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Robust low-dimensional modelling of falling liquid films subject to variable wall heating

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Title: Robust low-dimensional modelling of falling liquid films subject to variable wall heating
Authors: Thompson, AB
Gomes, SN
Denner, F
Dallaston, MC
Kalliadasis, S
Item 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.
Issue Date: 25-Oct-2019
Date of Acceptance: 1-Jul-2019
URI: http://hdl.handle.net/10044/1/73980
DOI: https://dx.doi.org/10.1017/jfm.2019.580
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.
Keywords: Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
thin films
thermocapillarity
low-dimensional models
LONG WAVES
FLOW
INSTABILITY
Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
thin films
thermocapillarity
low-dimensional models
LONG WAVES
FLOW
INSTABILITY
Fluids & Plasmas
01 Mathematical Sciences
09 Engineering
Publication Status: Published
Open Access location: https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/robust-lowdimensional-modelling-of-falling-liquid-films-subject-to-variable-wall-heating/F5EAEC79F50416DA2D38D886ACFE3658
Online Publication Date: 2019-08-27
Appears in Collections:Mathematics
Chemical Engineering
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences