R.J. Schotting

TL;DR: In this article, a set of nonlinear partial differential equations and derive explicit (exact) and semi-explicit solutions, under various assumptions, were derived for a wide range of density differences between resident and invading fluids.

TL;DR: In this article, a series of careful laboratory soil column experiments was carried out for the purpose of providing data for testing recently presented theories of miscible density-dependent flow and transport, in particular, modifications to the standard theory involve extensions to both Darcy's (for flow) and Fick's laws (for diffusive/dispersive solute flux).

TL;DR: In this paper, a new model for unsaturated flow in porous media, including capillary hysteresis and dynamic capillary effects, is analyzed, and the existence and uniqueness of solutions are established and qualitative and quantitative properties of (particular) solutions are analyzed.

TL;DR: In this article, three sets of laboratory column experiments were performed on coarse and medium sands, consisting of upward displacement of water by sodium chloride solutions with concentrations ranging from 5 to 200g/l. The experimental data were analyzed using a simplified approach based on Darcy's Law alone, applied with the assumption of a sharp interface.

TL;DR: In this paper, the Von Mises transformation was used to study brine transport in porous media, where the model involves mass balance equations for fluid and salt, Darcy's law and an equation of state, relating the salt mass fraction to the fluid density.