On the basis of a hydrodynamical model analogous to that in critical fluids,
we investigate the influences of shear flow upon the electrostatic contribution
to the viscosity of binary electrolyte solutions in the Debye-H\"{u}ckel
approximation. Within the linear-response theory, we reproduce the classical
limiting law that the excess viscosity is proportional to the square root of
the concentration of the electrolyte. We also extend this result for finite
shear. An analytic expression of the anisotropic structure factor of the charge
density under shear is obtained, and its deformation at large shear rates is
discussed. A non-Newtonian effect caused by deformations of the ionic
atmosphere is also elucidated for τD​γ˙​>1. This finding
concludes that the maximum shear stress that the ionic atmosphere can support
is proportional to λD−3​, where γ˙​, λD​ and
τD​=λD2​/D are, respectively, the shear rate, the Debye screening
length and the Debye relaxation time with D being the relative diffusivity at
the infinite dilution limit of the electrolyte.Comment: 13pages, 2figure