The HSP-VAT description of phenomena and transport in Heterogeneous Media includes the mathematical models, governing equations for both (or more) scales of the medium - lower spatial scale that can be Homogeneous media governing equations and the upper scale Heterogeneous media governing equations -
a) — solid – liquid surface scale with the roughness layer on the wall: 1- smooth pore convenient velocity profile; 2 - rough pore mean velocity distribution; b) — Pore scale modeling background; c) — third scale homogeneous porous medium capillary and globular morphologies
Multiscale (polyscale) almost periodic (weakly organized) morphology of heterogeneous medium (modified after Cushman, 1991)
See, for example, in few sciences as - in Fluid Mechanics
in Thermal Physics, and in any other science presented in this website.
Now, after more than 47 years of the world-wide development we can firmly make assertion that for every science presented here that either the substantial progress has already appeared and is evident or the results those have been achieved render the mathematical rigidity and value of outcomes leaving no chance to homogeneous approaches used in these areas.