Brownian Particle Thermal Drift Caused by Hydrodynamic Fluctuations

We have studied the thermophoretic drift of a Brownian particle within the framework of the theory of fluctuating hydrodynamics of Landau and Lifshitz. The stochastic motion of a dispersed particle results from the fluctuating part of the stress tensor of the liquid. In the presence of a temperature gradient, the mean volume force acting on the liquid assumes a finite value due to non-vanishing quadratic terms in the fluctuations, which originate from the temperature dependence of the viscosity. An analytical expression is derived for the drift velocity and compared to experimental results.