Thermophoresis of a spherical particle straddling the interface of a semi-infinite micropolar fluid

Abstract

The quasi-steady thermophoretic motion of a spherical particle straddling the flat interface of a semi-infinite micropolar fluid flow is investigated. The Reynolds numbers of the micropolar fluid and also the capillary number are assumed to be small. The case of 90° contact angle with flat surface is considered. The Knudsen number is assumed to be in the slip-flow regime. Various types of slip conditions are considered on the immersed portion of the particle surface: frictional and thermal slip for linear velocity and also microrotation slip. The cases of axisymmetric and asymmetric motions are studied. Expressions for thermophoretic velocities, forces and couples on the half-submerged sphere are obtained and their variations represented graphically as functions of the Fourier thermal conductivities, Knudsen number, micropolarity parameter, frictional slip parameter and the thermal stress slip parameter. The limiting cases of classical viscous fluid with thermophoresis are also discussed.