The Operational Significance of the Continuum Hypothesis in the Theory of Water Movement Through Soils and Aquifers

Abstract

The operational meaning of the representative elementary volume (REV) concept, on which current foundational theories of water movement through porous media are based, is analyzed critically. It is concluded that the REV concept as applied to real porous media is both unnecessarily restrictive and experimentally unverifiable. In its place a relativist concept is proposed in which macroscopic physical variables are defined as convolution products of microscopic properties of a porous medium with weighting functions that represent the appropriate measuring instruments. The effects of resolution and precision differences among experimental measuring devices, now recognized as critical in the assessment of spatial variability in the properties of soils and aquifers, can be incorporated naturally within the relativist concept but are excluded a priori in the REV concept. The relativist point of view, unlike the REV concept, has a clear operational meaning and, in principle, extends theoretical validity to all local measurements made on porous media. It is sufficient mathematically to derive conventional macroscopic balance equations for mass and linear momentum as well as a differential equation for the isothermal transport of water through an unsaturated, anisotropic, deformable soil or aquifer.