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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Computer Science Applications
- Applied Mathematics