Analysis of electro-osmotic flow by lattice Boltzmann simulation and Helmholtz-Smoluchowski formula

Numerical study of electro-osmotic flow (EOF) and theoretical exploration of relationship between EOF and electrical double layer (EDL) are carried out in the present work. Under the Poisson-Boltzmann and Debye-Hückel approximations, the analytic solution of electric potential, net charge, and flow pattern can be derived. The numerical results obtained by Poisson-Nernst-Planck (PNP) and Navier-Stokes equations are compared with the analytic solution and the solution based on the Helmholtz-Smoluchowski formula. Also, this article provides a clearer view on nondimensionalization applied on lattice Boltzmann method with different differential equation.