Modelling of electrokinetic flow using the lattice-Boltzmann method

Abstract

The lattice-Boltzmann method is used to model ow in electrokinetic systems. A modelling approach based on the coupling of Navier-Stokes, Nernst-Planck and Poisson's equation of electrostatics is utilised. Three lattice-Boltzmann methods are formulated for the three equations respectively. The method is implemented in C++ with the aim of being high performing. Topics as locality, instruction pipelines and parallel computing are considered. The implementation is tested for a number of classic examples with known solutions, e.g. Taylor-Green vortex ow, an Helmholtz equation and an advection-diffusion situation. The computed solutions agree well with the analytic solutions. The physical systems modelled consists mainly of various charged channel ows of ionic solutions. Electrokinetic effects, such as electroosmosis and the electrovicous effect are studied. This is done in thin channels where the thickness of the electrical double layers is comparable to the channel dimension. The electroviscous effect is shown to slow the ow down and a local minimum is found in the velocity profile for thick enough double layers. Other more complicated systems are also studied; electroosmotic ow in a channel with heterogeneously charged walls and ow in a an array of charged squares.