id":477368317,"identity":"9406d8fe-aa2e-4ea3-a933-d52cc071b4bd","order_by":5,"name":"Zeming Wang","email":"","orcid":"","institution":"College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, P. R. China","correspondingAuthor":false,"prefix":"","firstName":"Zeming","middleName":"","lastName":"Wang","suffix":""},{"id":477368318,"identity":"4ed55178-2e83-416f-9d38-2372e9dcb464","order_by":6,"name":"Cunjing Lv","email":"","orcid":"https://orcid.org/0000-0001-8016-6462","institution":"Department of Engineering Mechanics and Center for Nano and Micro Mechanics, AML, Tsinghua University, Beijing, 100084, P. R. China","correspondingAuthor":false,"prefix":"","firstName":"Cunjing","middleName":"","lastName":"Lv","suffix":""}],"badges":[],"createdAt":"2025-03-17 17:45:36","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6246861/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6246861/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":85756499,"identity":"3f8e3491-c9b0-4e49-bd64-892658537757","added_by":"auto","created_at":"2025-07-01 10:49:47","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":233015,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eBiellmann-Leidenfrost drop spin.\u003c/strong\u003e Schematics of (a) a Leidenfrost drop and (b) a spinning Biellmann-Leidenfrost drop. Time lapse photographs that compare the evaporation of (c) a traditional Leidenfrost drop and (d) a spinning Biellmann-Leidenfrost drop. (e) Top view of the contour centre of the Biellmann-Leidenfrost drop; each stage contains 200 scatter positions. Bar = 10 mm. (f) Side view images were presented to observe the air cushion of a Leidenfrost drop, and a spinning Biellmann-Leidenfrost drop. (g) Surface morphology of the bottom hole: (i) super depth-of-field image and (ii, iii) SEM images of the marked area. (h) Schematics show that the Faraday waves that are typically observed on a Leidenfrost drop are restricted by the cover plate in a vertical direction on a Biellmann- Leidenfrost drop.\u003c/p\u003e","description":"","filename":"image1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6246861/v1/e42a920bff29820cd216d9bd.jpg"},{"id":85756500,"identity":"cddf2b25-9859-4b72-a086-acf5c44f1ebf","added_by":"auto","created_at":"2025-07-01 10:49:47","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1408140,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eAnalysis of the Biellmann-Leidenfrost phenomenon.\u003c/strong\u003e (a) Time evolution of the angular velocity of spinning \u003cem\u003eω\u003c/em\u003e throughout the entire spinning process of a Biellmann-Leidenfrost drop (with a cover plate radius \u003cem\u003eR\u003c/em\u003e = 3 mm). Each point represents the average angular velocity of the drop in 0.1 s. The motion is categorized into three distinct stages: fluctuation (\u003cem\u003eω\u003c/em\u003efluctuates within a narrow range, accompanied by violent shaking of the drop), acceleration (continuous increase in spin with decreasing intensity of drop shaking), and breakdown (deceleration of spin). The inserts are optical images of drops covered by plates in each distinct stage. (b) Optical image and (c) illustration of the significant star oscillation under a cover plate. (d) Optical image and (e) illustration of the significant star oscillation without a cover plate. The arrows in (c) and (e) represent the vapour flow. (f) Schematic illustrating the origin of the driving torque during the initial stage (0 s \u0026lt; \u003cem\u003et\u003c/em\u003e \u0026lt; 20 s). Left: A schematic showing the vapour flows in the radial direction (red arrow) and in the circumferential direction (blue arrow). Right: An enlarged view highlighting the local details of the vapour flow directions, where \u003cem\u003eφ\u003c/em\u003e represents the angle between the radial direction (red arrow) and the resultant flow direction (black arrow). (g) Angular velocity of spinning \u003cem\u003eω\u003c/em\u003e varies with \u003cem\u003et\u003c/em\u003eduring the entire spinning process of drops with various plate radii (i.e., \u003cem\u003eR\u003c/em\u003e= 2, 2.5, 3, 3.5, 4, 4.5, and 5 mm). Each point represents the average angular velocity of the drop over 0.1 s).\u003c/p\u003e","description":"","filename":"image2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6246861/v1/9f123f5eb58ab521042ccc72.jpeg"},{"id":85756503,"identity":"5d4161a1-bf97-4c57-b6ef-a382ce7744bb","added_by":"auto","created_at":"2025-07-01 10:49:47","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":242921,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eAnalysis of influential factors of the Biellmann-Leidenfrost phenomenon.\u003c/strong\u003e (a) Relations of \u003cem\u003eω\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e vs \u003cem\u003er\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e and \u003cem\u003eω\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e vs \u003cem\u003eR\u003c/em\u003e, with the colours of the dots corresponding to (d). The curves represent the theoretical results. (b) \u003cem\u003eω\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e as a function of the temperature \u003cem\u003eT\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e of the hot plate. The red, cyan and purple curves represent the theoretical results for \u003cem\u003eR\u003c/em\u003e\u003csub\u003e \u003c/sub\u003e= 3.0, 4.0 and 5.0 mm, respectively. (c) \u003cem\u003eω\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e as a function of the mass of the cover plate\u003cem\u003e m\u003c/em\u003e\u003csub\u003ep\u003c/sub\u003e. The red, cyan and purple curves represent the theoretical results for \u003cem\u003eR\u003c/em\u003e\u003csub\u003e \u003c/sub\u003e= 3.0, 4.0 and 5.0 mm, respectively. Each dot in (b) and (c) denotes the average value of five experiments. The substrate temperature for (a) and (c) is 500 ℃. (d) Drop height \u003cem\u003eh \u003c/em\u003eas the function of the drop radius \u003cem\u003er\u003c/em\u003e throughout the entire pinning process. The pink, orange, red, green, cyan, blue and purple dots correspond to the cover plate with radii of \u003cem\u003eR\u003c/em\u003e = 2.0, 2.5, 3.0, 3.5, 4.0, 4.5 and 5.0 mm, respectively. As time progresses, the dots become lighter in colour, and the time interval between each adjacent point is 0.01s. The vertical colour lines represent the corresponding colours of the dots for \u003cem\u003eR\u003c/em\u003e ranging from 2.0 mm to 5.0 mm. The red dotted curve represents the theoretical solution for the configuration of a two-dimensional static drop obtained using the Young-Laplace equation. The black dotted curve represents the typical height \u003cem\u003eh\u003c/em\u003e of the drop when its radius \u003cem\u003er \u003c/em\u003eis close to \u003cem\u003eR\u003c/em\u003e. (e) Schematic and experimental snapshots of a drop undergoing different evaporation status, each corresponding to a different area in (d) based on the background colour. When \u003cem\u003er\u003c/em\u003e \u0026gt; \u003cem\u003eR\u003c/em\u003e, the drop shape appears similar to that without a cover plate. When \u003cem\u003er\u003c/em\u003e = \u003cem\u003eR\u003c/em\u003e (black dashed curve in (d)), the drop shape becomes similar to a cylinder. When \u003cem\u003er\u003c/em\u003e \u0026lt; \u003cem\u003eR\u003c/em\u003e, the drop shape appears similar to a bowl because the three-phase contact line above the drop is fixed on the edge of the cover plate due to the hydrophilicity of the bottom surface of the cover plate (Fig. S4).