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On efficient asymptotic modelling of thin films on thermally conductive substrates

Published online by Cambridge University Press:  31 March 2021

Ryan H. Allaire Open the ORCID record for Ryan H. Allaire [Opens in a new window] ,
Linda J. Cummings Open the ORCID record for Linda J. Cummings [Opens in a new window]  and
Lou Kondic Open the ORCID record for Lou Kondic [Opens in a new window]
Ryan H. Allaire*
Affiliation:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ07102, USA
Linda J. Cummings*
Affiliation:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ07102, USA
Lou Kondic*
Affiliation:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ07102, USA
*
†Email address for correspondence: [email protected], [email protected], [email protected]
†Email address for correspondence: [email protected], [email protected], [email protected]
†Email address for correspondence: [email protected], [email protected], [email protected]
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Abstract

We consider a free-surface thin film placed on a thermally conductive substrate and exposed to an external heat source in a set-up where the heat absorption depends on the local film thickness. Our focus is on modelling film evolution while the film is molten. The evolution of the film modifies local heat flow, which in turn may influence the film surface evolution through thermal variation of the film's material properties. Thermal conductivity of the substrate plays an important role in determining the heat flow and the temperature field in the evolving film and in the substrate itself. In order to reach a tractable formulation, we use asymptotic analysis to develop a novel thermal model that is accurate, computationally efficient, and that accounts for the heat flow in both the in-plane and out-of-plane directions. We apply this model to metal films of nanoscale thickness exposed to heating and melting by laser pulses, a set-up commonly used for self and directed assembly of various metal geometries via dewetting while the films are in the liquid phase. We find that thermal effects play an important role, and in particular that the inclusion of temperature dependence in the metal viscosity modifies the time scale of the evolution significantly. On the other hand, in the considered set-up the Marangoni (thermocapillary) effect turns out to be insignificant.

JFM classification

Interfacial Flows (free surface): Thin films Low-Reynolds-number flows: Lubrication theory Instability: Nonlinear instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A133
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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