#Master's thesis report Master's thesis I did in 2012 at the Department of Mathematical Sciences at Chalmers Univeristy of Technology, Gothenburg.

The published report can be found here: http://publications.lib.chalmers.se/records/fulltext/170015/170015.pdf

The presentation for the disputation ceremony can be found here: https://github.com/weierstrass/master-thesis/raw/master/report/pres/pres.pdf

The C++ code that was developed for the thesis can be found here: https://github.com/weierstrass/wlb

##Abstract The lattice-Boltzmann method is used to model flow 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 flow, 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 flows 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 flow down and a local minimum is found in the velocity profile for thick enough double layers. Other more complicated systems are also studied; electroosmotic flow in a channel with heterogeneously charged walls and flow in a an array of charged squares. Keywords: lattice-Boltzmann, electrokinetics, electrohydrodynamics, Nernst-Planck, Poisson-Boltzmann, high performance computing.