Uncoupling electrokinetic flow solutions

TL;DR

This paper presents an eigenvalue decomposition method to uncouple electrokinetic flow equations, simplifying the computation of electrokinetic phenomena and enabling reuse of existing solutions for complex coupled physics.

Contribution

The authors introduce an eigenvalue-based decoupling technique that transforms coupled electrokinetic equations into independent diffusion equations, facilitating easier analysis and computation.

Findings

The method accurately predicts streaming potential and electroosmosis in various scenarios.

It enables reuse of analytical and numerical solutions for coupled electrokinetic problems.

The approach simplifies complex coupled physics into manageable independent problems.

Abstract

The continuum-scale electrokinetic porous-media flow and excess charge redistribution equations are uncoupled using eigenvalue decomposition. The uncoupling results in a pair of independent diffusion equations for "intermediate" potentials subject to modified material properties and boundary conditions. The fluid pressure and electrostatic potential are then found by recombining the solutions to the two intermediate uncoupled problems in a matrix-vector multiply. Expressions for the material properties or source terms in the intermediate uncoupled problem may require extended precision or careful re-writing to avoid numerical cancellation, but the solutions themselves can be computed in typical double precision. The approach works with analytical or gridded numerical solutions and is illustrated through two examples. The solution for flow to a pumping well is manipulated to predict streaming potential and electroosmosis, and a periodic one-dimensional analytical solution is derived and used to predict electroosmosis and streaming potential in a laboratory flow cell subjected to low frequency alternating current and pressure excitation. The examples illustrate the utility of the eigenvalue decoupling approach, repurposing existing analytical solutions and leveraging simpler-to-derive solutions or numerical models for coupled physics.