Electroviscous effects of simple electrolytes under shear

TL;DR

This paper investigates how shear flow affects the electrostatic contribution to viscosity in electrolyte solutions, extending classical results to finite shear and analyzing ionic atmosphere deformation and non-Newtonian effects.

Contribution

It provides an analytic expression for the anisotropic structure factor under shear and explores the maximum shear stress ionic atmospheres can sustain, extending classical electroviscous theory.

Findings

Excess viscosity proportional to square root of electrolyte concentration.

Deformation of ionic atmosphere at large shear rates.

Maximum shear stress supported by ionic atmosphere scales with Debye length.

Abstract

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 $\tau_D\dot{\gamma}>1$. This finding concludes that the maximum shear stress that the ionic atmosphere can support is proportional to $\lambda_D^{-3}$, where $\dot{\gamma}$, $\lambda_D$ and $\tau_D=\lambda_D^2/D$ 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.