\u003c/p\u003e","description":"","filename":"image3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6246861/v1/d378ea903008fc936c4728ce.jpg"},{"id":85756505,"identity":"17da2fc9-c3ce-4083-9628-78fbe86a25a4","added_by":"auto","created_at":"2025-07-01 10:49:47","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":266593,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eContinuous Biellmann-Leidenfrost drop spin.\u003c/strong\u003e (a) Dynamic display of images on a spinning Biellmann-Leidenfrost drop. (b) Analyses of the resonance mode \u003cem\u003em\u003c/em\u003e and \u003cem\u003en\u003c/em\u003e of spinning Leidenfrost drops. (c) Sustainable Biellmann-Leidenfrost drop spin is achieved by continuous replenishment of water to meet the double resonance conditions.\u003c/p\u003e","description":"","filename":"image4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6246861/v1/49af664a1c9f339a14059180.jpg"},{"id":87996463,"identity":"5350b8d3-d975-4cb8-a8f4-d604e3918ecd","added_by":"auto","created_at":"2025-07-31 09:28:34","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2980569,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6246861/v1/badaed05-fa22-4356-9517-72402eb5fac3.pdf"},{"id":85756501,"identity":"3612acdd-6c91-453d-ae87-7fafa7c6e414","added_by":"auto","created_at":"2025-07-01 10:49:47","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":3726246,"visible":true,"origin":"","legend":"Supplementary 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8\u003c/p\u003e","description":"","filename":"Video8.mp4","url":"https://assets-eu.researchsquare.com/files/rs-6246861/v1/d6328b57b1665319d1676f84.mp4"},{"id":85757727,"identity":"fd6ad103-31c9-4e5a-a980-e3fe0d8687b6","added_by":"auto","created_at":"2025-07-01 10:57:47","extension":"docx","order_by":10,"title":"","display":"","copyAsset":false,"role":"supplement","size":119897,"visible":true,"origin":"","legend":"","description":"","filename":"ExtendedDataFig.docx","url":"https://assets-eu.researchsquare.com/files/rs-6246861/v1/0b5c0bcd31f953b459030421.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Enabling a Leidenfrost drop to perform Biellmann spin","fulltext":[{"header":"Introduction","content":"\u003cp\u003eWhen a liquid drop is placed on a substrate heated far above its boiling point, it can levitate over a cushion of its own vapour, this is a phenomenon known as the Leidenfrost effect\u003csup\u003e1\u003c/sup\u003e. Due to the absence of friction and the continuous escape of vapour from the Leidenfrost cushion, the drop exhibits remarkable mobility. At the same time, the vapour layer, with its poor heat conductivity, insulates the drop from the substrate, extending its lifetime to the order of a few minutes. These unique properties make Leidenfrost drops highly applicable in various fields, such as drop transport\u003csup\u003e2\u003c/sup\u003e, thermal engineering\u003csup\u003e3\u003c/sup\u003e, and cryopreservation\u003csup\u003e4\u003c/sup\u003e. Extending beyond liquids to solids, extensive research on the Leidenfrost effect has revealed intriguing transport behaviors and complex underlying physics\u003csup\u003e2,5-14\u003c/sup\u003e. A common approach to achieving directional motion involves exploiting the interaction between Leidenfrost drops and asymmetric substrates. This is often achieved using structured surfaces with features such as ratchets\u003csup\u003e2,6,15\u003c/sup\u003e, microtextures with geometric gradients\u003csup\u003e8\u003c/sup\u003e or curvatures\u003csup\u003e16\u003c/sup\u003e, and herringbone-like structures\u003csup\u003e17,18\u003c/sup\u003e, or by introducing temperature gradients that mimic a ratchet-like mechanism\u003csup\u003e19\u003c/sup\u003e. In these self-propelling systems, asymmetry serves as the primary driver of movement. Unidirectional self-transport is achieved by rectifying the vapour flow beneath the drop through asymmetric textures, imparting a well-defined velocity (typically around 10 cm/s). However, these asymmetric structural systems inherently limit the direction of drop motion. Moreover, directional transport of Leidenfrost drops has also been observed on flat solid surfaces due to spontaneous symmetry breaking of internal flows\u003csup\u003e14,20\u003c/sup\u003e. Furthermore, the inverse Leidenfrost effect where a liquid drop self-propels on a liquid surface such as in cryogenic baths\u003csup\u003e5,11,21,22\u003c/sup\u003e, occurs due to similar symmetry breaking within the vapour film that levitates the drop. However, these symmetry breaking effects are size-dependent, occurring only for drops within a specific size range. Beyond directional transport, Leidenfrost drops can also exhibit self-propulsion in the form of rotation. This is typically achieved by exploiting asymmetry to generate unbalanced vapour flows. For instance, a water drop that is partially adhered to a hot surface can undergo violent rotation\u003csup\u003e23\u003c/sup\u003e, but this phenomenon occurs randomly and remains difficult to control. Another approach involves designing wetting heterogeneity on the substrate to rectify vapour flow and induce drop spinning\u003csup\u003e24\u003c/sup\u003e. However, the long-term chemical stability of such substrates under high temperature remains a challenge.\u003c/p\u003e\n\u003cp\u003eIn this study, we investigate the dynamics of drops deposited on a hot substrate without any deliberate asymmetric patterns, confined by a cover plate on the top \u0026ndash; a \u0026ldquo;restricted\u0026rdquo; Leidenfrost scenario distinct from those previously studied. Contrary to the symmetry breaking induced by surface topography in conventional unrestricted Leidenfrost drops, we demonstrate that, in the absence of such topographic asymmetry, spontaneous symmetry breaking can induce rapid spinning of liquid drops, achieving velocities on the order of 1000 r/min. We term this phenomenon the \u0026ldquo;Biellmann-Leidenfrost effect\u0026rdquo;. Through both experimental and theoretical analyses, we show that the Biellmann-Leidenfrost spin is initiated by an asymmetric vapour flow acting on a petal of a star-shaped drop. This spinning motion is sustained and further accelerated due to star oscillations under double resonance conditions. We find that this phenomenon is robust across a wide range of drop sizes and cover plate shapes. Finally, we demonstrate that with a continuous supply of water, the spin can be precisely controlled and maintained indefinitely. This discovery challenges conventional understanding in two crucial aspects: first, it demonstrates that sustained motion can emerge in completely symmetric Leidenfrost systems; second, it reveals a previously unrecognized coupling between confinement, external disturbance, and the intrinsic properties such as resonant excitation of the drop itself. These findings open new possibilities for controlled fluid manipulation in high-temperature environments while providing fresh insights into non-equilibrium hydrodynamic systems.