  We present a mesoscopic hydrodynamic description of the dynamics of colloidal
suspensions. We consider the system as a gas of Brownian particles suspended in
a Newtonian heat bath subjected to stationary non-equilibrium conditions
imposed by a velocity field. Using results already obtained in previous studies
in the field by means of a generalized Fokker-Planck equation, we obtain a set
of coupled differential equations for the local diffusion current and the
evolution of the total stress tensor. We find that the dynamic shear viscosity
of the system contains contributions arising from the finite size of the
particles.
