Similarity solutions for slender dry patches with thermocapillarity View Full Text


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Article Info

DATE

2002-12

AUTHORS

D. Holland, S.K. Wilson, B.R. Duffy

ABSTRACT

The lubrication approximation is used to investigate slender dry patches in an infinitely wide film of viscous fluid flowing steadily on an inclined plane that is either heated or cooled relative to the surrounding atmosphere. Four non-isothermal situations in which thermocapillary effects play a significant role are considered. Similarity solutions describing a thermocapillary-driven flow with a dry patch that is widening or narrowing due to either gravitational or surface-tension effects on a non-uniformly heated or cooled substrate are obtained, and examples of these solutions, when the substrate temperature gradient depends on the longitudinal coordinate according to a general power law, are presented. When gravitational effects are strong, the solution contains a free parameter, and for each value of this parameter there is a unique solution representing both a narrowing pendent dry patch and a widening sessile dry patch, whose transverse profile has a monotonically increasing shape. When surface-tension effects are strong, the solution also contains a free parameter, and for each value of this parameter there is both a unique solution representing a narrowing dry patch, whose transverse profile has a monotonically increasing shape, and a one-parameter family of solutions representing a widening dry patch, whose transverse profile has a capillary ridge near the contact line and decays in an oscillatory manner far from it. Similarity solutions are also obtained for both a gravity-driven and a constant-surface-shear-stress-driven flow with a dry patch that is widening or narrowing due to thermocapillarity on a uniformly heated or cooled substrate. The solutions in both cases contain a free parameter, and for each value of this parameter there is a unique solution representing both a narrowing dry patch on a heated substrate and a widening dry patch on a cooled substrate, whose transverse profile has a monotonically increasing shape. More... »

PAGES

369-394

Identifiers

URI

http://scigraph.springernature.com/pub.10.1023/a:1021262720914

DOI

http://dx.doi.org/10.1023/a:1021262720914

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1009025374


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