High-frequency viscosity and generalized Stokes-Einstein relations in dense suspensions of porous particles.

We study the high-frequency limiting shear viscosity, η∞, of colloidal suspensions of uncharged porous particles. An individual particle is modeled as a uniformly porous sphere with the internal solvent flow described by the Debye-Bueche-Brinkman equation. A precise hydrodynamic multipole method with a full account of many-particle hydrodynamic interactions encoded in the HYDROMULTIPOLE program extended to porous particles, is used to calculate η∞ as a function of porosity and concentration. The second-order virial expansion for η∞ is derived, and its range of applicability assessed. The simulation results are used to test the validity of generalized Stokes-Einstein relations between η∞ and various short-time diffusion coefficients, and to quantify the accuracy of a simplifying cell model calculation of η∞. An easy-to-use generalized Saitô formula for η∞ is presented which provides a good description of its porosity and concentration dependence.