Summary
Expressions for the constitutive relation of a small domain in a suspension of identical, spherical particles in a newtonian fluid are put forward. The material parameters in these relations are estimated by approximately solving the microscopic fluid flow field using least squares boundary conditions (to smooth over the particulate irregularities) on the exterior of the domain and exact no-slip conditions on the interior of the fluid domain. The former is anisotropic to adjust for the permeability of the outer boundary. The parameters are compared to other theoretical estimates as found in the literature. Estimates are then presented as functions of the solids volume fraction in both analytical and graphical form, for isotropic and (small) anisotropic microstructures. An impression of the validity range is obtained. Effective expressions for a two-particle interactive force are also derived; these converge to the lubrication limit for high packing densities.
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Koenders, M.A. A first order constitutive model for a particulate suspension of spherical particles. Acta Mechanica 122, 1–19 (1997). https://doi.org/10.1007/BF01181986
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DOI: https://doi.org/10.1007/BF01181986