\u003c/p\u003e\n\u003cp\u003eTo confine the levitation of the Leidenfrost drop, we placed a copper plate (~0.21 g) onto a water drop (initial volume of ~350 \u0026micro;L, dyed red to aid visualisation), which was on a hot substrate (500 ℃) as shown in Supplementary Movie S1. The water drop shows a high-speed spin by adding water of room temperature. To study this high-speed spinning phenomenon, a bottom hole (diameter of 5.0 mm; depth of 0.3 mm) was fabricated on an aluminium substrate to restrict the horizontal movements of the Leidenfrost drop (Fig. 1a, b). Fig. 1c shows the evaporation of a 200 \u0026micro;L water drop on a 500 ℃ hot substrate, displaying a conventional Leidenfrost effect and it took 105 s for the drop to fully evaporate (Supplementary Movie S2). However, when a cover plate (coloured with red, yellow and blue to aid visualisation) was applied on the top of the 200 \u0026micro;L water drop, it performed a high-speed spin with a maximum angular velocity (\u003cem\u003e\u0026omega;\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e) of ~835 r/min, on the 500 ℃ substrate, i.e. the Biellmann-Leidenfrost spin (Fig. 1d and Supplementary Movie S2). Under the same condition, it took only 59 s for the Biellmann-Leidenfrost drop to evaporate, indicating that this spin significantly favours the evaporation process of a Leidenfrost drop. To study the trace of the Biellmann-Leidenfrost drop, we monitored the distribution of its mass centre during evaporation (Fig. 1e). At the initial stage, there was a scattered distribution of the mass centre, indicating that the Biellmann-Leidenfrost drop vibrates significantly within the confinement of the bottom hole. The spinning motion gradually stabilized as the increase of the angular velocity to its maximum at ~40.1 s. From 40.1 s to 54.3 s, the mass centre became scattered again and the angular velocity deceased until the water drop fully evaporated at 59 s. To determine if there is any contact between the spinning drop and the substrate, we used a circular needle to restrict the position of the spinning Biellmann-Leidenfrost drop on the plateau, and a stable air cushion was observed with a thickness of ~100 \u0026mu;m\u003csup\u003e25,26\u003c/sup\u003e, indicating that there is no direct contact between the spinning Biellmann-Leidenfrost drop and the substrate (Fig. 1f and\u0026nbsp;Supplementary Movie S3). In contrast, no spinning was observed for the drop without a cover plate\u003csup\u003e14\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eThe spinning behaviour of the Biellmann-Leidenfrost drop is conceptually different from numerous previous studies on controlling a Leidenfrost drop through morphology manipulation of the substrate\u003csup\u003e8,16,23,24,27\u003c/sup\u003e, because the substrate morphology has negligible influence on the Biellmann-Leidenfrost phenomenon. Fig. 1g and Fig. S1 shows a\u0026nbsp;super depth-of-field image and scanning electron microscopy (SEM) images of the bottom hole. The depth of the groove structures was ~0.16 \u0026mu;m, which is significantly smaller than the vapour layer with a thickness of ~100 \u0026mu;m. Therefore, the impact of the groove structures on the drop spin can be ignored.\u0026nbsp;To further understand the influence of the surface structures of the bottom hole on the Biellmann-Leidenfrost spin, we fabricated three bottom holes with the same parameters, i.e., diameter of 5 mm and depth of 0.3 mm, and counted the number of spins in each direction, either clockwise or anticlockwise. We performed 50 experiments using each bottom hole as shown in Fig. S2, and we found that the direction of spin was random, with no singularity in each direction. Although there was a tendency for a preferential spin direction within each bottom hole, the surface structure of the bottom hole is not a decisive factor that influences the spin direction because the drop spun in both clockwise and anticlockwise directions. This is fundamentally different from the previous research on the Leidenfrost effect, where the morphology of the substrate typically dictates drop behaviour\u003csup\u003e8,16,23,24,27\u003c/sup\u003e. To study the key factor that influences the direction of the Biellmann-Leidenfrost spin, we used a needle to inject air in the Biellmann-Leidenfrost drop, in clockwise and anticlockwise directions, respectively; and repeated this process for 50 times in each direction, to initiate the spin (Fig. S3 and\u0026nbsp;Supplementary Movie S4). A glass cover plate was used to aid the visualisation of this experiment. Remarkably, the spin direction of the drop 100% follows the direction of the injected bubbles, indicating that the direction of the Biellmann-Leidenfrost spin is decided by the direction of the initial driving force. Although the direction of the initial driving force can be well controlled using injected bubbles, it remains random under the influence of the surface structures of the bottom hole.\u003c/p\u003e\n\u003cp\u003eTo quantify the spin velocity, we utilized an aluminium foil cover plate onto which a paper sheet was stuck. The top surface of the paper was marked to aid in velocity measurements. Additionally, we placed a polystyrene sphere in the drop to observe if there is any slip between the drop and the cover plate, and found that under the optimal condition of the spin stability, there is no displacement between the sphere and the marker during drop spinning (Supplementary Movie S5), indicating a non-slip condition between the drop and the cover plate. Therefore, we measure the spin velocity of a Biellmann-Leidenfrost drop by taking the spin velocity of the cover plate through detecting the marker, details on reading the angular velocity of the spinning drop are in \u003cstrong\u003eMethods\u003c/strong\u003e. Moreover, wettability of the cover plate is a key factor that enables the Biellmann-Leidenfrost spin. The wettability of the paper and aluminium layers was manipulated to test the stability of the spin (Fig. S4). When superhydrophobic treatment was applied to the upper paper layer with a water contact angle of 158\u0026deg;\u0026plusmn;1.2\u0026deg;, and the bottom aluminium layer was untreated with a water contact angle of 89\u0026deg;\u0026plusmn;2.6\u0026deg;, the spin achieved the best stability. Furthermore, the Biellmann-Leidenfrost drop spin can also be achieved by other shapes of cover plates such as triangles, crosses, circles, rectangles and squares (Fig. S5). To facilitate the visualisation and characterisation of the Biellmann-Leidenfrost phenomenon, we used circular cover plates throughout this paper unless otherwise specified.