Thermocapillary migration of a fluid sphere in a circular Tube
Journal
American Journal of Heat and Mass Transfer
Journal Volume
3
Journal Issue
1
Pages
15-36
Date Issued
2016
Author(s)
Chiu H.C.
Abstract
The thermocapillary motion of a spherical fluid drop along the axis of a circular tube, whose wall may be either insulated or prescribed with a linear temperature distribution, is investigated theoretically in the steady limit of negligible Marangoni and Reynolds numbers. The proximity of the tube wall causes two effects on the thermocapillary migration velocity of the drop: The temperature gradients along the drop surface are altered, thereby the drop is slowed down or speeded up, and the viscous drag on the drop is enhanced. The general solutions to the energy and momentum equations are constructed in combined circular cylindrical and spherical coordinates, and then the boundary conditions are enforced on the tube wall by the Fourier transform and along the drop surface by a collocation method. The collocation results for the normalized drop velocity, obtained as decreasing functions of the drop-to-tube radius ratio, are in good agreement with the asymptotic formulas derived from a method of reflections. The normalized thermocapillary mobility increases/decreases with an increase in the relative thermal conductivity of the drop for the case of a conducting/insulating tube wall and increases with an increase in the relative viscosity of the drop. The boundary effect on the thermocapillary migration of a drop in a tube, which is relatively weak in comparison with the corresponding effect on its sedimentation, is found to be conspicuously different from that in a slit with two plane walls. ? 2016 The author(s).
Subjects
Boundary Effect
Circular Tube
Gas Bubble
Spherical Drop
Thermocapillary Motion
Type
journal article