Thompson, Alice B., Gomes, Susana N., Denner, Fabian, Dallaston, Michael C. and Kalliadasis, Serafim (2019) Robust low-dimensional modelling of falling liquid films subject to variable wall heating. Journal of Fluid Mechanics, 877 . pp. 844-881. doi:10.1017/jfm.2019.580 ISSN 0022-1120.

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Abstract

Accurate low-dimensional models for the dynamics of falling liquid films subject to localized or time-varying heating are essential for applications that involve patterning or control. However, existing modelling methodologies either fail to respect fundamental thermodynamic properties or else do not accurately capture the effects of advection and diffusion on the temperature profile. We argue that the best-performing long-wave models are those that give the surface temperature implicitly as the solution of an evolution equation in which the wall temperature alone (and none of its derivatives) appears as a source term. We show that, for both flat and non-uniform films, such a model can be rationally derived by expanding the temperature field about its free-surface values. We test this model in linear and nonlinear regimes, and show that its predictions are in remarkable quantitative agreement with full Navier–Stokes calculations regarding the surface temperature, the internal temperature field and the surface displacement that would result from temperature-induced Marangoni stresses.

Item Type:	Journal Article
Subjects:	Q Science > QC Physics T Technology > TA Engineering (General). Civil engineering (General)
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Thin films , Thin films -- Thermal properties, Thin films -- Effect of temperature on, Thin films -- Surfaces
Journal or Publication Title:	Journal of Fluid Mechanics
Publisher:	Cambridge University Press
ISSN:	0022-1120
Official Date:	25 October 2019
Dates:	Date Event 25 October 2019 Published 27 August 2019 Available 1 July 2019 Accepted
Volume:	877
Page Range:	pp. 844-881
DOI:	10.1017/jfm.2019.580
Status:	Peer Reviewed
Publication Status:	Published
Reuse Statement (publisher, data, author rights):	This article has been published in a revised form in Journal of Fluid Mechanics [http://doi.org/XXX]. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © copyright holder.
Access rights to Published version:	Open Access (Creative Commons)
Copyright Holders:	© The Author(s) 2019
Date of first compliant deposit:	4 July 2019
Date of first compliant Open Access:	27 January 2020
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID EP/K041134/1 [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266 EP/M021556/1 [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266 EP/K008595/1 [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266 EP/L020564/1 [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266 EP/K023154/1 [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266 EP/P026044/1 [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266 ECF-2018-536 Leverhulme Trust http://dx.doi.org/10.13039/501100000275
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