A nonlinear effective slip interface law for transport phenomena between a fracture flow and a porous medium

TL;DR

This paper derives a quadratic nonlinear slip interface law for flow between a fracture and porous medium, valid across various flow regimes, challenging traditional linear assumptions and impacting modeling approaches.

Contribution

The paper introduces a rigorous derivation of a nonlinear quadratic slip law at the interface, extending the understanding beyond linear models for different flow regimes.

Findings

The slip law is nonlinear and quadratic, independent of flow regime.

The derived law applies for a range of Reynolds numbers and fracture widths.

Implications for rethinking boundary slip laws in fluid dynamics modeling.

Abstract

We present modeling of an incompressible viscous flow through a fracture adjacent to a porous medium. We consider a fast stationary flow, predominantly tangential to the porous medium. Slow flow in such setting can be described by the Beavers-Joseph-Saffman slip. For fast flows, a nonlinear filtration law in the porous medium and a non- linear interface law are expected. In this paper we rigorously derive a quadratic effective slip interface law which holds for a range of Reynolds numbers and fracture widths. The porous medium flow is described by the Darcys law. The result shows that the interface slip law can be nonlinear, independently of the regime for the bulk flow. Since most of the interface and boundary slip laws are obtained via upscaling of complex systems, the result indicates that studying the inviscid limits for the Navier-Stokes equations with linear slip law at the boundary should be rethought.