I am working with hydraulic permeability of hydrogels. I am not sure at what extend the Darcy law is applicable and at what values of pressure, volume flow rate, the Darcy law becomes invalid. Any related papers or ideas would be helpful.
These may help Nusrat, and other works are referenced.
https://pubs.rsc.org/en/content/articlelanding/2020/sm/c9sm01678c
https://www.sciencedirect.com/topics/engineering/darcys-law
Article Darcy's Law and the Field Equations of the Flow of Underground Fluids
Article Boundary condition for Darcy's flow through porous media
Darcy's law describes a linear relationship between specific discharge and the hydraulic gradient. This relationship is valid for most all groundwater conditions. However, as the flow rate approaches zero or when high rates of flow occur in high hydraulic conductivity material like fractures or karst features, the flow may not be linear and thus, Darcy’s law does not appropriately represent groundwater flow.
Darcy’s law is strictly applicable for the laminar flow of an incompressible fluid in a solid matrix (non-deforming) of a porous medium in which the gradient of mechanical energy is the only driving force (Figure 29). It is applicable under steady-state or transient conditions.
Bear (1972) states “Darcy’s law is valid as long as the Reynolds number, based on average grain diameter, does not exceed some value between 1 and 10 (page 126)”. Most authors on the topic agree that when Re is less than one, laminar flow occurs, and Darcy’s law is valid.
Darcy’s law is not applicable if the density of the fluid varies due to differing pressure, temperature, and/or high concentrations of dissolved constituents; it is not applicable if there are substantial differences in density from location to location within a flow system; and it is not applicable if thermal, chemical, or electrical gradients drive fluid flow. However, forms of flux equations based on Darcy’s Law have been developed to accommodate density variations due to compressibility, non-uniform solute concentrations and non-uniform temperature. These equations are usually referred to as representing Darcy’s Law.
Again, fortunately, the density and viscosity changes of water are usually trivial at the low pressures and narrow range of temperatures occurring in most of the Earth’s shallow subsurface making Darcy’s law applicable.
Regards
Check on this presentation
https://www.slideshare.net/parthhjoshi/darcys-law-15277923
As the flow rate approaches zero or when high rates of flow occur in high hydraulic conductivity material like fractures or karst features, the flow may not be linear and thus, Darcy's law does not appropriately present at these conditions.
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