\u003c/p\u003e\n\u003cp\u003eWe now explain the underlying physics behind the spectacular spinning behaviours of the drop. In the literature, numerous studies on the Leidenfrost phenomenon were focused on unrestricted water drops\u003csup\u003e14,28-31\u003c/sup\u003e, where vertical vibrations of the vapour film beneath the Leidenfrost drop trigger Faraday waves\u003csup\u003e32-34\u003c/sup\u003e. In contrast, we found that the restriction imposed by the cover plate on the top of the drop is the key factor enabling the high-speed spinning motion of the Biellmann-Leidenfrost drop by restricting the Faraday waves (Fig. 1h).\u0026nbsp;When both the equatorial and polar hemiperimeters of the drop are integer multiples of their corresponding wavelengths, the drop satisfies the double resonance condition and acts as a resonant cavity, leading to the formation of a classic Leidenfrost star\u003csup\u003e28,30\u003c/sup\u003e. However, in the Biellmann-Leidenfrost phenomenon, the Faraday wave at the top of the drop is suppressed by the cover plate, resulting in an energy transfer from the Faraday wave to other forms of kinetic energy, including horizontal translation\u0026nbsp;and spin. Since the levitation is restricted by gravity and\u0026nbsp;horizontal translation is confined by the bottom hole, the energy from the restricted Faraday wave was converted to the kinetic energy of spinning of the Leidenfrost drop due to the vertical restriction of the cover plate (see\u0026nbsp;\u003cstrong\u003eSupplementary Note 3\u003c/strong\u003e for analysis). Faraday waves are always present, which triggers the spin when the drop is placed on a hot surface.\u003c/p\u003e\n\u003cp\u003eFig. 2a and Supplementary Movie S6 illustrate the time dependence of the angular velocity \u003cem\u003e\u0026omega;\u0026nbsp;\u003c/em\u003ethroughout the lifespan of a spinning Biellmann-Leidenfrost drop. Upon depositing the drop on the substrate and covering it with a plate, a vigorous fluctuation was observed and \u003cem\u003e\u0026omega;\u003c/em\u003e stabilized at a characteristic angular velocity \u003cem\u003e\u0026omega;\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e (150 r/min). Subsequently, the drop underwent a significant acceleration process, reaching a maximum spinning velocity \u003cem\u003e\u0026omega;\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e (720 r/min) after ~20 s. The drop then experienced a sudden deceleration, coming to a halt. The initial fluctuation stage could be viewed as the process through which the drop transitions from a static to a spinning state. Although the continuous input of energy from the Faraday wave may sustain the spin of the drops, it does not explain the sudden appearance of a significant acceleration stage. Our findings suggest that, the star oscillation emerges almost simultaneously with the acceleration stage (Fig. S6). Fig. 2b, c shows an exemplary image and an illustration of a drop with a cover plate, while Fig 2d, e shows drops without a cover plate. In a sense, the star oscillation breaks the symmetry of round drops. For a spinning drop (Fig. 2c), the reaction forces of the vapour flow exerted to a petal is asymmetric due to environmental disturbances when drops have a star shape, unlike the symmetric reaction forces experienced by round drops. This asymmetry provides the driving torque accounting for the drop spin. Fig. 2c, e provides comparisons with and without the cover plate, respectively. Ultimately, as the drop shrank and the plate-water-air three-phase contact line pinned, the star-oscillations disappeared, the drop dramatically lost momentum and halted its spinning due to the dominant drag torque. These observations indicate that the three stages of behaviour correspond to three distinct mechanisms, for which we developed a mathematical model for clarification below. Fig. 2f shows the origin of the driving torque during the initial stage, detailed force analysis can be found in \u003cstrong\u003eSupplementary Note 4\u003c/strong\u003e. Fig. 2g illustrates the results of the temporal evolution of the angular velocity of the drop under a cover plate with a radius \u003cem\u003eR\u003c/em\u003e (2 mm \u0026le; \u003cem\u003eR\u003c/em\u003e \u0026le; 5 mm) during evaporation. The results indicate that within this range of \u003cem\u003eR\u003c/em\u003e, a smaller size of the cover plate corresponds to a higher maximum angular velocity that a Biellmann-Leidenfrost drop can achieve.\u003c/p\u003e\n\u003cp\u003e, we explore the underlying physics of the drop throughout the spinning process. In the initial stage, a vigorous fluctuation is observed, and we attribute the driving torque to the deviation of the vapour flow (between the drop and the substrate) from the radial direction. The driving torque can be derived by integrating the shear force of the vapour over the entire contact area, resulting in \u003cem\u003eT\u003c/em\u003e\u003csub\u003edri\u003c/sub\u003e ~ \u003cem\u003e\u0026eta;\u003c/em\u003e\u003csub\u003ev\u003c/sub\u003e\u003cem\u003eU\u003c/em\u003e\u003csub\u003e||\u003c/sub\u003e\u003csup\u003e*\u003c/sup\u003e\u003cem\u003er\u003c/em\u003e\u003csup\u003e3\u003c/sup\u003e/\u003cem\u003e\u0026delta;\u003c/em\u003e (see \u003cstrong\u003eSupplementary Note 4\u003c/strong\u003e). Meanwhile, the drop must overcome the drag torque resulting from the liquid viscosity to transition from a static state to a spinning state, yielding \u003cem\u003eT\u003c/em\u003e\u003csub\u003edrag\u003c/sub\u003e ~ \u003cem\u003e\u0026eta;\u003c/em\u003e\u003csub\u003ew\u003c/sub\u003e\u003cem\u003er\u003c/em\u003e\u003csup\u003e4\u003c/sup\u003e\u003cem\u003e\u0026omega;\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e/\u003cem\u003eh\u003c/em\u003e. Here, \u003cem\u003e\u0026eta;\u003c/em\u003e\u003csub\u003ev\u003c/sub\u003e and \u003cem\u003e\u0026eta;\u003c/em\u003e\u003csub\u003ew\u003c/sub\u003e represent the viscosity of vapour and water, respectively. The variables \u003cem\u003er\u003c/em\u003e and \u003cem\u003eh\u003c/em\u003e represent the maximum radius and the height of the spinning drop with a characteristic angular velocity \u003cem\u003e\u0026omega;\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e in this stage.