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Hydrodynamic boundary effects on thermophoresis of confined colloids

We study hydrodynamic slowing-down of a particle moving in a temperature gradient perpendicular to a wall. At distances much smaller than the particle radius, $h\ll a$, lubrication approximation leads to the reduced velocity $u/u_{0}=3\frac{h}{a}\ln \frac{a}{h}$, with respect to the bulk value $u_{0}$. With Brenner's result for confined diffusion, we find that the trapping efficiency, or effective Soret coefficient, increases logarithmically as the particle gets very close to the wall. This provides a quantitative explanation for the recently observed enhancement of thermophoretic trapping at short distances. Our discussion of parallel and perpendicular thermophoresis in a capillary, reveals a very a good agreement with five recent experiments on charged polystyrene particles.