We present a versatile theoretical method for calculating the steady-state viscosity and shear relaxation function of strong electrolyte solutions. In this method, the ions are described on a primitive model level as charged Brownian spheres, and the essential ion-ion hydrodynamic interactions (HIs) are accounted for in the shear relaxation effect of the ionic atmosphere. The method combines a many-component mode-coupling theory (MCT) approach by Nägele et al (1998 J. Chem. Phys. 108 9893) with a simplified solution scheme, leading to an analytic expression for the shear relaxation contribution to the viscosity. This expression accounts for both the excluded volumes of the ions and their HIs. We show that the limiting law results for the viscosity of electrolyte mixtures by Falkenhagen and by Onsager and Fuoss are recovered at very low concentrations, and we discuss HIs corrections appearing at higher concentrations. Our numerical results for a 1:1 electrolyte reveal a strong enlargement of the viscosity caused by the HIs. The high-frequency viscosity gives the largest contribution to the total viscosity at higher concentrations.
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