TY - JOUR
T1 - The permeability of pillar arrays in microfluidic devices
T2 - an application of Brinkman's theory towards wall friction
AU - Hulikal Chakrapani, Thejas
AU - Bazyar, Hanieh
AU - Lammertink, Rob G.H.
AU - Luding, Stefan
AU - den Otter, Wouter K.
N1 - Funding Information:
THC acknowledges the Industrial Partnership Programme of the Foundation for Fundamental Research on Matter (FOM, project code:i43), which is financially supported by The Netherlands Organisation for Scientific Research (NWO). This research program was co-financed by Canon Production Printing (Venlo, The Netherlands). HB acknowledges the Netherlands Organisation for Scientific Research (NWO) for a Vici grant (project code: STW 016.160.312). This work was performed in the cooperation framework of Wetsus, the European Centre of Excellence for Sustainable Water Technology ( www.wetsus.nl ). Wetsus is co-funded by the Dutch Ministry of Economic Affairs, the Ministry of Infrastructure and Environment, the European Union Regional Development Fund, the Province of Fryslân and the Northern Netherlands Provinces. We thank Jan W. van Nieuwkasteele (University of Twente) for the fabrication of the chips.
Funding Information:
THC acknowledges the Industrial Partnership Programme of the Foundation for Fundamental Research on Matter (FOM, project code:i43), which is financially supported by The Netherlands Organisation for Scientific Research (NWO). This research program was co-financed by Canon Production Printing (Venlo, The Netherlands). HB acknowledges the Netherlands Organisation for Scientific Research (NWO) for a Vici grant (project code: STW 016.160.312). This work was performed in the cooperation framework of Wetsus, the European Centre of Excellence for Sustainable Water Technology (www.wetsus.nl). Wetsus is co-funded by the Dutch Ministry of Economic Affairs, the Ministry of Infrastructure and Environment, the European Union Regional Development Fund, the Province of Fryslân and the Northern Netherlands Provinces. We thank Jan W. van Nieuwkasteele (University of Twente) for the fabrication of the chips.
Publisher Copyright:
© 2023 The Royal Society of Chemistry.
PY - 2023/1/21
Y1 - 2023/1/21
N2 - 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.
AB - 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.
KW - UT-Hybrid-D
UR - http://www.scopus.com/inward/record.url?scp=85144333813&partnerID=8YFLogxK
U2 - 10.1039/d2sm01261h
DO - 10.1039/d2sm01261h
M3 - Article
C2 - 36511444
AN - SCOPUS:85144333813
SN - 1744-683X
VL - 19
SP - 436
EP - 450
JO - Soft matter
JF - Soft matter
IS - 3
ER -