Suspension of solid particles in a newtonian fluid

Abstract We consider the motion of a Newtonian fluid containing solid particles in the case of high concentration (the partial volume of solid is comparable to that of fluid) by using a homogeniztion technique associated with the small parameter ϵ (the ratio of the particle length to the characteristic macroscopical length). The limit behaviour as ϵ → 0 is that of fluid with anisotropy properties associated with a microstructure. The evolution equations for the limit flow and for the microstructure are given.