Darcy’s Law for a relates the volumetric flow rate Q through a porous media in response to a pressure gradient ΔP …
Where κ is an intrinsic permeability of the media, μ is the fluid viscosity, L is the length of the media that fluid must travel through to exit, and A is the cross section normal to the fluid flow direction.
From Wikipedia
The permeability κ in this equation is an intrinsic characteristic of the media. Although the flow rate will vary in proportion to the media cross section, and inversely with fluid viscosity, and length; these quantities are excluded from κ. So κ is strictly a function of the ultrastructure of the media (porosity, pore size, etc.).
For us it is important to distinguish this definition of permeability from Hydraulic Permeability we use for nanomembrane research:
The relationship between the two permeabilities is (derived in our paper by Henry Chung [1]):
From this it is clear that what we refer to as the ‘permeability’ of a nanomembrane is not an intrinsic material property. Changing the extrinsic parameters L (the membrane thickness) or μ will change the permeability.
The reason we use ε instead of κ is because only ε quantifies the advantages of using thin membranes. We get higher flow rates for the same pressure and area as conventional membranes precisely because of the membrane thinness. By normalizing by membrane thickness, these differences become apparent.
1. Chung, H.H., Chan, C.K., Khire, T.S., Clark Jr., A., Waugh, R.E., McGrath, J.L. (2014) Highly Permeable Silicon Membranes for Shear Fee Chemotaxis and Rapid Cell Labeling, Lab on a Chip 14:2456-68
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