\u0026nbsp;\u003cem\u003eU\u003c/em\u003e\u003csub\u003e||\u003c/sub\u003e\u003csup\u003e*\u003c/sup\u003e =\u0026nbsp;\u003cem\u003e\u0026phi;\u003c/em\u003e\u003cem\u003eU\u003c/em\u003e\u003csub\u003e||\u003c/sub\u003e represent the velocity of the vapour flow deviated from the radius direction\u0026nbsp;\u003cem\u003eU\u003c/em\u003e\u003csub\u003e||\u003c/sub\u003e, with\u0026nbsp;\u003cem\u003e\u0026phi;\u0026nbsp;\u003c/em\u003ebeing a coefficient estimated as\u0026nbsp;\u003cem\u003e\u0026phi;\u003c/em\u003e = tan 1\u0026deg;\u0026nbsp;\u0026asymp;\u0026nbsp;0.02. This also indicates that even a slight deviation of the vapour flow could trigger a significant spinning of the drop. Moreover,\u0026nbsp;\u003cem\u003eU\u003c/em\u003e\u003csub\u003e||\u003c/sub\u003e = [(\u003cem\u003ek\u003c/em\u003e\u0026Delta;\u003cem\u003eT\u003c/em\u003e\u003cem\u003e\u0026rho;\u003c/em\u003e\u003csub\u003ew\u003c/sub\u003e\u003cem\u003egh\u003c/em\u003e)/(6\u003cem\u003e\u0026rho;\u003c/em\u003e\u003csub\u003ev\u003c/sub\u003e\u003cem\u003eL\u003c/em\u003e\u003cem\u003e\u0026eta;\u003c/em\u003e\u003csub\u003ev\u003c/sub\u003e)]\u003csup\u003e1/2\u003c/sup\u003e and the vapour film thickness\u0026nbsp;\u003cem\u003e\u0026delta;\u003c/em\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003e= [3\u003cem\u003ek\u003c/em\u003e\u0026Delta;\u003cem\u003eT\u003c/em\u003e\u003cem\u003e\u0026eta;\u003c/em\u003e\u003csub\u003ev\u003c/sub\u003e/(2\u003cem\u003eL\u003c/em\u003e\u003cem\u003e\u0026rho;\u003c/em\u003e\u003csub\u003ev\u003c/sub\u003e\u003cem\u003e\u0026rho;\u003c/em\u003e\u003csub\u003ew\u003c/sub\u003e\u003cem\u003egh\u003c/em\u003e)]\u003csup\u003e1/4\u003c/sup\u003e\u003cem\u003er\u003c/em\u003e\u003csup\u003e1/2\u003c/sup\u003e are derived based on the classical theory\u003csup\u003e25\u003c/sup\u003e. Here, \u003cem\u003ek\u003c/em\u003e, \u003cem\u003eL\u003c/em\u003e and\u0026nbsp;\u003cem\u003eg\u003c/em\u003e represent the vapour thermal conductivity, latent heat of water, and gravitational acceleration, respectively. Additionally,\u0026nbsp;\u003cem\u003e\u0026rho;\u003c/em\u003e\u003csub\u003ev\u003c/sub\u003e and\u0026nbsp;\u003cem\u003e\u0026rho;\u003c/em\u003e\u003csub\u003ew\u003c/sub\u003e represent the mass densities of vapour and water, respectively. The temperature difference between the substrate \u003cem\u003eT\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e and water \u003cem\u003eT\u003c/em\u003e\u003csub\u003ew\u003c/sub\u003e is defined as \u0026Delta;\u003cem\u003eT\u003c/em\u003e = \u003cem\u003eT\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e \u0026ndash; \u003cem\u003eT\u003c/em\u003e\u003csub\u003ew\u003c/sub\u003e. A combination of \u003cem\u003eT\u003c/em\u003e\u003csub\u003edri\u003c/sub\u003e and \u003cem\u003eT\u003c/em\u003e\u003csub\u003edrag\u003c/sub\u003e leads to \u003cem\u003e\u0026omega;\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e ~\u0026nbsp;[\u003cem\u003ek\u003c/em\u003e\u0026Delta;\u003cem\u003eT\u003c/em\u003e\u003cem\u003e\u0026eta;\u003c/em\u003e\u003csub\u003ev\u003c/sub\u003e/(\u003cem\u003eL\u003c/em\u003e\u003cem\u003e\u0026rho;\u003c/em\u003e\u003csub\u003ev\u003c/sub\u003e)])\u003csup\u003e1/4\u003c/sup\u003e(\u003cem\u003e\u0026rho;\u003c/em\u003e\u003csub\u003ew\u003c/sub\u003e\u003cem\u003egh\u003c/em\u003e)\u003csup\u003e3/4\u003c/sup\u003e\u003cem\u003e\u0026nbsp;\u0026eta;\u003c/em\u003e\u003csub\u003ew\u003c/sub\u003e\u003csup\u003e\u0026ndash;1\u003c/sup\u003e\u003cem\u003ehr\u003c/em\u003e\u003csup\u003e\u0026ndash;3/2\u003c/sup\u003e. At this point, we consider the value of \u003cem\u003er\u003c/em\u003e when the first stage ends and denoted it as \u003cem\u003er\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e, which is slightly larger than \u003cem\u003eR\u003c/em\u003e. Subsequently, the drop begins to accelerate with a smoother spin while evaporating more rapidly than a typical Leidenfrost drop, indicating a significantly stronger vapour release. Due to the disturbance, the vapour flow evaporated from the drop exhibits an asymmetric behaviour (Fig. 2c). Base on the conservation of momentum, we derive the driving torque exerted on the petals during this stage, \u003cem\u003eT\u003c/em\u003e\u003csub\u003edri\u003c/sub\u003e = d\u003cem\u003eL\u003c/em\u003e\u003csub\u003em\u003c/sub\u003e/d\u003cem\u003et\u003c/em\u003e = (\u0026Delta;\u003cem\u003eM\u003c/em\u003e/\u0026Delta;\u003cem\u003et\u003c/em\u003e)\u003cem\u003er\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003cem\u003e\u0026omega;\u003c/em\u003e ~\u0026nbsp;\u003cem\u003e\u0026rho;\u003c/em\u003e\u003csub\u003ev\u003c/sub\u003e\u003cem\u003e\u0026delta;\u003c/em\u003e\u003cem\u003eU\u003c/em\u003e\u003csub\u003e||\u003c/sub\u003e\u003cem\u003er\u003c/em\u003e\u003csup\u003e3\u003c/sup\u003e\u003cem\u003e\u0026omega;\u003c/em\u003e, with \u003cem\u003eL\u003c/em\u003e\u003csub\u003em\u003c/sub\u003e being angular momentum, and\u0026nbsp;\u0026Delta;\u003cem\u003eM\u003c/em\u003e being the decrease in drop mass over a time span\u0026nbsp;\u0026Delta;\u003cem\u003et\u003c/em\u003e. In this scenario, the formation of an air boundary layer on the cover plate contributes a dominant torque to resulting from the viscous force of the air on the top of the cover plate, and we obtain \u003cem\u003eT\u003c/em\u003e\u003csub\u003edrag\u003c/sub\u003e ~ (\u003cem\u003e\u0026eta;\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e\u003cem\u003e\u0026rho;\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e)\u003csup\u003e1/2\u003c/sup\u003e\u003cem\u003er\u003c/em\u003e\u003csup\u003e4\u003c/sup\u003e\u003cem\u003e\u0026omega;\u003c/em\u003e\u003csup\u003e3/2\u003c/sup\u003e, with \u003cem\u003e\u0026eta;\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e and\u003cem\u003e\u0026nbsp;\u0026rho;\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e representing the dynamic viscosity and mass density of air, respectively. As a consequence, we formulate the kinetic equation of the spinning drop considering the drop with mass\u0026nbsp;\u003cem\u003eM\u003c/em\u003e (including the mass of the cover plate),\u0026nbsp;\u003cem\u003eI\u0026alpha;\u003c/em\u003e = \u003cem\u003eT\u003c/em\u003e\u003csub\u003edri\u003c/sub\u003e \u0026ndash; \u003cem\u003eT\u003c/em\u003e\u003csub\u003edrag\u003c/sub\u003e, with\u0026nbsp;\u003cem\u003eI\u003c/em\u003e = \u003cem\u003eMr\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e/2\u0026nbsp;and\u0026nbsp;\u003cem\u003e\u0026alpha;\u003c/em\u003e being the moment of inertia of the spinning drop and the angular acceleration, respectively. Finally, as the drop radius\u0026nbsp;\u003cem\u003er\u003c/em\u003e approaches\u0026nbsp;\u003cem\u003eR\u003c/em\u003e, star-like oscillations are significantly dampened due to the pinning of the three-phase contact line, resulting a notable decrease in driving torque. Furthermore, a noticeable oscillation of the entire drop re-emerges, leading us to attribute the drag torque to the viscous force within the vapour layer between the drop and the substrate. As a result, we derive \u003cem\u003eT\u003c/em\u003e\u003csub\u003edrag\u003c/sub\u003e = \u003cem\u003e\u0026eta;\u003c/em\u003e\u003csub\u003ev\u003c/sub\u003e\u003cem\u003er\u003c/em\u003e\u003csup\u003e4\u003c/sup\u003e\u003cem\u003e\u0026omega;\u003c/em\u003e/\u003cem\u003e\u0026delta;\u003c/em\u003e, and the corresponding dynamic equation becomes\u0026nbsp;\u003cem\u003eI\u0026alpha;\u003c/em\u003e = \u0026ndash; \u003cem\u003eT\u003c/em\u003e\u003csub\u003edrag\u003c/sub\u003e.