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Thermocapillary flows on heated substrates with sinusoidal topography

Published online by Cambridge University Press:  27 November 2018

Jaehyun Yoo ,
Jaewook Nam Open the ORCID record for Jaewook Nam [Opens in a new window]  and
Kyung Hyun Ahn
Jaehyun Yoo
Affiliation:
School of Chemical and Biological Engineering, Institute of Chemical Processes, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Korea
Jaewook Nam*
Affiliation:
School of Chemical and Biological Engineering, Institute of Chemical Processes, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Korea
Kyung Hyun Ahn
Affiliation:
School of Chemical and Biological Engineering, Institute of Chemical Processes, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Korea
*
†Email address for correspondence: jaewooknam@snu.ac.kr
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Abstract

Two-dimensional steady thermocapillary flows in a liquid layer over a substrate, which has a uniform temperature and sinusoidal topography, are investigated by asymptotic theory. Here, the buoyancy effect is negligible and the interface is not significantly disturbed under low Marangoni number and low capillary number. A temperature gradient along the gas/liquid interface causes recirculating flows. For a small aspect ratio, which yields a sinusoidal topography with a long wavelength relative to the mean depth of the liquid layer, the second-order solutions are obtained analytically. The basic solutions show vertical diffusion of heat and vorticity from the substrate and interface, respectively. In the second corrections, the horizontal diffusion of heat weakens the overall flow and the convection of heat intensifies it.

JFM classification

Interfacial Flows (free surface): Capillary flows Convection: Marangoni convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 859 , 25 January 2019 , pp. 992 - 1021
Copyright
© 2018 Cambridge University Press 

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