Thermocapillary migration of a drop with a thermally conducting stagnant cap

Abstract

Hypothesis The thermocapillary migration of a spherical drop with a stagnant cap in the presence of a constant applied temperature gradient can be strongly affected by the finite thermal conductivity of the stagnant cap. Numerics The heat conduction of the stagnant cap is analytically modeled. The effects of the additional interfacial stresses generated by the disturbances to the local temperature field due to the presence of the cap at the fluid-fluid interface and the corresponding velocity of migration of the drop are evaluated by solving for the temperature and hydrodynamic field equations in and around the drop. An asymptotic model is derived to predict the terminal velocity in the presence of an infinitely conducting stagnant cap. Findings The effects of the surface conductivity and size of the stagnation region alongside the bulk thermal conductivities and viscosities of the drop and surrounding media are evaluated. The terminal velocity of the drop is shown to have a monotonic dependence on the conductivity of the stagnant cap. The bounds to the terminal velocity increment due to the stagnant cap are derived. These bounds can be of significance to multiphysics problems involving particle laden drops, Pickering emulsions and other multi-phase technologies where the conductivity of the surface adsorbents is non-negligible.

Keywords: Bubbles; Drops; Emulsions; Multiphase flow; Surface tension; Thermocapillary migration.