### 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 E in such a way that the sizes of particles are of order E^{3}, the distances between the nearest particles are of order E, and the stiffness of the interaction force is of order E^{2}. 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.

Original language | English (US) |
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Pages (from-to) | 831-862 |

Number of pages | 32 |

Journal | Networks and Heterogeneous Media |

Volume | 3 |

Issue number | 4 |

DOIs | |

State | Published - Dec 11 2008 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Engineering(all)
- Computer Science Applications
- Applied Mathematics

### Cite this

*Networks and Heterogeneous Media*,

*3*(4), 831-862. https://doi.org/10.3934/nhm.2008.3.831