Most of the current literature on the simulation of the electro-osmotic flow in micro-channels decompose electric potential to two components; internal and external potentials. They usually approximate the near wall changes in the ion concentration (called double layer) which is physically responsible for electro-osmotic force by a model (like Poisson equilibrium distribution or Debye-Huckel approximation). There are reports in the literature which show that the approximations lose their fidelity for more complex situations. In this thesis we solve the full system of Nernst-Planck and Navier-Stokes equations by resolving electric double layer. The proposed...