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The axisymmetric thermocapillary motion of a fluid particle in a tube

Published online by Cambridge University Press:  26 April 2006

Jinnan Chen ,
Zeev Dagan  and
Charles Maldarelli
Jinnan Chen
Affiliation:
Department of Mechanical Engineering, City College of New York, NY 10031, USA
Zeev Dagan
Affiliation:
Department of Mechanical Engineering, City College of New York, NY 10031, USA
Charles Maldarelli
Affiliation:
Levich Institute for Physicoehemical Hydrodynamics, Department of Chemical Engineering, City College of New York, NY 10031, USA
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Abstract

The thermocapillary migration of a fluid particle in a tube, owing to an imposed axial temperature gradient, is studied theoretically for the case of steady, axisymmetric, creeping, translation in the absence of thermal convection and fluid particle distortion from sphericity, and for an insulated tube. Formulated with these assumptions, the migration is a linear Stokes flow which is separable into two fixed-fluid particle flow idealizations. One is the fluid motion in a quiescent continuous phase, owing only to the thermocapillary surface stress. This stress causes fluid streaming which exerts a lift force on the fluid particle in the direction of the warmer fluid described by a lift coefficient. The second idealization is uniform flow in the absence of thermocapillary forces. The force on the fluid particle owing to this flow represents the hydrodynamic resistance to the forward motion of the fluid particle in the presence of the tube wall, and is described in terms of a drag coefficient. Numerical solutions for the lift and drag coefficients are obtained by a boundary collocation technique.

The migration velocity in the tube relative to that under identical conditions in an infinite medium is computed from the ratio of the lift and drag coefficients. The calculations show that for a fixed ratio of the sphere to the tube diameter, as the conductivity of the fluid particle phase decreases relative to that of the continuous phase, a greater proportion of energy is conducted through the gap between the insulated tube wall and the fluid particle. This conduction pattern creates a larger surface temperature gradient, and causes the relative migration velocity to increase. The enhancement in migration for decreasing fluid particle conductivity at a fixed ratio of the sphere to the tube diameter becomes more pronounced as the later ratio increases and the surface gradient intensifies. However, as the gap distance between the sphere and the tube decreases, hydrodynamic retarding forces develop, and these forces are overriding in the sense that the relative migration velocity in the tube decreases monotonically from the value of one as the gap thickness decreases, and therefore the migration velocity in the tube never exceeds the value in an infinite medium.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 233 , December 1991 , pp. 405 - 437
Copyright
© 1991 Cambridge University Press

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