Transport of colloidal size particulate matter is of special interest of environmental studies because colloids and adsorbed chemicals can be transported over long distances. Colloid facilitated transport can pose potentially high risk for pollution of ground water. Visualizations of colloid transport using bright field and confocal microscopes have discovered interesting phenomena such colloids moving in circles that cannot be described by the traditional Darcy scale models. That is why computational pore scale models are needed to better understand colloid transport and fate in porous media. Transport and fate of colloids depend largely on flow field in the pores and it is, therefore, important to simulate the flow field while taking grain surface properties into account. The aim of this dissertation is hence to determine the flow fields in realistic pores by solving the incompressible Navier-Stokes equation with a powerful commercial available finite element program COMSOL Multiphysics. The dissertation has five chapters. In the first chapter a short introduction is given. In the second chapter the COMSOL Multiphysics program is tested by revisiting the classical colloid filtration theory on colloid retention on a spherical sand grain. Retention of colloids on grains simulated with COMSOL is found to be similar to semi-analytical solutions previously published. Subsequently colloid retention on an air bubble is simulated and greater colloid retention is calculated than on a soil grain due to the slip boundary condition at the Air-Water interface which creates higher velocities and more fluid flow around air bubble resulting in greater amounts of colloids that can diffuse to the interface. In the third chapter the effect of surface roughness on hydrodynamics of colloid transport in a saturated porous media is investigated by simulating the flow fields around perfectly smooth, smoothed, and naturally rough sand grains. The results show that micron scale surface asperities of rough grains create greater vorticity and more stagnant flow regions compared to smooth grains likely resulting in greater colloid retention for the rough grains. In the fourth chapter the dependence of dynamic contact angle between the interface of two immiscible fluids and solid surface on the interface velocity is simulated in an empty capillary channel to provide a new understanding on the formation of unstable wetting fronts in coarse or water repellent soils. The results show an increase in contact angle when the velocity of the front increases, which is consistent with experimental studies in the literature. In the fifth chapter the problems encountered during the research and future directions are briefly explained.