\u003c/p\u003e\n\u003cp\u003eFig. 3a shows comparisons between our experimental and theoretical results for the relations\u003cem\u003e\u0026nbsp;\u0026omega;\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e vs.\u0026nbsp;\u003cem\u003er\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e and\u0026nbsp;\u003cem\u003e\u0026omega;\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e vs.\u0026nbsp;\u003cem\u003eR\u003c/em\u003e. In the former, the theoretical curve for the relation between\u0026nbsp;\u003cem\u003e\u0026omega;\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e and\u0026nbsp;\u003cem\u003er\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e are derived from the above analyses, while in the latter, the theoretical predictions of\u0026nbsp;\u003cem\u003e\u0026omega;\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e are numerical results based on the dynamic equation\u0026nbsp;\u003cem\u003eI\u0026alpha;\u003c/em\u003e = \u003cem\u003eT\u003c/em\u003e\u003csub\u003edri\u003c/sub\u003e \u0026ndash; \u003cem\u003eT\u003c/em\u003e\u003csub\u003edrag\u003c/sub\u003e over a duration of 20 s. Moreover, the comparisons between the experimental and theoretical results of \u003cem\u003e\u0026omega;\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e and \u003cem\u003eT\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e are shown in Fig. 3b. All\u0026nbsp;the experimental results are based on direct measurements from experiments with errors.\u0026nbsp;When \u003cem\u003eT\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e is sufficiently high, Fig. 3b shows that \u003cem\u003e\u0026omega;\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e no longer increases with \u003cem\u003eT\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e, a trend similar to that observed in conventional Leidenfrost drops transported on asymmetric ratchet\u003csup\u003e35,36\u003c/sup\u003e and microstructured\u003csup\u003e37\u003c/sup\u003e surfaces. This phenomenon can be attributed to the thickening of the vapour film beneath the drop, which suppresses asymmetric environmental disturbances from the substrate, leading to increased symmetry in the system and a weakened driving force.\u003c/p\u003e\n\u003cp\u003eTo understand the influence of the mass of the cover plate \u003cem\u003em\u003c/em\u003e\u003csub\u003ep\u003c/sub\u003e on \u003cem\u003e\u0026omega;\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e, we added layers of aluminum foil to adjust \u003cem\u003em\u003c/em\u003e\u003csub\u003ep\u003c/sub\u003e. Fig. 3c shows the relation between \u003cem\u003e\u0026omega;\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e and \u003cem\u003em\u003c/em\u003e\u003csub\u003ep\u003c/sub\u003e for the cover plates with radii of \u003cem\u003eR\u003c/em\u003e = 3.0 mm, 4.0 mm and 5.0 mm, respectively. In this context, \u003cem\u003e\u0026omega;\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e is derived by considering the dynamic equation of the drop, but with \u003cem\u003em\u003c/em\u003e\u003csub\u003ep\u003c/sub\u003e updated (see\u0026nbsp;\u003cstrong\u003eSupplementary Note 4\u003c/strong\u003e). The theoretical results in Fig. 3a, 3b, and 3c agree well with the experimental data, although \u003cem\u003e\u0026omega;\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e exhibits fluctuations (error bars). These fluctuations arise due to the uncertainty of the resonance state and other random influences caused by the violent shakes, e.g., the variation of the geometrical centre (Fig. S9, \u003cstrong\u003eSupplementary Note 5\u003c/strong\u003e), even when the experiments are repeated under identical conditions.\u003c/p\u003e\n\u003cp\u003eThroughout the entire spinning process, the shape of the drop evolves due to evaporation. Fig. 3d and \u003cstrong\u003eSupplementary Note 6\u0026nbsp;\u003c/strong\u003edemonstrate the relation between the drop height \u003cem\u003eh\u0026nbsp;\u003c/em\u003eand radius \u003cem\u003er\u003c/em\u003e. The drop height \u003cem\u003eh\u003c/em\u003e and radius \u003cem\u003er\u003c/em\u003e are defined as follows: in the side view of the drop, we approximate the maximum width of the drop as its diameter (2\u003cem\u003er\u003c/em\u003e), and the maximum height of the drop as its height (\u003cem\u003eh\u003c/em\u003e). The red dashed curve represents the theoretical solution for \u003cem\u003eh\u0026nbsp;\u003c/em\u003evs.\u003cem\u003e\u0026nbsp;r\u003c/em\u003e of a two-dimensional static drop obtained from the Young-Laplace equation\u003csup\u003e38,39\u003c/sup\u003e, which serves as the upper bound for the height of the Biellmann-Leidenfrost drop. The constraining effect of the upper cover plate is more pronounced as \u003cem\u003er\u0026nbsp;\u003c/em\u003edecreases. The drop height \u003cem\u003eh\u003c/em\u003e and drop radius \u003cem\u003er\u003c/em\u003e did not decrease in the same manner over time \u003cem\u003et\u003c/em\u003e, particularly when the drop radius \u003cem\u003er\u003c/em\u003e was similar to the cover plate radius \u003cem\u003eR\u003c/em\u003e. The three-phase contact line would pin at the edge of the cover plate due to the hydrophilicity of its bottom side, impeding the reduction of the drop radius. Consequently, over a relatively long period, the drop radius \u003cem\u003er\u003c/em\u003e remained nearly constant, facilitating the generation and maintenance of the resonance conditions. Under these circumstances, the drop would persist until it reached the appropriate size to satisfy the resonance conditions\u003csup\u003e25\u003c/sup\u003e, thereby enhancing the Biellmann-Leidenfrost spin (see \u003cstrong\u003eSupplementary Note 7\u003c/strong\u003e). Fig. 3e illustrates typical Biellmann-Leidenfrost drop shapes at various stages. When the drop radius satisfies \u003cem\u003er\u003c/em\u003e \u0026lt; \u003cem\u003eR\u003c/em\u003e (the vertical lines in Fig. 3d) due to the pinning of the solid-liquid-gas three-phase contact line, the spin abruptly halts.\u003c/p\u003e\n\u003cp\u003eThe Biellmann-Leidenfrost phenomenon may find applications in thermal engineering\u003csup\u003e3,40,41\u003c/sup\u003e. For example, Fig. 4a shows the persistence of vision effect of a spinning Biellmann-Leidenfrost drop under a cover plate of 3 mm in radius at a substrate of 500\u0026nbsp;℃. There are eight motions of the Biellmann\u0026rsquo;s spin in figure skating on the cover plate, forming a series of actions due to the drop spin at an angular velocity of 225 r/min (Supplementary Movie S7). The Biellmann-Leidenfrost drop provided a stable display at a high temperature, and may be used for \u003cem\u003ein-situ\u003c/em\u003e monitoring the temperature of a hot object by detecting the spin velocity.