Effective viscosity of dense colloidal crystals

An exact scheme is presented to determine the effective viscosity tensor fo r periodic arrays of hard spherical particles, suspended in a Newtonian flu id. In the highly symmetric case of cubic lattices this tensor is character ized by only two parameters. These parameters are calculated numerically fo r the three cubic lattice types and for the whole range of volume fractions . The correctness of the present method and its numerical implementation is confirmed by a comparison with the numerical and analytical results known from the literature. Some regular terms are determined that enter singular perturbation expansions suitable for high concentrations. Previous results for these terms are shown to be highly inaccurate. The modified expansions approach the exact numerical results over a range of densities extending to relatively low concentrations. The effective viscosity is examined for sim ple tetragonal (st) lattices and the results for various structures of the st type can be qualitatively understood on the basis of the motion of the s pheres in response to the ambient shear flow. The angular velocity of the s pheres-relative to the shear flow-is shown to be nonzero for certain orient ations of the st lattice with respect to the shear flow, in contrast to wha t has been known for cubic arrays. Finite viscosities are found in most cas es where the particles are in contact as they are allowed to move in either rigid planar or linelike structures, or they can perform a smooth rolling motion. The only occurrence where the viscosity diverges for a st structure , or equally any other Bravais lattice, is for the case of close packing. M oreover, the concentration-dependent shear viscosity is determined for a va riety of microstructures and the results are compared with recent data obta ined from experiments on ordered hard-sphere suspensions.