Analytical solution of the solute transport equation for the binary homovalent ion exchange in groundwater

Abstract

A binary homovalent ion exchange transport model governed by local chemical equilibrium is considered for a one-dimensional, steady flow in a homogeneous soil column. An analytical solution of the aqueous concentration distribution for the convex exchange is obtained by applying nonlinear shock wave theory. The main nonlinear feature is the breaking of fronts into shock waves. The corresponding mathematical theory is the method of characteristics with a special treatment of shock waves. The wave velocity and front thickness are also obtained to illustrate the front propagation and structure. The derivation of the solution presented may offer a wide range of application opportunities and may also provide a good approach for solving the binary heterovalent exchange transport model.