Thermocapillary motion of a fluid droplet perpendicular to two plane walls
Resource
Chemical Engineering Science 61 (16): 5221-5235
Journal
Chemical Engineering Science
Journal Volume
61
Journal Issue
16
Pages
5221-5235
Date Issued
2006
Date
2006
Author(s)
Chang, Yu C.
Abstract
The quasisteady problem of the thermocapillary migration of a spherical fluid droplet situated at an arbitrary position between two infinite parallel plane walls is studied theoretically in the limit of negligible Marangoni and Reynolds numbers. The applied temperature gradient is constant and perpendicular to the plane walls. The presence of the plane walls causes two basic effects on the droplet velocity: first, the local temperature gradient on the droplet surface is altered by the walls, thereby speeding up or slowing down the droplet; secondly, the walls increase viscous retardation of the moving droplet. To solve the thermal and hydrodynamic governing equations, the general solutions are constructed from the fundamental solutions in both cylindrical and spherical coordinates. The boundary conditions are enforced first at the plane walls by the Hankel transforms and then on the droplet surface by a collocation technique. Numerical results for the thermocapillary migration velocity of the droplet relative to that under identical conditions in an unbounded medium are presented for various values of the relative viscosity and thermal conductivity of the droplet as well as the relative separation distances between the droplet and the confining walls. The collocation results agree well with the approximate analytical solutions obtained by using a method of reflections. The presence of the walls always reduces the droplet velocity, irrespective of the relative transport properties of the droplet or the relative droplet-wall separation distances. The boundary effect on thermocapillary migration of a droplet normal to two plane walls, which is relatively weak in comparison with the corresponding effect on sedimentation, is found to be quite significant and generally stronger than that parallel to the plane walls. © 2006 Elsevier Ltd. All rights reserved.
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