A microscopic approach to thermophoresis in colloidal suspensions

We present a general description of thermophoretic phenomena in dilute suspensions of spherical colloids which lie at the basis of the Ludwig/Soret effect. We first consider how a thermal gradient affects a homogeneous fluid showing that, to linear order, no momentum flux is generated in the bulk. The presence of a colloidal particle, however, modifies the pressure tensor of the fluid, thereby creating a velocity field in the neighbourhood of the surface of the colloid, which can be calculated by use of the Navier–Stokes equation. As a consequence, momentum transfer to the colloid takes place. When this effective force is substituted into a Smoluchowski equation for the particle motion, we arrive at a simple and general expression of the Soret coefficient in terms of the colloid–liquid surface tension.