Imperial College London
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ProfessorDarrenCrowdy

Faculty of Natural Sciences, Department of Mathematics

Professor in Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8587d.crowdy Website

 
 
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Location

 

735Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Yariv:2020:10.1137/19M1252351,
author = {Yariv, E and Crowdy, D},
doi = {10.1137/19M1252351},
journal = {SIAM Journal on Applied Mathematics},
pages = {1--19},
title = {Longitudinal thermocapillary flow over a dense bubble mattress},
url = {http://dx.doi.org/10.1137/19M1252351},
volume = {80},
year = {2020}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - A common form of superhydrophobic surface is made out of a periodically groovedsolid substrate, wherein cylindrical bubbles are trapped in a Cassie state.  When a macroscopic tem-perature gradient is externally applied, Marangoni forces generate thermocapillary flow of character-istic magnitudeU=−aGσT/μ, in which 2ais the groove width,Gthe applied-gradient magnitude,μthe liquid viscosity, andσTthe derivative of interfacial-tension coefficient with respect to the temper-ature.  We consider the case of a gradient which is applied parallel to the grooves.  Assuming a highlyconducting solid substrate,  we seek to calculate the longitudinal velocity component,  anti-parallelto the applied gradient, and in particular its “slip” value, attained at large distances away from thesurface.  Normalized byU, this value depends only upon the bubble protrusion angle and the solidfraction .  In this paper we consider the small solid-fraction limit  1 and focus upon the case of90protrusion angle, for which this limit is known to be highly singular in the comparable problemof shear-driven flow [Schnitzer,  Phys.  Rev.  Fluids,  1 (2016),  052101].  Using matched asymptoticexpansions, we find that the dimensionless slip velocity is given byπ2/√8 + ln +I−ln(8π2) +o(1).The first two terms in this expansion follow from a lubrication-type analysis of the narrow gap regionseparating two neighboring bubbles.  The subsequentO(1) terms follow from asymptotic matchingwith the bubble-scale region, where the bubbles appear to be touching.  The solution in that regionis obtained using conformal mapping techniques, with the constantIgiven as an explicit integral,evaluated numerically to be 2.27.
AU  - Yariv,E
AU  - Crowdy,D
DO  - 10.1137/19M1252351
EP  - 19
PY  - 2020///
SN  - 0036-1399
SP  - 1
TI  - Longitudinal thermocapillary flow over a dense bubble mattress
T2  - SIAM Journal on Applied Mathematics
UR  - http://dx.doi.org/10.1137/19M1252351
UR  - http://hdl.handle.net/10044/1/73503
VL  - 80
ER  -
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