Research papersSolute dispersion in a semi-infinite aquifer with specified concentration along an arbitrary plane source

- Three-dimensional solution of ADE subject to plane source of contamination.
- Two-dimensional solution of ADE subject to line source of contamination.One-dimensional solution of ADE subject to point source of contamination.
- Generalization of source using hyper-plane concept.

Mathematical modeling is carried out to investigate the behavior of solute transport in groundwater with non-point sources of contamination i.e., plane and line sources. Generalized form of plane is considered to study the most general case for non-point sources. Using the hyper-plane concept, the closed-form solution is derived for line sources in two-dimensions as well as the point source in one-dimension as special cases of the general plane source contamination problem. The domain is considered semi-infinite and the velocity of groundwater is in the positive direction of the axes. The three-dimensional advection-dispersion equation (ADE) with non-point source of contamination is solved analytically using the Laplace transform technique. The obtained solution is validated numerically using the finite difference technique. The proposed general solution of the three-dimensional ADE may be of interest to researchers working in surface water and vadose zone hydrology areas as well.