The homogenized model of small oscillations of complex fluids

Abstract. We consider the system of equations that describes small nonstationary 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 ε in such a way that the sizes of particles are of order ε, the distances between the nearest particles are of order ε, and the stiffness of the interaction force is of order ε. 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.