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 $\varepsilon$ in
such a way that the sizes of particles are of order
$\varepsilon^{3}$, the distances between the nearest particles are
of order $\varepsilon$, and the stiffness of the interaction force
is of order $\varepsilon^{2}$.
We study the asymptotic behavior of the microscopic model as
$\varepsilon\rightarrow 0$ and obtain the homogenized equations
that can be considered as a macroscopic model of diluted solutions
of interacting colloidal particles.
Citation: M. Berezhnyi, L. Berlyand, Evgen Khruslov. The homogenized model of small oscillations of complex fluids[J]. Networks and Heterogeneous Media, 2008, 3(4): 831-862. doi: 10.3934/nhm.2008.3.831
Abstract
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 $\varepsilon$ in
such a way that the sizes of particles are of order
$\varepsilon^{3}$, the distances between the nearest particles are
of order $\varepsilon$, and the stiffness of the interaction force
is of order $\varepsilon^{2}$.
We study the asymptotic behavior of the microscopic model as
$\varepsilon\rightarrow 0$ and obtain the homogenized equations
that can be considered as a macroscopic model of diluted solutions
of interacting colloidal particles.
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