Phoresis of inclusions in viscous media under the combined action of electromagnetism and thermocapillarity: theory

Abstract

The motion of a spherical inclusion in a fluid medium under the combined action of crossed electric and magnetic fields and thermocapillarity is studied theoretically. This motion (phoresis) can be qualified as an elementary motion of fine particles in suspensions, emulsions, aerosols, and liquid foamed materials. A term is introduced into the Stokes equation for a fluid inclusion, which takes into account the thermocapillary force acting on the inclusion due to temperature nonuniformity. Boundary conditions on the particle–medium surface are formulated properly. The solution to the system of equations (Stokes equations for the inclusions and medium, boundary conditions) provides an expression for the velocity of an inclusion in a viscous conducting medium under the combined action of thermocapillarity and electromagnetism. The expression for the velocity of phoresis in dimensionless categories provides the ratio between the viscosity and thermal conductivity of the particle and medium and contains a new dimensionless term, such as the ratio between the thermocapillary and electromagnetic effects (analogue of the Weber number). The formulas derived can be used to calculate the rate of transfer in conducting suspensions and emulsions containing various inclusions. The velocity of bubbles in molten metals (Cu, Al, Fe, Ag) is calculated to show that the effects of electromagnetism and thermocapillarity are comparable. The theoretical approach can be useful for developing a flexible method in the electrotechnology of fluid materials.