Affiliations: Darmstadt University of Technology, Darmstadt, Germany. E-mails: berezhnyi@mathematik.tu-darmstadt.de, berezhnoy_m@rambler.ru | Institute for Low Temperature Physics and Engineering, Ukrainian Academy of Sciences, Kharkiv, Ukraine. E-mail: khruslov@ilt.kharkov.ua
Abstract: A viscous incompressible fluid with a large number of small axially symmetric solid particles is considered. It is assumed that the particles are identically oriented and under the influence of the fluid move translationally or rotate around a symmetry axis with the direction of their symmetry axes unchanged. The asymptotic behavior of oscillations of the system is studied, when the diameters of particles and distances between the nearest particles are decreased. The equations, describing the homogenized model of the system, are derived. It is shown that the homogenized equations correspond to a non-standard hydrodynamics. Namely, the homogenized stress tensor linearly depends not only on the strain tensor but also on the rotation tensor.
