Numerical electrokinetics

TL;DR

This paper introduces a novel lattice method for efficiently solving electrokinetic equations, enabling detailed analysis of charge cloud structures and electrophoretic mobility around colloids, with insights into screening effects and charge orientation.

Contribution

A new numerical lattice method for solving electrokinetic equations that accounts for electrostatic and hydrodynamic effects in colloidal systems.

Findings

Electrophoretic mobility shows weak dependence on screening mechanisms.

Charge cloud orientation depends on colloid charge due to electrostatic and hydrodynamic interactions.

The method efficiently solves complex electrokinetic problems with iterative algorithms.

Abstract

A new lattice method is presented in order to efficiently solve the electrokinetic equations, which describe the structure and dynamics of the charge cloud and the flow field surrounding a single charged colloidal sphere, or a fixed array of such objects. We focus on calculating the electrophoretic mobility in the limit of small driving field, and systematically linearise the equations with respect to the latter. This gives rise to several subproblems, each of which is solved by a specialised numerical algorithm. For the total problem we combine these solvers in an iterative procedure. Applying this method, we study the effect of the screening mechanism (salt screening vs. counterion screening) on the electrophoretic mobility, and find a weak non-trivial dependence, as expected from scaling theory. Furthermore, we find that the orientation of the charge cloud (i. e. its dipole moment) depends on the value of the colloid charge, as a result of a competition between electrostatic and hydrodynamic effects.