Desalination shocks in microstructures

TL;DR

This paper predicts nonlinear desalination shocks in charged microstructures at high voltages, revealing their structure, stability, and potential applications in separation and energy storage.

Contribution

It introduces a mathematical theory for desalination shocks, explaining their dynamics and effects in microstructures with variable geometries and surface charges.

Findings

Desalination shocks accelerate and sharpen in narrowing channels.

They decelerate, weaken, or disappear in widening channels.

The theory predicts shock stability and structure under various conditions.

Abstract

Salt transport in bulk electrolytes is limited by diffusion and convection, but in microstructures with charged surfaces (e.g. microfluidic devices, porous media, soils, or biological tissues) surface conduction and electro-osmotic flow also contribute to ionic fluxes. For small applied voltages, these effects lead to well known linear electrokinetic phenomena. In this paper, we predict some surprising nonlinear dynamics that can result from the competition between bulk and interfacial transport at higher voltages. When counter-ions are selectively removed by a membrane or electrode, a "desalination shock" can propagate through the microstructure, leaving in its wake an ultrapure solution, nearly devoid of co-ions and colloidal impurities. We elucidate the basic physics of desalination shocks and develop a mathematical theory of their existence, structure, and stability, allowing for slow variations in surface charge or channel geometry. Via asymptotic approximations and similarity solutions, we show that desalination shocks accelerate and sharpen in narrowing channels, while they decelerate and weaken, and sometimes disappear, in widening channels. These phenomena may find applications in separations (desalination, decontamination, biological assays) and energy storage (batteries, supercapacitors) involving electrolytes in microstructures.