Bulk stresses due to deformation of the electrical double layer around a charged sphere

A charged particle suspended in an electrolyte solution attracts ions of opposite charge and repels those of like charge. The surface charge and the resulting distributed charge in the fluid comprise an electrical double layer. When a shear flow deforms the diffuse part of the double layer from equilibrium, stresses are generated which make the effective viscosity of the suspension greater than it would be if there were no charges present. In this paper these stresses are calculated for a dilute dispersion of spheres which have small surface charges and which are surrounded by thin double layers. The viscosity is predicted to be Newtonian in extensional flow but shear-thinning with non-zero normal-stress differences in shear flow. For more complex flows a constitutive equation couples the bulk stress directly to the micro-structural deformation responsible for non-Newtonian effects.