Domenico solution--is it valid?

The Domenico solution is widely used in several analytical models for simulating ground water contaminant transport scenarios. Unfortunately, many textbook as well as journal article treatments of this approximate solution are full of empirical statements that are developed without mathematical rigor. For this reason, a rigorous analysis of this solution is warranted. In this article, we present a mathematical method to derive the Domenico solution and explore its limits. Our analysis shows that the Domenico solution is a true analytical solution when the value of longitudinal dispersivity is zero. For nonzero longitudinal dispersivity values, the Domenico solution will introduce a finite amount of error. We use an example problem to quantify the nature of this error and suggest some general guidelines for the appropriate use of this solution.