Issue 3, 2023

The permeability of pillar arrays in microfluidic devices: an application of Brinkman's theory towards wall friction

Abstract

Darcy's law describes the flow of Newtonian fluids through bulk porous media as the product of the applied pressure difference, the fluid's viscosity and the medium's permeability. Brinkman extended Darcy's law with a viscous stress term, thereby enabling boundary conditions to the flow field at the surface of the medium. The validity of Brinkman's term, and the value of its effective viscosity, have been heavily debated since their introduction nearly 75 years ago. We use experiments and Multibody Dissipative Particle Dynamics (MDPD) simulations to study flows through ordered and disordered pillar arrays in microfluidic channels of limited height. We find that the simulated velocity profiles are well described by an expedient interpretation of Brinkman's theory. Depending on the solid volume fraction and pillar arrangement, the effective viscosity varies between two and three times the bulk fluid viscosity. The calculated effective permeabilities of the flow devices, combining the flow resistances due to the pillars and the walls by Brinkman's theory, agree well with the experimental data. This approach enables fast and accurate estimates of the effective permeability of micropillared chips. The simulated force distributions over the walls and pillars require an effective viscosity equal to the bulk viscosity and an elevation-dependent permeability of the pillar array.

Graphical abstract: The permeability of pillar arrays in microfluidic devices: an application of Brinkman's theory towards wall friction

Supplementary files

Article information

Article type
Paper
Submitted
16 Sep 2022
Accepted
06 Dec 2022
First published
13 Dec 2022
This article is Open Access
Creative Commons BY-NC license

Soft Matter, 2023,19, 436-450

The permeability of pillar arrays in microfluidic devices: an application of Brinkman's theory towards wall friction

T. Hulikal Chakrapani, H. Bazyar, R. G. H. Lammertink, S. Luding and W. K. den Otter, Soft Matter, 2023, 19, 436 DOI: 10.1039/D2SM01261H

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