Material coordinate formulation and use in one-dimensional soil solute and water flow

Description of one-dimensional water now in saturated swelling soils is facilitated by using a space-like coordinate based on the distribution of solids; a water-based space-like coordinate facilitates analysis of solute movement during non-steady water flow in unsaturated soils. These space-like material coordinates are simply defined and measured for many practical situations. Furthermore, their mathematical formulations are similar and result in similar non-linear diffusion equations that may be solved for important initial and boundary conditions. The approach may be extended to solute transport during non-steady flow of water in a swelling soil. This paper illustrates the similarity of methods of formulating now equations, it discusses the benefits of the use of such coordinates, and it comments on the need for dimensional consistency between coordinates and intrinsic soil properties.