Modeling electrokinetic flows by the smoothed profile method

We propose an efficient modeling method for electrokinetic flows based on the smoothed profile method (SPM) 1, 2, 3 and 4 and spectral element discretizations. The new method allows for arbitrary differences in the electrical conductivities between the charged surfaces and the surrounding electrolyte solution. The electrokinetic forces are included into the flow equations so that the Poisson–Boltzmann and electric charge continuity equations are cast into forms suitable for SPM. The method is validated by benchmark problems of electroosmotic flow in straight channels and electrophoresis of charged cylinders. We also present simulation results of electrophoresis of charged microtubules, and show that the simulated electrophoretic mobility and anisotropy agree with the experimental values.