  We theoretically investigate general properties of driven (sheared) colloidal
suspensions in confinement, based on methods of classical density functional
theory. In the absence of an exact closed (Smoluchowski-) equation for the
one-particle density under shear, we formulate a set of general conditions for
approximations, and show that a simple closure fulfills them. The exact
microscopic stress tensor is identified. Exemplifying the situation near a wall
(oriented parallel to the direction of shear), we note that the microscopic
shear stress is not necessarily homogeneous. Formulating a second equation
additional to the Smoluchowski equation, we achieve a homogeneous shear stress,
and thereby compute the local flow velocity near the wall. This finally leads
to a slip length of the complex fluid at the wall.
