Linear response functions of an electrolyte solution in a uniform flow

TL;DR

This paper analytically investigates how a uniform flow affects the steady-state electrostatic and ionic responses of a dilute electrolyte, revealing flow-induced distortions and screening effects.

Contribution

It provides a novel analytical framework for understanding electrolyte responses under flow, extending classical theories to include flow-induced symmetry breaking.

Findings

Flow breaks radial symmetry of electrolyte response functions.

Moving charges experience altered screening, with under- and over-screening effects.

Flow induces dipolar electric fields and currents far from the source.

Abstract

We study the steady state response of a dilute monovalent electrolyte solution to an external source with a constant relative velocity with respect to the fluid. The source is taken as a combination of three perturbations: an external force acting on the fluid, an externally imposed ionic chemical potential, and an external charge density. The linear response functions are obtained analytically and can be decoupled into three independent terms, corresponding to (i) fluid flow and pressure, (ii) total ionic number density and current, and (iii) charge density, electrostatic potential and electric current. It is shown how the uniform flow breaks the equilibrium radial symmetry of the response functions, leading to a distortion of the ionic cloud and electrostatic potential, which deviate from the standard Debye-H\"uckel result. The potential of a moving charge is under-screened in its direction of motion and over-screened in the opposite direction and normal plane. As a result, an unscreened dipolar electric field and electric currents are induced far from the charged source. We relate our general formalism to several experimental setups, such as colloidal sedimentation.