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Non-isothermal bubble rise: non-monotonic dependence of surface tension on temperature

Published online by Cambridge University Press:  10 December 2014

M. K. Tripathi ,
K. C. Sahu ,
G. Karapetsas ,
K. Sefiane  and
O. K. Matar
M. K. Tripathi
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Yeddumailaram 502 205, Andhra Pradesh, India
K. C. Sahu
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Yeddumailaram 502 205, Andhra Pradesh, India
G. Karapetsas
Affiliation:
Department of Mechanical Engineering, University of Thessaly, Volos 38334, Greece
K. Sefiane
Affiliation:
School of Engineering, University of Edinburgh, Edinburgh EH9 3JL, UK International Institute for Carbon-Neutral Energy Research (I2CNER) Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
O. K. Matar*
Affiliation:
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: o.matar@imperial.ac.uk
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Abstract

We study the motion of a bubble driven by buoyancy and thermocapillarity in a tube with a non-uniformly heated walls, containing a so-called ‘self-rewetting fluid’; the surface tension of the latter exhibits a parabolic dependence on temperature, with a well-defined minimum. In the Stokes flow limit, we derive the conditions under which a spherical bubble can come to rest in a self-rewetting fluid whose temperature varies linearly in the vertical direction, and demonstrate that this is possible for both positive and negative temperature gradients. This is in contrast to the case of simple fluids whose surface tension decreases linearly with temperature, for which bubble motion is arrested only for negative temperature gradients. In the case of self-rewetting fluids, we propose an analytical expression for the position of bubble arrestment as a function of other dimensionless numbers. We also perform direct numerical simulation of axisymmetric bubble motion in a fluid whose temperature increases linearly with vertical distance from the bottom of the tube; this is done for a range of Bond and Galileo numbers, as well as for various parameters that govern the functional dependence of surface tension on temperature. We demonstrate that bubble motion can be reversed and then arrested only in self-rewetting fluids, and not in linear fluids, for sufficiently small Bond numbers. We also demonstrate that considerable bubble elongation is possible under significant wall confinement, and for strongly self-rewetting fluids and large Bond numbers. The mechanisms underlying the phenomena observed are elucidated by considering how the surface tension dependence on temperature affects the thermocapillary stresses in the flow.

JFM classification

Drops and Bubbles: Drops and Bubbles Multiphase and Particle-laden Flows: Multiphase flow Drops and Bubbles: Thermocapillarity
Type
Papers
Information
Journal of Fluid Mechanics , Volume 763 , 25 January 2015 , pp. 82 - 108
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Copyright
© 2014 Cambridge University Press 

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