Thermophoresis of an aerosol spheroid along its axis of revolution

Abstract

The thermophoretic motion of a spheroidal particle freely suspended in a gaseous medium prescribed with a uniform temperature gradient along the axis of revolution of the particle is studied theoretically in the steady limit of small Peclet and Reynolds numbers. The Knudsen number is assumed to be small so that the fluid flow is described by a continuum model with a temperature jump, a thermal slip, and a frictional slip at the particle surface. The general solutions in prolate and oblate spheroidal coordinates can be expressed in infinite-series forms of separation of variables for the temperature distribution and of semiseparation of variables for the stream function. The jump/slip boundary conditions on the particle surface are applied to these general solutions to determine the unknown coefficients of the leading orders, which can be numerical results obtained from a boundary-collocation method or explicit formulas derived analytically. Numerical results for the thermophoretic velocity of the spheroidal particle are obtained in a broad range of its aspect ratio with good convergence behavior for various cases. For the axisymmetric thermophoresis of an aerosol spheroid, prolate, or oblate, with no temperature jump and frictional slip at its surface, our results agree excellently with the analytical solution obtained previously. The agreement between our results and the available numerical solutions obtained by using a singularity method is also very good. For most practical cases of a spheroid with a specified aspect ratio, the thermophoretic mobility of the particle is not a monotonic function of its relative jump/slip coefficients and thermal conductivity. The axisymmetric thermophoretic mobilities of a prolate spheroid and of an oblate spheroid with large aspect ratios can be much greater and smaller, respectively, than that of a sphere with the same equatorial radius.