\u003c/p\u003e\n\u003cp\u003eTo support a sustainable Biellmann-Leidenfrost drop spin, we explored the conditions that enable this phenomenon. The acceleration of\u0026nbsp;Biellmann-Leidenfrost\u0026nbsp;spin is closely related to the star oscillation under double resonance conditions\u003csup\u003e28\u003c/sup\u003e. Fig. 4b shows the\u0026nbsp;analyses of the resonance mode \u003cem\u003en\u003c/em\u003e and \u003cem\u003em\u003c/em\u003e of spinning Leidenfrost drops. The\u0026nbsp;solid\u0026nbsp;curves represent the equatorial resonance mode \u003cem\u003en\u003c/em\u003e = \u0026pi;\u003cem\u003er/\u0026lambda;\u003c/em\u003e, where \u0026pi;\u003cem\u003er\u003c/em\u003e denotes the equatorial hemiperimeter of the drop and\u0026nbsp;\u003cem\u003e\u0026lambda;\u003c/em\u003e \u0026asymp;\u0026nbsp;[2\u0026pi;\u003cem\u003e\u0026sigma;\u003c/em\u003e\u003csub\u003eLV\u003c/sub\u003e/(\u003cem\u003e\u0026rho;\u003c/em\u003e\u003csub\u003ew\u003c/sub\u003e\u003cem\u003ef\u003c/em\u003e\u003csup\u003e3\u003c/sup\u003e)]\u003csup\u003e1/3\u003c/sup\u003e denotes the forcing wavelength caused by Faraday instability\u003csup\u003e32-34\u003c/sup\u003e, with\u0026nbsp;\u003cem\u003e\u0026sigma;\u003c/em\u003e\u003csub\u003eLV\u003c/sub\u003e and\u0026nbsp;\u003cem\u003ef\u003c/em\u003e representing the liquid-vapour interfacial tension and the frequency of the capillary wave, respectively. Additionally, the dotted and\u0026nbsp;dashed lines represent the boundaries of\u0026nbsp;the polar resonance mode \u003cem\u003em\u003c/em\u003e = (2\u003cem\u003er\u003c/em\u003e+\u003cem\u003eh\u003c/em\u003e)\u003cem\u003e/\u0026lambda;\u003c/em\u003e, where (2\u003cem\u003er\u003c/em\u003e+\u003cem\u003eh\u003c/em\u003e) denotes the polar hemiperimeter of the drop. Specifically, in the upper panel of Fig. 4b, we consider the condition of subharmonic resonance, i.e., \u003cem\u003ef\u003c/em\u003e = \u003cem\u003ef\u003c/em\u003e\u003csub\u003ev\u003c/sub\u003e/2, with \u003cem\u003ef\u003c/em\u003e\u003csub\u003ev\u003c/sub\u003e being the vibration frequency of the vapour film beneath the drop. The dotted and dashed blue curves represent the lower and upper bounds of \u003cem\u003eh\u003c/em\u003e in the mode \u003cem\u003em\u003c/em\u003e. The red areas satisfy the subharmonic resonance conditions, which is the most common situation in the Faraday instability. Furthermore, employing a similar approach, we also illustrate the condition of harmonic resonance (green areas) in the lower panel of Fig. 4b, where \u003cem\u003ef\u003c/em\u003e = \u003cem\u003ef\u003c/em\u003e\u003csub\u003ev\u003c/sub\u003e/2 is satisfied. The dotted and dashed green curves represent the lower and upper bounds of \u003cem\u003eh\u003c/em\u003e in the mode \u003cem\u003em\u003c/em\u003e (more details in \u003cstrong\u003eSupplementary Notes 7-9\u003c/strong\u003e). Combining the upper and lower panels of Fig. 4b, it becomes evident that\u0026nbsp;all areas within \u003cem\u003er\u003c/em\u003e = 2-6 mm satisfy the resonance conditions, indicating that a\u0026nbsp;Biellmann-Leidenfrost drop spin could be achieved by confining the drop radius within this range.\u003c/p\u003e\n\u003cp\u003eTo facilitate the practical applications (e.g., \u003cem\u003ein-situ\u003c/em\u003e temperature monitoring), water could be continuously replenished to sustain the Biellmann-Leidenfrost drop by dynamically meeting the double resonance conditions. Previous research and our work suggest that there is not a systematic match between modes \u003cem\u003en\u003c/em\u003e and \u003cem\u003em\u003c/em\u003e, and the empirical condition for observing a star mode satisfies \u0026Delta;\u003cem\u003er\u003c/em\u003e/\u003cem\u003er\u003c/em\u003e ~ 10%\u003csup\u003e28\u003c/sup\u003e. Due to evaporation, the drop radius shrank at a rate of\u0026nbsp;\u003cem\u003ev\u003c/em\u003e = |d\u003cem\u003er\u003c/em\u003e/d\u003cem\u003et\u003c/em\u003e| \u0026asymp; 30 \u0026mu;m/s; to preserve its original resonance conditions, additional water should be supplemented in a time span of\u0026nbsp;\u0026Delta;\u003cem\u003er\u003c/em\u003e/\u003cem\u003ev\u003c/em\u003e = (\u0026Delta;\u003cem\u003er\u003c/em\u003e/\u003cem\u003er\u003c/em\u003e)(\u003cem\u003er\u003c/em\u003e/\u003cem\u003ev\u003c/em\u003e), which is in a few seconds. During the evaporation, the evaporation rate can be calculated by\u0026nbsp;\u0026part;\u003cem\u003eM\u003c/em\u003e/\u0026part;\u003cem\u003et\u003c/em\u003e = \u0026minus; \u003cem\u003ek\u003c/em\u003e\u0026Delta;\u003cem\u003eTA\u003c/em\u003e/(\u003cem\u003eL\u0026delta;\u003c/em\u003e), where \u003cem\u003eA\u003c/em\u003e = \u003cem\u003e\u0026pi;r\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e is the contact area between the drop and the hot substrate\u003csup\u003e42\u003c/sup\u003e.\u0026nbsp;Taking typical values for the different parameters\u0026nbsp;(\u003cem\u003ek\u003c/em\u003e \u0026asymp; 0.05 W/(m⸱K), \u0026Delta;\u003cem\u003eT\u003c/em\u003e \u0026asymp; 400 K, \u003cem\u003eL\u003c/em\u003e \u0026asymp;\u0026nbsp;2.26\u0026nbsp;\u0026acute;\u0026nbsp;10\u003csup\u003e6\u003c/sup\u003e J/kg, \u003cem\u003er\u003c/em\u003e \u0026asymp;\u0026nbsp;2 mm and\u0026nbsp;\u003cem\u003e\u0026delta;\u003c/em\u003e \u0026asymp;\u0026nbsp;100\u0026nbsp;\u0026mu;m), we find that \u0026part;\u003cem\u003eM\u003c/em\u003e/\u0026part;\u003cem\u003et\u003c/em\u003e is on the order of\u0026nbsp;1.0 mg/s.\u003csup\u003e25\u003c/sup\u003e To maintain a balanced evaporation rate, we\u0026nbsp;added small droplets with a radius of ~ 0.9 mm for every 3 s, to replenish the evaporating drop. This allowed for a continuous Biellmann-Leidenfrost spin over a significantly extended period, with an angular velocity of ~800-1200 r/min for over 350 s (Fig. 4c and Supplementary Movie S8). In this way, we could \u003cem\u003ein-situ\u003c/em\u003e monitor the condition of a hot surface.\u003c/p\u003e\n\u003cp\u003eIn summary, we discover a new phenomenon of a water drop with a Biellmann-spin behaviour, by confining the vertical movement of a Leidenfrost drop. This finding challenges the prevailing paradigm that spatially asymmetric textures are required for liquid control. Through both experimental and theoretical analysis, we found that the driving torque of the Biellmann-Leidenfrost spin is initiated by an asymmetric vapour flow acting on a petal of a star-shaped drop, and is sustained and accelerated due to star oscillation under double resonance conditions. The selection of the spin is influenced by initial perturbations, with each petal functioning like a propeller, generating a propulsion force through dynamic symmetry breaking. An intriguing question that arises is how other types of Biellmann-spin behaviour manifest work in broader systems, such as on curved solid surface, on liquid baths, or on an air cushion blown from below. Our findings significantly enhance the fundamental understanding of self-propulsion of liquids and the dynamics of liquid-solid interfaces, with promise far-reaching implications for fluid dynamics, surface science, spontaneous symmetry breaking in dynamical systems, as well as for broad applications in liquid metal, energy conversion and harvesting, and heat transfer manipulation.