Axisymmetric Thermocapillary Migration of Two Deformable Viscous Drops

Abstract

The axisymmetric motion and deformation of two viscous drops in a temperature field with an imposed gradient along their line of centers are considered. When heat convection and inertial effects are neglected, the temperature and velocity fields for significant drop deformations are computed using boundary-integral techniques for Laplace's and Stokes’ equations, respectively. Detailed 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 two drops, in terms of both drop motion and drop deformation. Deformation has a large effect on the rate of drainage of the thin film between the drops, but relatively little effect on the velocities of the drop centers. The results are discussed in light of previous theoretical and computational studies of two spherical drops or bubbles in thermocapillary motion, as well as existing lubrication analyses on the close approach and interaction of two deforming drops. The numerical results discussed herein are consistent with and complementary to the theoretical findings of S. G. Yiantsios and R. H. Davis ( J. Colloid Interface Sci. 144,412 (1991)), who performed a lubrication analysis for two deforming drops in near-contact motion due to gravity and showed that small drop deformations reduce the film drainage rate and prevent drop coalescence in the absence of attractive forces.