Intrinsic viscosity of dispersions of core-shell particles

An analytic solution of the Brinkman and Stokes equations for a rigid sphere surrounded by a porous shell in pure straining flow is presented. The solution permits for an analytic determination of the intrinsic viscosity in the dilute-limiting expansion for the steady shear viscosity. The porous layer, characterized by a thickness and a constant permeability, alters the intrinsic viscosity from the Einstein value. A hydrodynamic layer thickness based on the intrinsic viscosity exhibits only a tenuous connection to the actual layer thickness within the present model. Together with the analytical solution for the translational diffusion coefficient, derived previously by Masliyah and co-workers, the present solution allows for a more detailed characterization of polymerically stabilized particles than the commonly used effective hard-sphere model.