The virial expansion of the high-frequency effective viscosity is considered for hard sphere suspensions at equilibrium. The term of the third order in volume fraction, which involves three-particle hydrodynamic interactions, is calculated with high accuracy and the corresponding coefficient in the Saito representation is also evaluated. The method is based on a regularization procedure, which gives the effective viscosity as the sum of convergent integrals over particle configurations. To calculate the hydrodynamic interactions, we apply the efficient algorithm based on the multipole expansion, corrected for lubrication, which has been earlier applied to evaluate the self-diffusion and the sedimentation coefficients. However, in the context of the effective viscosity, we have faced a slower convergence of the results with the increasing number of the included multipoles.
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