The suppression of electro-osmotic flow (EOF) through the use of either a polymer brush or a dynamicaly adsorbed polymer coating is widely used in microfluidics, particularly for capillary electrophoresis. In this presentation, I will review the results of our Molecular Dynamics simulations of this problem. For polymer brushes, our data agree with the best available theory; this suggests ways to improve coating. For dynamic coating, our simulation data show that the optimal adsorption strength for the suppression of EOF is around the phase transition for the adsorption of the polymer, a very interesting result which suggests ways to design new coating agents. Finally, we examine block copolymers.