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Contact lines over random topographical substrates. Part 1. Statics

Savva, Nikos, Pavliotis, Grigirios A. and Kalliadasis, Serafim 2011. Contact lines over random topographical substrates. Part 1. Statics. Journal of Fluid Mechanics 672 , pp. 358-383. 10.1017/S0022112010005975

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Abstract

We investigate theoretically the statistics of the equilibria of two-dimensional droplets over random topographical substrates. The substrates are appropriately represented as families of certain stationary random functions parametrized by a characteristic amplitude and wavenumber. In the limit of shallow topographies and small contact angles, a linearization about the flat-substrate equilibrium reveals that the droplet footprint is adequately approximated by a zero-mean, normally distributed random variable. The theoretical analysis of the statistics of droplet shift along the substrate is highly non-trivial. However, for weakly asymmetric substrates it can be shown analytically that the droplet shift approaches a Cauchy random variable; for fully asymmetric substrates its probability density is obtained via Padé approximants. Generalization to arbitrary stationary random functions does not change qualitatively the behaviour of the statistics with respect to the characteristic amplitude and wavenumber of the substrate. Our theoretical results are verified by numerical experiments, which also suggest that on average a random substrate neither enhances nor reduces droplet wetting. To address the question of the influence of substrate roughness on wetting, a stability analysis of the equilibria must be performed so that we can distinguish between stable and unstable equilibria, which in turn requires modelling the dynamics. This is the subject of Part 2 of this study.

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: 04 Jun 2017 03:50
URI: http://orca.cf.ac.uk/id/eprint/27703

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Cited 19 times in Web of Science. View in Web of Science.

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