Imperial College London
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DrOrySchnitzer

Faculty of Natural Sciences, Department of Mathematics

Reader in Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 3833o.schnitzer Website

 
 
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Location

 

739Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Schnitzer:2020:10.1017/jfm.2020.650,
author = {Schnitzer, O and Davis, AMJ and Yariv, E},
doi = {10.1017/jfm.2020.650},
journal = {Journal of Fluid Mechanics},
pages = {A25--1--A25--29},
title = {Rolling of non wetting droplets down a gently inclined plane},
url = {http://dx.doi.org/10.1017/jfm.2020.650},
volume = {903},
year = {2020}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We analyse the near-rolling motion of nonwetting droplets down a gently inclined plane.Inspired by the scaling analysis of Mahadevan & Pomeau (Phys. Fluids, vol. 11, 1999,pp. 2449), we focus upon the limit of small Bond numbers, where the drop shape is nearlyspherical and the internal flow is approximately a rigid-body rotation except close to theflat spot at the base of the drop. In that region, where the fluid interface appears flat,we obtain an analytical approximation for the flow field. By evaluating the dissipationassociated with that flow we obtain a closed-form approximation for the drop speed.This approximation reveals that the missing prefactor in the Mahadevan–Pomeau scalinglaw is (3π/16)p3/2 ≈ 0.72 — in good agreement with experiments. An unexpectedfeature of the flow field is that it happens to satisfy the no-slip and shear-free conditionssimultaneously over both the solid flat spot and the mobile fluid interface in its vicinity.Furthermore, we show that close to the near-circular contact line the velocity field liesprimarily in the plane locally normal to the contact line; it is analogous there to thelocal solution in the comparable problem of a two-dimensional rolling drop. This analogybreaks down near the two points where the contact line propagates parallel to itself,the local flow being there genuinely three dimensional. These observations illuminate aunique ‘peeling’ mechanism by which a rolling droplet avoids the familiar non-integrablestress singularity at a moving contact line.
AU  - Schnitzer,O
AU  - Davis,AMJ
AU  - Yariv,E
DO  - 10.1017/jfm.2020.650
EP  - 1
PY  - 2020///
SN  - 0022-1120
SP  - 25
TI  - Rolling of non wetting droplets down a gently inclined plane
T2  - Journal of Fluid Mechanics
UR  - http://dx.doi.org/10.1017/jfm.2020.650
UR  - https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/rolling-of-nonwetting-droplets-down-a-gently-inclined-plane/8A6C42922B80C947808FBAD18A51BF50
UR  - http://hdl.handle.net/10044/1/81561
VL  - 903
ER  -
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