Eulerian Kinematics of Flow through Spatially Periodic Models of Porous Media.

摘要

For spatially periodic models of porous media, and incompressible fluids, we consider here in detail the physical interpretation of averaged velocity fields in terms of a purely continuum-level Eulerian seepage flux relation involving the mass flow across an arbitrarily oriented 'macroscale' surface element. We prove that the appropriately averaged microscale velocities do indeed satisfy a macroscale Eulerian flux relation (albeit to some approximation), provided that the surface 'element is large compared with the pore lengthscale (microscale). A quantitative discussion of an 'intermediate scale' (lying between the pore scale and a characteristic macroscale) is achieved through the use of locally periodic velocity fields. Within the context of seepage velocity kinematics, our developments provide a conceptual foundation that renders continuum theories of flow of incompressible fluids through (periodic) porous media entirely self-contained on the macroscale -- free from any details of the discrete microscale structure (inaccessible to macroscopic observers) from which this continuum theory sprang. Keywords: Reprints. (kr)