A Perspective on Darcy’s Law across the Scales: From Physical Foundations to Particulate Mechanics

This paper puts forward a perspective or opinion that we can demonstrate Darcy’s law is valid at any scale where fluid be modeled/analyzed as continuum. describes the flow of through porous medium by linear relationship between rate and pore pressure gradient permeability tensor. We show such established scale, so long tensor expressed function adequate parameters describe space geometry, properties, physical phenomena. Analytical models provide essential information on key variables depends under different regimes. Upscaling techniques based Lippman-Schwinger equation, network models, Eshelby’s homogenization theory make it possible to predict beyond scale. One challenges validate these characterize microstructure measure transport properties multiple scales. Recent developments in imaging, multiscale modeling, advanced computing offer new possibilities address some challenges.