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Instability, rupture and fluctuations in thin liquid films: Theory and computations

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Title: Instability, rupture and fluctuations in thin liquid films: Theory and computations
Authors: Durán-Olivencia, MA
Gvalani, RS
Kalliadasis, S
Pavliotis, GA
Item Type: Journal Article
Abstract: Thin liquid films are ubiquitous in natural phenomena and technological applications. They have been extensively studied via deterministic hydrodynamic equations, but thermal fluctuations often play a crucial role that needs to be understood. An example of this is dewetting, which involves the rupture of a thin liquid film and the formation of droplets. Such a process is thermally activated and requires fluctuations to be taken into account self-consistently. In this work we present an analytical and numerical study of a stochastic thin-film equation derived from first principles. Following a brief review of the derivation, we scrutinise the behaviour of the equation in the limit of perfectly correlated noise along the wall-normal direction, as opposed to the perfectly uncorrelated limit studied by Grün et al. (J Stat Phys 122(6):1261–1291, 2006). We also present a numerical scheme based on a spectral collocation method, which is then utilised to simulate the stochastic thin-film equation. This scheme seems to be very convenient for numerical studies of the stochastic thin-film equation, since it makes it easier to select the frequency modes of the noise (following the spirit of the long-wave approximation). With our numerical scheme we explore the fluctuating dynamics of the thin film and the behaviour of its free energy in the vicinity of rupture. Finally, we study the effect of the noise intensity on the rupture time, using a large number of sample paths as compared to previous studies.
Issue Date: 28-Feb-2019
Date of Acceptance: 28-Nov-2018
URI: http://hdl.handle.net/10044/1/66627
DOI: https://dx.doi.org/10.1007/s10955-018-2200-0
ISSN: 0022-4715
Publisher: Springer Nature
Start Page: 579
End Page: 604
Journal / Book Title: Journal of Statistical Physics
Volume: 174
Issue: 3
Copyright Statement: © 2019 The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Sponsor/Funder: Commission of the European Communities
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: 247031
Keywords: physics.flu-dyn
01 Mathematical Sciences
02 Physical Sciences
Fluids & Plasmas
Publication Status: Published
Open Access location: https://link.springer.com/article/10.1007/s10955-018-2200-0
Online Publication Date: 2019-01-21
Appears in Collections:Mathematics
Chemical Engineering
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences