In previous work, lattice density functional theory equations have been recast into differential form to determine a property whose gradient is universally proportional to the diffusive flux. For color counter diffusion, this property appears as the impingement rate onto vacancies and molecules of a species whose density gradient can be influenced by diffusion. Therefore, the impingement rate of a diffusing molecule depends on the mobility of its surroundings. In order to determine the validity of this finding, molecular dynamics simulations of color counter diffusion were performed in which the mobility of the solvent was varied to determine if the flux of the diffusing species responded to the change when all other factors, such as density gradient, available volume, and temperature are held constant.

Hard sphere molecular dynamics simulations are used to study the mean free path of molecules traveling down a density gradient at fluid densities ranging between 0.05sigma(-3) and 0.7sigma(-3). Gradients are developed using semipermeable boundaries in the x-direction and, as a result, a net flow develops in the positive x-direction. Over the course of the simulation, the free paths of colliding molecules are calculated and it was determined that the mean free path in the positive x-direction is greater than the mean free path in the negative x-direction at each density studied. These results are compared to the mean free paths in the positive and negative y- and z-directions (in which there is no net flow) and the distribution of free paths for molecules traveling in the positive and negative x-directions gives insight into the physics of the system. In addition, the dependency of the mean free path on speed is studied and compared to kinetic theory predictions. The results have application in the modification of the classical model of diffusion for low density systems undergoing flow in which the mean free path is finite, large, and can be anisotropic.

An analysis of classical approximations is performed for diffusion in fluids with density gradients. This approach gives a new diffusion equation taking into account the asymmetry of molecular mean-free paths and the velocity distribution in the flux term. It is shown that new model is consistent with Einstein's evolution equation for an asymmetric distribution of spatial displacements and with molecular dynamic simulations for hard spheres.