Electrolyte flows under magnetic fields: Manning-like counterion condensation in one dimension

TL;DR

This paper develops a theoretical model for electrolyte flows under magnetic fields, revealing a magnetic-field-induced Manning-like counterion condensation transition in one dimension, with potential applications in microfluidics and electrochemistry.

Contribution

It introduces a new theoretical framework showing how magnetic fields induce Manning-like counterion condensation in electrolyte flows, extending classical electrostatics to non-equilibrium systems.

Findings

Magnetic fields cause a Manning-like condensation transition in electrolyte flows.

Derived an eigenvalue equation predicting a sharp threshold for counterion enrichment.

Magnetic parameters can tune the Manning criterion in cylindrical flows.

Abstract

We present a theoretical framework for unidirectional electromagnetohydrodynamic flow of dilute electrolytes under perpendicular magnetic fields. Starting from the Navier--Stokes equation coupled with the Poisson--Nernst--Planck formulation, we show that the problem admits a sequential decoupling: the Stokes equation is solved first to obtain the velocity profile, which defines a hydrodynamic potential entering the Nernst--Planck description of ions. This Lorentz-force-induced potential competes with electrostatic attraction and significantly alters ionic distributions. We analyze this mechanism in two canonical geometries. In planar Couette shear, it produces a Manning--Oosawa-like condensation transition in one dimension, a phenomenon absent in classical electrostatics. We derive an eigenvalue equation predicting a sharp threshold between counterion enrichment and depletion at the charged wall. In cylindrical Taylor--Couette flow, the same effect shifts the classical Manning criterion by a magnetic parameter, enabling tunable control of condensation. These findings extend Manning--Oosawa phenomenology to driven, non-equilibrium systems and provide a basis for magnetic manipulation of screening in electrolytes, with implications for microfluidics, electrochemical systems, and nonlinear boundary-value theory.