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An extended Landau–Levich model for the dragging of a thin liquid film with a propagating surface acoustic wave

Published online by Cambridge University Press:  25 November 2016

Matvey Morozov  and
Ofer Manor
Matvey Morozov
Affiliation:
Department of Chemical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
Ofer Manor*
Affiliation:
Department of Chemical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
*
†Email address for correspondence: [email protected]
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Abstract

In this paper we revisit the Landau and Levich analysis of a coating flow in the case where the flow in the thin liquid film is supported by a Rayleigh surface acoustic wave (SAW), propagating in the solid substrate. Our theoretical analysis reveals that the geometry of the film evolves under the action of the propagating SAW in a manner that is similar to the evolution of films that are being deposited using the dip coating technique. We show that in a steady state the thin-film evolution equation reduces to a generalized Landau–Levich equation with the dragging velocity, imposed by the SAW, depending on the local film thickness. We demonstrate that the generalized Landau–Levich equation has a branch of stable steady state solutions and a branch of unstable solutions. The branches meet at a saddle-node bifurcation point corresponding to the threshold value of the SAW intensity. Below the threshold value no steady states were found and our numerical computations suggest a gradual thinning of the liquid film from its initial geometry.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Low-Reynolds-number flows: Lubrication theory Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 810 , 10 January 2017 , pp. 307 - 322
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Copyright
© 2016 Cambridge University Press 

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