High-frequency viscosity of concentrated porous particles suspensions.

We determine the high-frequency limiting shear viscosity, eta(infinity), in colloidal suspensions of rigid, uniformly porous spheres of radius a as a function of volume fraction phi and (inverse) porosity parameter x. Our study covers the complete fluid-state regime. The flow inside the spheres is modeled by the Debye-Bueche-Brinkman equation using the boundary condition that fluid velocity and stress change continuously across the sphere surfaces. The many-sphere hydrodynamic interactions in concentrated systems are fully accounted for by a precise hydrodynamic multipole method encoded in our HYDROMULTIPOLE program extended to porous particles. A truncated virial expansion is used to derive an accurate and easy-to-use generalized Saito; formula for eta(infinity). The simulation data are used to test the performance of two simplifying effective particle models. The first model describes the effective particle as a nonporous sphere characterized by a single effective radius a(eff)(x)<a. In the more refined second model, the porous spheres are modeled as spherical annulus particles with an inner hydrodynamic radius a(eff)(x) defining the nonporous dry core and characterizing hydrodynamic interactions, and an outer excluded volume radius a characterizing the unchanged direct interactions. Only the second model is in a satisfactory agreement with the simulation data.