Contact lines over random topographical substrates. Part 2. Dynamics

Savva, Nikos ORCID: https://orcid.org/0000-0003-1549-3154, Pavliotis, G. A. and Kalliadasis, S. 2011. Contact lines over random topographical substrates. Part 2. Dynamics. Journal of Fluid Mechanics 672 , pp. 384-410. 10.1017/S0022112010005987

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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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	contact lines; drops; thin films
Additional Information:	Pdf uploaded in accordance with publisher's policy at http://www.sherpa.ac.uk/romeo/issn/0022-1120/ (accessed 21/02/2014).
Publisher:	Cambridge University Press
ISSN:	0022-1120
Date of First Compliant Deposit:	30 March 2016
Last Modified:	03 May 2023 20:15
URI:	https://orca.cardiff.ac.uk/id/eprint/27702

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