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Leidenfrost levitation of a spherical particle above a liquid bath: Evolution of the vapour-film morphology with particle size

Part of: Basic methods in fluid mechanics Asymptotic theory Incompressible viscous fluids

Published online by Cambridge University Press:  17 February 2022

R. BRANDÃO  and
O. SCHNITZER Open the ORCID record for O. SCHNITZER [Opens in a new window]
R. BRANDÃO
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK emails: o.schnitzer@imperial.ac.uk, r.brandao18@imperial.ac.uk
O. SCHNITZER
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK emails: o.schnitzer@imperial.ac.uk, r.brandao18@imperial.ac.uk
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Abstract

We consider a spherical particle levitating above a liquid bath owing to the Leidenfrost effect, where the vapour of either the bath or sphere forms an insulating film whose pressure supports the sphere’s weight. Starting from a reduced formulation based on a lubrication-type approximation, we use matched asymptotics to describe the morphology of the vapour film assuming that the sphere is small relative to the capillary length (small Bond number) and that the densities of the bath and sphere are comparable. We find that this regime is comprised of two formally infinite sequences of distinguished limits which meet at an accumulation point, the limits being defined by the smallness of an intrinsic evaporation number relative to the Bond number. These sequences of limits reveal a surprisingly intricate evolution of the film morphology with increasing sphere size. Initially, the vapour film transitions from a featureless morphology, where the thickness profile is parabolic, to a neck–bubble morphology, which consists of a uniform pressure bubble bounded by a narrow and much thinner annular neck. Gravity effects then become important in the bubble leading to sequential formation of increasingly smaller neck–bubble pairs near the symmetry axis. This process terminates when the pairs closest to the symmetry axis become indistinguishable and merge. Subsequently, the inner section of that merger transitions into a uniform-thickness film that expands radially, gradually squishing increasingly larger neck–bubble pairs into a region of localised oscillations sandwiched between the uniform film and what remains of the bubble whose radial extent is presently comparable to the uniform film; the neck–bubble pairs farther from the axis remain essentially intact. Ultimately, the uniform film gobbles up the largest outermost bubble, whereby the morphology simplifies to a uniform film bounded by localised oscillations. Overall, the asymptotic analysis describes the continuous evolution of the vapour film from a neck–bubble morphology typical of a Leidenfrost drop levitating above a flat solid substrate to a uniform-film morphology which resembles that in the case of a large liquid drop levitating above a liquid bath.

Keywords

Leidenfrost effectlevitationcapillary wavesasymptotic analysisthin films

MSC classification

Primary: 76D08: Lubrication theory
Secondary: 76M45: Asymptotic methods, singular perturbations 34E10: Perturbations, asymptotics
Type
Papers
Information
European Journal of Applied Mathematics , Volume 33 , Issue 6 , December 2022 , pp. 1117 - 1169
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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