The axisymmetric motion and deformation of two viscous drops to high temperature regions due to the variation of interfacial in a temperature field with an imposed gradient along their line tension that is usually a decreasing function of increasing of centers are considered. When heat convection and inertial eftemperature. In the case of negligible convective transport fects are neglected, the temperature and velocity fields for signifiof momentum and energy, the theoretical prediction develcant drop deformations are computed using boundary-integral oped by Young et al. (3) for the velocity of a spherical gas techniques for Laplace's and Stokes' equations, respectively. Debubble or liquid drop is tailed numerical results on drop motion, drop deformation, and the temporal evolution of gap width between the drops are presented for equal viscosities of the drops and surrounding fluid.
The effects of the capillary number, the drop size ratio, and the drop-to-medium conductivity ratio on drop motion and deformation are illustrated. It is found that the hydrodynamic interactions between the drops have a stronger effect on the smaller of the where a is the bubble or drop radius, (รT ) ฯฑ is the applied two drops, in terms of both drop motion and drop deformation. temperature gradient, dg/dT is the rate of change of interfa-Deformation has a large effect on the rate of drainage of the thin cial tension with temperature, m is the viscosity of the susfilm between the drops, but relatively little effect on the velocities pending fluid, l is the viscosity ratio, and k is the thermal of the drop centers. The results are discussed in light of previous conductivity ratio between the bubble or drop and the sustheoretical and computational studies of two spherical drops or pending fluid. Such thermocapillary migration of fluid partibubbles in thermocapillary motion, as well as existing lubrication cles has been the subject of extensive research in the past analyses on the close approach and interaction of two deforming few decades due to continued interest in materials processing drops. The numerical results discussed herein are consistent with technologies in space and other microgravitational environand complementary to the theoretical findings of S. G. Yiantsios and R. H. Davis ( J. Colloid Interface Sci. 144, 412 (1991)), who ments. A comprehensive review of recent theoretical and performed a lubrication analysis for two deforming drops in nearexperimental developments is given by Subramanian (4).
contact motion due to gravity and showed that small drop defor-
There exist several theoretical studies on the interaction mations reduce the film drainage rate and prevent drop coalesbetween two spherical drops or bubbles, or among a chain cence in the absence of attractive forces.