Thermophoretic motion of slightly deformed aerosol spheres

The thermophoretic motion of a slightly deformed aerosol sphere in a uniformly prescribed but arbitrarily oriented temperature gradient is analyzed in the steady limit of negligible 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 surface of the particle. The energy and momentum equations governing the system are solved asymptotically using a method of perturbed expansions. To the second order in the small parameter characterizing the deformation of the aerosol particle from the spherical shape, the thermal and hydrodynamic problems are formulated for the general case, and explicit expressions for the thermophoretic velocity of the particle are obtained for the special cases of prolate and oblate spheroids. The agreement between our asymptotic results for a thermophoretic spheroid and the relevant exact or numerical solutions in the literature is quite good, even if the particle deformation from the spherical shape is not very small. Depending on the values of the relative thermal and surface properties of the aerosol spheroid, its thermophoretic mobility normalized by the corresponding value for a spherical particle with equal equatorial radius is not necessarily a monotonic function of the aspect ratio of the spheroid.