Predicting tensorial electrophoretic effects in asymmetric colloids

TL;DR

This paper introduces a numerical method to predict the tensorial electrophoretic response of asymmetric colloids by modeling fluid and charge interactions with high accuracy, applicable to biological and technological colloids.

Contribution

The paper presents a novel Stokeslet-based numerical approach for accurately predicting the electrophoretic response of asymmetric colloids with complex charge distributions.

Findings

Sphere with 1999 stokeslets matches solid sphere flow within 1%

Charged sphere with 3998 stokeslets obeys Smoluchowski prediction

Dipolar and quadrupolar charge distributions rotate and translate as predicted

Abstract

We formulate a numerical method for predicting the tensorial linear response of a rigid, asymmetrically charged body to an applied electric field. This prediction requires calculating the response of the fluid to the Stokes drag forces on the moving body and on the countercharges near its surface. To determine the fluid's motion, we represent both the body and the countercharges using many point sources of drag known as stokeslets. Finding the correct flow field amounts to finding the set of drag forces on the stokeslets that is consistent with the relative velocities experienced by each stokeslet. The method rigorously satisfies the condition that the object moves with no transfer of momentum to the fluid. We demonstrate that a sphere represented by 1999 well-separated stokeslets on its surface produces flow and drag force like a solid sphere to one-percent accuracy. We show that a uniformly-charged sphere with 3998 body and countercharge stokeslets obeys the Smoluchowski prediction \cite{Morrison} for electrophoretic mobility when the countercharges lie close to the sphere. Spheres with dipolar and quadrupolar charge distributions rotate and translate as predicted analytically to four percent accuracy or better. We describe how the method can treat general asymmetric shapes and charge distributions. This method offers promise as a way to characterize and manipulate asymmetrically charged colloid-scale objects from biology (e.g. viruses) and technology (e.g. self-assembled clusters).