On the asymptotic analysis of surface-stress-driven thin-layer flow

Leonard W. Schwartz
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Leonard W. Schwartz: Department of Mechanical Engineering The University of Delaware Newark

A chapter in Practical Asymptotics, 2001, pp 171-188 from Springer

Abstract: Abstract It has been demonstrated experimentally that thin liquid layers may be applied to a solid surface or substrate if a temperature gradient is applied which results in a surface tension gradient and surface traction. Two related problems are considered here by means of the long-wave or lubrication theory. In the first problem, an improved estimate of the applied liquid coating thickness for a liquid being drawn from a bath is found through asymptotic and numerical matching. Secondly, the theory is extended to consider substrates that are not perfectly wetted but exhibit a finite equilibrium contact angle for the coating liquid. This extension incorporates the substrate energetics using a disjoining pressure functional. Unsteady flows are calculated on a substrate of nonuniform wettability. The finite contact angle value required to stop stress-driven flow is predicted and the resulting steady profiles are compared with experimental results for several values of the applied stress.

Keywords: thin-layer flow; asymptotic analysis; Marangoni effect; finite contact angle; numerical simulation (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-010-0698-9_9

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DOI: 10.1007/978-94-010-0698-9_9

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