Droplet interactions in thermocapillary migration

Abstract

The thermocapillary motion of an arbitrary finite cluster of spherical droplets is considered. The droplets are allowed to differ in radius and in physical properties. The theory developed is the most general solution to the problem of thermocapillary motion of an assemblage of fluid spheres in a three-dimensional unbounded medium. Using a boundary collocation technique, the appropriate energy and momentum equations are solved in the quasi-steady situation and the interaction effects among the droplets are calculated for various cases. For the thermocapillary motion of two-droplet systems, our results for the droplet interaction parameters agree very well with the exact solutions obtained by using spherical bipolar coordinates or the asymptotic solutions obtained by using a method of reflections. The mobility parameters of linear chains of three droplets have been calculated, showing that the existence of the third droplet can significantly affect the mobilities of the other two droplets. All of our data for the specialcase of multiple gas bubbles demonstrate the fact that the thermocapillary migration velocity of each bubble is unaffected by the presence of the others if all the bubbles have identical radii. Finally, our numerical results for the interaction between two droplets are used to find the effect of volume fractions of droplets of each type on the average thermocapillary migration velocities in a bounded dilute suspension.