Brownian dynamics are used to relate the time dependent concentration of particles constrained in a pore to the observed flux and to study the flow induced by wall effects. The joint probability for a particle is calculated, not only to be at a certain position but with a given velocity as well. The persistence of the velocity direction and the resulting coupling between position and velocity alter the particle dynamics. In constrained geometries, transport though the pore is enhanced. With time, an average particle velocity flow field is set up along with the initial slow evolution by diffusion. For reflecting boundary conditions on the wall, the increase of the density along the walls causes particles to flow toward the center of the pore. (C) 2001 American Institute of Physics.