Flow through randomly curved manifolds

TL;DR

This paper investigates fluid flow through randomly curved manifolds, revealing hysteresis in flow-curvature relations and developing a lattice kinetic model to simulate complex curved spaces efficiently.

Contribution

It introduces a novel lattice kinetic model for fluid flow in arbitrarily curved manifolds and uncovers hysteresis and interference effects in flow behavior.

Findings

Flow exhibits hysteresis depending on curvature perturbation scale.

Flow decreases sublinearly with increasing curvature perturbations.

Developed an efficient model for simulating flow in complex curved spaces.

Abstract

We have found that the relation between the flow through campylotic (generically curved) media, consisting of randomly located curvature perturbations, and the average Ricci scalar of the system exhibits two distinct functional expressions (hysteresis), depending on whether the typical spatial extent of the curvature perturbation lies above or below the critical value maximizing the overall Ricci curvature. Furthermore, the flow through such systems as a function of the number of curvature perturbations presents a sublinear behavior for large concentrations due to the interference between curvature perturbations that, consequently, produces a less curved space. For the purpose of this study, we have developed and validated a lattice kinetic model capable of describing fluid flow in arbitrarily curved manifolds, which allows to deal with highly complex spaces in a very compact and efficient way.