Primary electroviscous effect in a suspension of charged porous spheres

Primary electroviscous effect for a dilute suspension of porous spheres with fixed volumetric charge density is investigated theoretically. In the absence of flow, the electrical potential and solution charge density are assumed to satisfy the linearized Poisson-Boltzmann equation. With incorporation of the electrical body force, the Brinkman equation and the Stokes equation are used to govern the fluid flow inside and outside a sphere. The theory is formulated by assuming weak deviation of the charge cloud from its equilibrium state. However, the electrical body force is not restricted to be small compared to the viscous force in the fluid momentum equation. The results show that the double layer distortion is increased with increasing particle permeability, thereby enhancing the relative importance of its stress contribution. Nonetheless, the intrinsic viscosity remains a decreasing function of permeability, similar to the case of uncharged particles.