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Spontaneous dynamics of two-dimensional Leidenfrost wheels

Rodolfo Brandão and Ory Schnitzer
Phys. Rev. Fluids 5, 091601(R) – Published 18 September 2020
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Abstract

Recent experiments have shown that liquid Leidenfrost drops levitated by their vapor above a flat hot surface can exhibit symmetry-breaking spontaneous dynamics [A. Bouillant et al., Nat. Phys. 14, 1188 (2018)]. Motivated by these observations, we theoretically investigate the translational and rotational dynamics of Leidenfrost drops on the basis of a simplified two-dimensional model, focusing on near-circular drops small relative to the capillary length. The model couples the equations of motion of the drop, which flows as a rigid wheel, and thin-film equations governing the vapor flow, the profile of the deformable vapor-liquid interface, and thus the hydrodynamic forces and torques on the drop. In contrast to previous analytical models of Leidenfrost drops levitating above a flat surface which predict only symmetric solutions, we find that the symmetric Leidenfrost state is unstable above a critical drop radius: R1 for a free drop and R2>R1 for an immobilized drop. In these respective cases, symmetry breaking is manifested in supercritical pitchfork bifurcations into steady states of pure rolling and constant angular velocity. In further qualitative agreement with the experiments, when a symmetry-broken immobilized drop is suddenly released it initially moves at an acceleration αg, where α is an angle characterizing the slope of the liquid-vapor profile and g is the gravitational acceleration; moreover, α exhibits a maximum with respect to the drop radius at a radius increasing with the temperature difference between the surface and the drop.

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  • Received 12 April 2020
  • Accepted 20 August 2020

DOI:https://doi.org/10.1103/PhysRevFluids.5.091601

©2020 American Physical Society

Physics Subject Headings (PhySH)

Fluid DynamicsNonlinear DynamicsPolymers & Soft Matter

Authors & Affiliations

Rodolfo Brandão and Ory Schnitzer

  • Department of Mathematics, Imperial College London, SW7 2AZ London, United Kingdom

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Issue

Vol. 5, Iss. 9 — September 2020

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