Hydrodynamic behavior of Brownian particles in a position-dependent constant force field

The diffusion equation in physical space-time for a Brownian particle drive n by an external force field has been derived by Smoluchowski in the two pa rticular cases where the external field is uniform or varies linearly with position (elastic force). In more general cases, correction terms must be a dded to the Smoluchowski equation. We show here how to use a multi-scale Ch apman-Enskog expansion to obtain, in the hydrodynamic limit, the first corr ective terms to the Smoluchowski equation, without any restriction on the f riction coefficient, and for any sufficiently small position-dependent cons tant force field. We also compare our approach with the works of Wilemski, Titulaer, and van Kampen. (C) 1999 American Institute of Physics. [S0022-24 88(99)00806-3].