Thermocapillary migration of spherical droplet with a particle laden interface – Limit of Conducting Stagnant Cap.

The thermocapillary migration of a drop under an applied temperature gradient is a well-established phenomenon (Young et al. 1959). Often in practical applications, this migration is hindered by the presence of a stagnation region due to the downstream accumulation of surface impurities/surfactants along the drop surface. Models incorporating the effect of this stagnant region (stagnant cap) on the hydrodynamics of the drop have been effective in determining the forces on the drop and its terminal velocity (Kim and Subramaniam 1989). Applications in microfluidics/microgravity problems involving larger adsorbed quantities on the fluid interface (Ex. colloidal particles adsorbed onto larger drops/bubbles/foams etc. (Lan 2012)) raise the interesting prospect that the stagnant cap can not only affect the flow field, but also the local temperature field. We show that the surface area and thermal conductivity of the stagnant cap play a significant role in determining the Marangoni stresses on the drop. We also investigate the role of the transport properties of the drop and suspending medium in this system. Finally, we use asymptotic models to analytically determine the bounds of the effect of the stagnant cap conductivity on the terminal velocity of the drop.