Thermocapillary migration of a spherical drop in an arbitrary transient Stokes flow

Abstract

The present problem is concerned with an arbitrary transient Stokes flow past a viscous drop. The interfacial tension gradient is assumed to be dependent on temperature which is unsteady and hence governed by unsteady heat conduction equation. Solenoidal decomposition method is used to solve the hydrodynamic problem. The unknown coefficients have been computed by using non-isothermal boundary conditions. The drag force and torque exerted on the surface of the drop are computed in the form of Faxen’s laws. Some special cases like flow due to an unsteady Stokeslet and thermal field due to a heat source have been discussed. Asymptotic expansions for drag and torque have been calculated. Further, we have computed migration velocity.