Computation of free-molecular flow in nuclear materials

Generally, the transport of gases and vapors in nuclear materials is adequately described by the diffusion equation with an effective diffusion coefficient. There are instances however, in which the flow pathway can be so restrictive that the diffusion description has limitations. In general, molecular transport is governed by intermolecular forces and collisions (interactions between multiple gas/vapor molecules) and by molecule–surface interactions. However, if nano-scale pathways exist within these materials, as has been suggested, then molecular transport can be characterized as being in the free-molecular flow regime where intermolecular interactions can be ignored and flow is determined entirely by molecule–surface collisions. Our purpose in this investigation is to focus on free-molecular transport in fine capillaries of a range of shapes and to explore the effect of geometry on this transport. We have employed Monte Carlo techniques in our calculations, and for simple geometries we have benchmarked our results against some analytical and previously available results. We have used Mathematica® which has exceptional built-in symbolic and graphical capabilities, permitting easy handling of complicated geometries and good visualization of the results. Our computations provide insights into the role of geometry in molecular transport in nuclear materials with narrow pathways for flows, and also will be useful in guiding computations that include intermolecular collisions and more realistic gas–surface collision operators.