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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.
We investigate the elastoviscoplastic flow through porous media by numerical simulations. We solve the Navier-Stokes equations combined with the elastoviscoplastic model proposed by Saramito for the stress tensor evolution. In this model, the materia
Hypothesis Control of capillary flow through porous media has broad practical implications. However, achieving accurate and reliable control of such processes by tuning the pore size or by modification of interface wettability remains challenging. He
We present a theoretical framework for immiscible incompressible two-phase flow in homogeneous porous media that connects the distribution of local fluid velocities to the average seepage velocities. By dividing the pore area along a cross-section tr
Immiscible fluid-fluid displacement in porous media is of great importance in many engineering applications, such as enhanced oil recovery, agricultural irrigation, and geologic CO2 storage. Fingering phenomena, induced by the interface instability,
Diverse processes rely on the viscous flow of polymer solutions through porous media. In many cases, the macroscopic flow resistance abruptly increases above a threshold flow rate in a porous medium---but not in bulk solution. The reason why has been