Flow through randomly curved manifolds

Abstract

We present a computational study of the transport properties of campylotic (intrinsically curved) media. It is found that the relation between the flow through a campylotic media, consisting of randomly located curvature perturbations, and the average Ricci scalar of the system, exhibits two distinct functional expressions, depending on whether the typical spatial extent of the curvature perturbation lies above or below the critical value maximizing the overall scalar of curvature. Furthermore, the flow through such systems as a function of the number of curvature perturbations is found to present a sublinear behavior for large concentrations, due to the interference between curvature perturbations leading to an overall less curved space. We have also characterized the flux through such media as a function of the local Reynolds number and the scale of interaction between impurities. For the purpose of this study, we have also developed and validated a new lattice Boltzmann model.