\u003c/p\u003e"},{"header":"Methods","content":"\u003cdiv id=\"Sec2\" class=\"Section2\"\u003e \u003ch2\u003eFabrication and characterisation of the bottom hole\u003c/h2\u003e \u003cp\u003eThe bottom hole that was used to confine the horizontal movement of the Biellmann-Leidenfrost drop was machined with a diameter of 5 mm and a depth of 0.3 mm using a 1500 W water-cooled CNC engraving machine (YD3040, Shenzhen Yidiao Technology Co., Ltd, China). The formation of the groove structures in the bottom hole was due to the nature of the machining technique and was not intentionally designed to guide the direction of drop spin. The substrate was heated to 500\u0026deg;C for the experiments throughout this paper unless otherwise specified.\u003c/p\u003e \u003cp\u003eAn optical drop analyser (JC2000D4F, Zhongchen, China) was used to observe the vapour layer generated by the Biellmann-Leidenfrost drops on the surface of the hole. The macroscopic morphology of the hole was observed using an ultra-depth 3D microscope (VHX-6000, Keenes, Japan). Scanning electron microscopy (SEM, SUPRA 55 SAPPHIRE, Germany) was used to examine the microscopic morphology of the bottom of the hole.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eFabrication of the cover plate\u003c/h2\u003e \u003cp\u003eThe cover plate consisted of aluminium foil with a paper sheet on the upper surface. The thickness of the cover plate was 0.15 mm and its density was 0.24 g/cm\u003csup\u003e3\u003c/sup\u003e. The superhydrophobic treatment on the upper cover plate was achieved using a commercially available superhydrophobic coating (Never Wet Multi Purpose Kit, Rust Oleum 274232, USA).\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eThe method of reading the angular velocity of the spinning drop\u003c/h3\u003e\n\u003cp\u003eAs illustrated in (a), by employing a high-speed colour camera (100 fps), we captured the entire process of the drop from the top view. To achieve better recognition of the cover plate boundary, we added a small amount of red ink into the drops without affecting their physical properties. Specifically, we first read the boundary of the cover plate, and then measured the angular velocity of the drop by marking a pointer on the cover plate. As shown in Fig. S4a, the cover plate remained synchronized with the spinning drop, enabling us to calculate the angular velocity frame-by-frame by employing a custom-made MATLAB code. The average values of the angular velocity are presented in (b) and (c), obtained by averaging the angular velocity in 0.01 s and 0.1 s, respectively.\u003c/p\u003e \u003cp\u003eUpon examination, it is evident that by utilizing a larger time interval of 0.1 s, the error associated with this method can be minimized. (c) supports the notion that the outcome remains highly credible. In this regard, when plotting the relation between \u003cem\u003eω\u003c/em\u003e and \u003cem\u003et\u003c/em\u003e (i.e., Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ef) or determining the maximum \u003cem\u003eω\u003c/em\u003e (i.e., Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea, b, c), we employed a time interval of 0.1 s. Nevertheless, for the purpose of better elucidation, the time interval used in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea has been adjusted to 1.0 s.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was partially supported by the National Natural Science Foundation of China (NSFC, Grant No. 52275420, U23A20632, 12172189), the National Key R\u0026amp;D Program of China (2002YFB3403304). Y. Lu acknowledges the Royal Society Research Grant (RGS∖R1∖201071) for financial support. We thank Professor Julia Yeomens in the Department of Physics, University of Oxford, for constructive advice on building the mathematical model.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eS.H., Y.L. and C.L. conceptualised this work, and K.F., Y.L. and C.L. supervised this work. S.H., M.L., Y.L designed the experiments. M.L., Z.W. performed the experiments. C.L., E.L. developed the mathematical model and performed theoretical analyses. S.H., Y.L., C.L., M.L., E.L. drafted the initial manuscript and all authors discussed the results and commented on the paper. S.H., M.L., E.L. contributed equally.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eLeidenfrost, J. G. \u003cem\u003eDe aquae communis nonnullis qualitatibus tractatus\u003c/em\u003e. (Ovenius, 1756).\u003c/li\u003e\n\u003cli\u003eLinke, H., Alem\u0026aacute;n, B. J., Melling, L. D., Taormina, M. J., Francis, M. J., Dow-Hygelund, C. C., Narayanan, V., Taylor, R. P. \u0026amp; Stout, A. 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(John Wiley \u0026amp; Sons, Inc., 2007).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"","lastPublishedDoi":"10.21203/rs.3.rs-6246861/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6246861/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eLeidenfrost phenomenon refers to the levitation of a liquid drop on a sufficiently hot surface and has been studied since its discovery in 1756. Extensive research has explored this effect across both liquids and solids, uncovering fascinating behaviours and intricate underlying mechanisms. However, most research on this phenomenon only focused on unrestricted drops, such as self-rotating motions, trampolining, and manipulating substrate morphology to control drop motions, few reports have explored the behaviour of a restricted Leidenfrost drop due to the significant challenge to manipulate a highly mobile levitating drop. Here we report a new phenomenon of a high-speed spinning Leidenfrost drop by confining both its vertical and horizontal movements. We term this phenomenon the Biellmann-Leidenfrost spin because it is reminiscent of the Biellmann spin in figure skating. This phenomenon originates from the vertical restriction on a Leidenfrost drop that initiates star-like oscillations, and is enhanced when the drop satisfies the double resonance conditions, enabling a maximum angular velocity of ~ 1700 r/min, and can be sustained by replenishing water. The Biellmann-Leidenfrost effect holds significant potential for converting waste heat into mechanical energy, for applications in energy conversion and conservation.\u003c/p\u003e","manuscriptTitle":"Enabling a Leidenfrost drop to perform Biellmann spin","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-01 10:49:42","doi":"10.21203/rs.3.rs-6246861/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":"51577cd7-07be-4fa0-b213-63a183cc114f","owner":[],"postedDate":"July 1st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":50693571,"name":"Physical sciences/Materials science"},{"id":50693572,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2025-07-31T09:20:26+00:00","versionOfRecord":[],"versionCreatedAt":"2025-07-01 10:49:42","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6246861","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6246861","identity":"rs-6246861","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}