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Regimes of thermocapillary migration of droplets under partial wetting conditions

Published online by Cambridge University Press:  18 March 2010

J. M. GOMBA  and
G. M. HOMSY
J. M. GOMBA*
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, California 93106-5070, USA
G. M. HOMSY
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, California 93106-5070, USA
*
†Present address: Instituto de Física Arroyo Seco, UNCPBA and CONICET, 7000 Tandil, Argentina. Email address for correspondence: jgomba@engineering.ucsb.edu
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Abstract

We study the thermocapillary migration of two-dimensional droplets of partially wetting liquids on a non-uniform heated substrate. An equation for the thickness profile of the droplet is derived by employing lubrication approximations. The model includes the effect of a non-zero contact angle introduced through a disjoining–conjoining pressure term. Instead of assuming a fixed shape for the droplet, as in previous works, here we allow the droplet to change its profile with time. We identify and describe three different regimes of behaviour. For small contact angles, the droplet spreads into a long film profile with a capillary ridge near the leading edge, a behaviour that resembles the experiments on Marangoni films reported by Ludviksson & Lightfoot (Am. Inst. Chem. Eng. J., vol. 17, 1971, pp. 1166). For large contact angles, the droplet moves as a single entity, weakly distorted from its static shape. This regime is the usual one reported in experiments on thermocapillary migration of droplets. We also show some intriguing morphologies that appear in the transition between these two regimes. The occurrence of these three regimes and their dependence on various parameters is analysed.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 647: Dedicated to Professor S. H. Davis on his 70th birthday , 25 March 2010 , pp. 125 - 142
Copyright
Copyright © Cambridge University Press 2010

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