Robust low-dimensional modelling of falling liquid films subject to variable wall heating
File(s)
Published version
Author(s)
Thompson, Alice B
Gomes, Susana N
Denner, Fabian
Dallaston, Michael C
Kalliadasis, Serafim
Type
Journal Article
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.
Date Issued
2019-10-25
Date Acceptance
2019-07-01
Citation
Journal of Fluid Mechanics, 2019, 877, pp.844-881
ISSN
0022-1120
Publisher
Cambridge University Press (CUP)
Start Page
844
End Page
881
Journal / Book Title
Journal of Fluid Mechanics
Volume
877
Copyright Statement
©The Author(s) 2019. This is an Open Access article, distributed under the terms of the Creative Commons Attributionlicence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, andreproduction in any medium, provided the original work is properly cited.
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000485198600001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
thin films
thermocapillarity
low-dimensional models
LONG WAVES
FLOW
INSTABILITY
Publication Status
Published
Date Publish Online
2019-08-27