Phoresis Theory for Inclusions in Viscous Media under Common Action of Electromagnetism and Thermocapillarity

Abstract

The motion of a spherical inclusion in a viscous fluid medium under joint action of crossed electric and magnetic fields and thermocapillarity is studied theoretically. This motion (phoresis) can be qualified as an elementary act of the motion of fine particles in suspensions, emulsions, aerosols, and liquid foamed materials. A term is introduced into the Stokes-type equation for a fluid inclusion, which takes into account the thermocapillary force acting on the inclusion due to the nonuniformity of temperature field. Boundary conditions on the particle–medium surface are formulated properly. The solution to the system of equations (Stokes-type equations for the inclusions and medium and boundary conditions) provides the formula for the motion velocity of the viscous inclusion under joint action of thermocapillarity and electromagnetism. The formula for the phoresis rate in dimensionless categories pro-vides the ratio between the viscosity and heat conduction 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 are suitable for calculations of transfer processes in conductive suspensions and emulsions containing various inclusions. The calculation of bubble velocities in molten metals (for example, Cu, Al, Fe, Ag) shows that the effects of electromagnetism and thermocapillarity are comparable. The theoretical approach can be useful for developing quite a flexible method in the electrotechnology of fluid materials.