Anisotropic mean free path in simulations of fluids traveling down a density gradient

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Abstract
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 0.05σ−3 and 0.7σ−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.

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