The homogenized model of small oscillations of complex fluids
Maksym Berezhnyi, Leonid V. Berlyand, Evgen Khruslov · Networks and Heterogeneous Media · 2008
We consider the system of equations that describes smallnon-stationary motions of viscous incompressible fluid with alarge number of small rigid interacting particles. This system isa microscopic mathematical model of complex fluids such ascolloidal suspensions, polymer solutions etc. We suppose that thesystem of particles depends on a small parameter $\varepsilon$ insuch a way that the sizes of particles are of order$\varepsilon^{3}$, the distances between the nearest particles areof order $\varepsilon$, and the stiffness of the interaction forceis of order $\varepsilon^{2}$.We study the asymptotic behavior of the microscopic model as$\varepsilon\rightarrow 0$ and obtain the homogenized equationsthat can be considered as a macroscopic model of diluted solutionsof interacting colloidal particles.