Analytical Solutions to the Differential Equation of Mass Transport for Conservative Solutes

In this chapter, analytical solutions to the differential equation of mass transport for conservative solutes are illustrated. Their derivation relies on a number of simplifying hypotheses, including that: the medium is saturated, homogeneous and isotropic; water has constant density and viscosity, regardless of solute concentration; Darcy’s law is valid; flow directions and rates are uniform; transport parameters are constant within the domain; boundary conditions are constant in time. Solutions for one-, two- and three-dimensional geometries are presented, the former being mainly used for the interpretation of laboratory experiments, the latter two being more relevant for practical applications. Pulse and continuous solute release are considered. Notably, in a three-dimensional geometry a pulse input from a point source and a continuous input from a plane source are illustrated. A solution of the differential equation of mass transfer for the former contamination scenario was derived by Baetslé, while Domenico and Robbins proposed a model for the latter.