Electric-field-induced displacement of a charged spherical colloid embedded in an elastic Brinkman medium

TL;DR

This study models and analyzes how charged colloidal particles embedded in an elastic hydrogel displace under electric fields, revealing dependencies on particle size, charge, electrolyte conditions, and gel elasticity, with potential experimental validation.

Contribution

The paper provides numerically exact solutions for electrokinetic and elastic interactions in a hydrogel, linking particle displacement to physical parameters and experimental measurement techniques.

Findings

Displacement depends on particle size, charge, ionic strength, and Young's modulus.

Analytical boundary-layer theory agrees with numerical results in certain limits.

Proposes an experimental method to measure nanometer-scale displacements.

Abstract

When an electric field is applied to an electrolyte-saturated polymer gel embedded with charged colloidal particles, the force that must be exerted by the hydrogel on each particle reflects a delicate balance of electrical, hydrodynamic and elastic stresses. This paper examines the displacement of a single charged spherical inclusion embedded in an uncharged hydrogel. We present numerically exact solutions of coupled electrokinetic transport and elastic-deformation equations, where the gel is treated as an incompressible, elastic Brinkman medium. This model problem demonstrates how the displacement depends on the particle size and charge, the electrolyte ionic strength, and Young's modulus of the polymer skeleton. The numerics are verified, in part, with an analytical (boundary-layer) theory valid when the Debye length is much smaller than the particle radius. Further, we identify a close connection between the displacement when a colloid is immobilized in a gel and its velocity when dispersed in a Newtonian electrolyte. Finally, we describe an experiment where nanometer-scale displacements might be accurately measured using back-focal-plane interferometry. The purpose of such an experiment is to probe physicochemical and rheological characteristics of hydrogel composites, possibly during gelation.