The Brinkman viscosity for porous media exposed to a free flow

TL;DR

This paper proposes a method to determine the effective Brinkman viscosity for porous media using interface slip length and interior permeability, enabling more accurate modeling of flow between free fluid and porous structures.

Contribution

It introduces a way to estimate the Brinkman viscosity from pore-scale properties, improving the accuracy of the Brinkman model without detailed pore resolution.

Findings

Modeling errors are typically around 10%

Errors do not exceed 40%

Brinkman model is more accurate for irregular structures

Abstract

The Brinkman equation has found great popularity in modelling the interfacial flow between free fluid and a porous medium. However, it is still unclear how to determine an appropriate effective Brinkman viscosity without resolving the flow at the pore scale. Here, we propose to determine the Brinkman viscosity for rough porous media from the interface slip length and the interior permeability. Both slip and permeability can be determined from unit-cell analysis, thus enabling an a priori estimate of the effective viscosity. By comparing the velocity distribution in the porous material predicted from the Brinkman equation with that obtained from pore-scale resolved simulations, we show that modelling errors are $\sim 10\%$ and not larger than $40\%$. We highlight the physical origins of the obtained errors and demonstrate that the Brinkman model can be much more accurate for irregular porous structures.