The homogenized model of small oscillations of complex fluids

We consider the system of equations that describes small non-stationary motions of viscous incompressible fluid with a large number of small rigid interacting particles. This system is a microscopic mathematical model of complex fluids such as colloidal suspensions, polymer solutions etc. We suppose that the system of particles depends on a small parameter E in such a way that the sizes of particles are of order E³, the distances between the nearest particles are of order E, and the stiffness of the interaction force is of order E². We study the asymptotic behavior of the microscopic model as ε → 0 and obtain the homogenized equations that can be considered as a macroscopic model of diluted solutions of interacting colloidal particles.