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Spreading and bistability of droplets on differentially heated substrates

Published online by Cambridge University Press:  17 May 2013

J. B. Bostwick
J. B. Bostwick*
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA
*
†Email address for correspondence: [email protected]
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Abstract

An axisymmetric drop spreads on a radially heated, partially wetting solid substrate in a rotating geometry. The lubrication approximation is applied to the field equations for this thin viscous drop to yield an evolution equation that captures the dependence of viscosity, surface tension, gravity, centrifugal forces and thermocapillarity. We study the quasi-static spreading regime, whereby droplet motion is controlled by a constitutive law that relates the contact angle to the contact-line speed. Non-uniform heating of the substrate can generate both vertical and radial temperature gradients along the drop interface, which produce distinct thermocapillary forces and equivalently flows that affect the spreading process. For the non-rotating system, competition between surface chemistry (wetting) and thermocapillary flows induced by the thermal gradients gives rise to bistability in certain regions of parameter space in which the droplets converge to an equilibrium shape. The centrifugal forces that develop in a rotating geometry enlarge the bistability regions. Parameter regimes in which the droplet spreads indefinitely are identified and spreading laws are computed to compare with experimental results from the literature.

JFM classification

Drops and Bubbles: Drops and Bubbles Interfacial Flows (free surface): Interfacial Flows (free surface) Drops and Bubbles: Thermocapillarity
Type
Papers
Information
Journal of Fluid Mechanics , Volume 725 , 25 June 2013 , pp. 566 - 587
Copyright
©2013 Cambridge University Press 

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