High-frequency effective viscosity of hard-sphere suspensions

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Abstract
We present a method to determine a theoretical expression for the high-frequency effective viscosity of a suspension of hard spheres. In the explicit calculations we have used two-particle hydrodynamic interactions only. The expression of the effective viscosity has a Saito-like form with a pole near cphi≊0.70, which is comparable to the maximum packing fraction of a hard-sphere system. The final result is in good agreement with experimental and numerical results up to higher volume fractions, as will be shown in comparisons with recent experiments and computer-simulation results. Three- and more-particle hydrodynamic interactions are expected to be important for dense suspensions, but with the presented method it appears that these higher-order interactions give more subtle contributions to the presented expression of the effective viscosity in comparison with the commonly used methods to derive a virial expansion of the effective viscosity itself. This advantageous point will be discussed briefly in the discussion.