Thermophoretic Motion of a Slightly Deformed Sphere Through a Viscous Fluid

This paper provides a general approach to the solution of the problem of nonisothermal Stokes flow relative to a heat-conducting particle having the shape of a slightly deformed sphere, taking account of Maxwell’s [J. C. Maxwell, Philos. Trans. R. Soc. Lond., 170 (1879), pp. 231–256] thermal creep condition at the surface of the particle. The results, which are of interest in connection with the phenomenon of thermophoresis, have potential applications in aerosol technology, and in the nonisothermal transport and processing of particulate matter. For the specific case of thermally nonconducting particles, the results obtained herein accord with Morrison’s [F. A. Morrison, J. Colloid Interface Sci., 34 (1970), pp. 210–214] proof in the comparable electrophoretic case that the phoretic velocity of a nonconducting, forceand torque-free, nonspherical particle undergoing electrophoresis in a fluid that is otherwise at rest is independent of the size, shape and orientation of the particle, and is identical to that of a sphere.