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@article{Brandao:2022:10.1017/S095679252200002X,
author = {Brandao, R and Schnitzer, O},
doi = {10.1017/S095679252200002X},
journal = {European Journal of Applied Mathematics},
pages = {1117--1169},
title = {Leidenfrost levitation of a spherical particle above a liquid bath: evolution of the vapour-film morphology with particle size},
url = {http://dx.doi.org/10.1017/S095679252200002X},
volume = {33},
year = {2022}
}

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TY  - JOUR
AB  - 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 sur16 prisingly 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 im20 portant 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 sym metry axis become indistinguishable and merge. Subsequently, the inner section of that merger transitions into a uniform-thickness film that expands radially, gradually squish24 ing larger and 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 es sentially 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 cont
AU  - Brandao,R
AU  - Schnitzer,O
DO  - 10.1017/S095679252200002X
EP  - 1169
PY  - 2022///
SN  - 0956-7925
SP  - 1117
TI  - Leidenfrost levitation of a spherical particle above a liquid bath: evolution of the vapour-film morphology with particle size
T2  - European Journal of Applied Mathematics
UR  - http://dx.doi.org/10.1017/S095679252200002X
UR  - https://www.cambridge.org/core/journals/european-journal-of-applied-mathematics/article/leidenfrost-levitation-of-a-spherical-particle-above-a-liquid-bath-evolution-of-the-vapourfilm-morphology-with-particle-size/5024A97482E3C5F187BEC3746607BFB8
UR  - http://hdl.handle.net/10044/1/94245
VL  - 33
ER  -

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