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Contact lines over random topographical substrates. Part 2. Dynamics

Published online by Cambridge University Press:  11 February 2011

NIKOS SAVVA ,
GRIGORIOS A. PAVLIOTIS  and
SERAFIM KALLIADASIS
NIKOS SAVVA
Affiliation:
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
GRIGORIOS A. PAVLIOTIS
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
SERAFIM KALLIADASIS*
Affiliation:
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

We examine the dynamics of a two-dimensional droplet spreading over a random topographical substrate. Our analysis is based on the formalism developed in Part 1 of this study, where a random substrate was modelled as band-limited white noise. The system of integrodifferential equations for the motion of the contact points over deterministic substrates derived by Savva and Kalliadasis (Phys. Fluids, vol. 21, 2009, 092102) is applicable to the case of random substrates as well. This system is linearized for small substrate amplitudes to obtain stochastic differential equations for the droplet shift and contact line fluctuations in the limit of shallow and slowly varying topographies. Our theoretical predictions for the time evolution of the statistical properties of these quantities are verified by numerical experiments. Considering the statistics of the dynamics allows us to fully address the influence of the substrate variations on wetting. For example, we demonstrate that the droplet wets the substrate less as the substrate roughness increases, illustrating also the possibility of a substrate-induced hysteresis effect. Finally, the analysis of the long-time limit of spreading dynamics for a substrate represented by a band-limited white noise is extended to arbitrary substrate representations. It is shown that the statistics of spreading is independent of the characteristic length scales that naturally arise from the statistical properties of a substrate representation.

JFM classification

Interfacial Flows (free surface): Contact lines Drops and Bubbles: Drops Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 672 , 10 April 2011 , pp. 384 - 410
Copyright
Copyright © Cambridge University Press 2011

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References

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