We discuss complex fluids that are comprised of a solvent, which is an incompressible Newtonian fluid, and particulate matter in it. The complex fluid occupies a region in physical space. The particles are described using a finite dimensional manifold M, which serves as configuration space. Simple models [15, 29] represent complicated objects by retaining very few degrees of freedom, and in those cases or. In general, there is no reason why the number of degrees of freedom of the particles should equal, or be related to the number of degrees of freedom of ambient physical space. We will consider as starting point kinetic descriptions of the particles.