Journal of Hydrology, 63 (1983) 345--358 345 Elsevier Science Publishers B.V., Amsterdam- Printed in The Netherlands [a] UNSTEADY FLOW AGAINST DISPERSION IN FINITE POROUS MEDIA NAVEEN KUMAR Department of Mathematics, B.H. U., Varanasi 221 005 (India) (Received January 5, 1982; revised and accepted June 25, 1982) ABSTRACT Kumar, N., 1983. Unsteady flow against dispersion in finite porous media. J. Hydrol., 63: 345--358. Analytical solutions are presented for dispersion (in a finite non-adsorbing and adsorb- ing porous medium) which is controlled by flow (with unsteady unidirectional velocity distribution) of a low concentration fluid towards a region of higher concentration. An exponential function concentration is enforced at the source of the dispersion, while zero concentration, or a condition in which the change in concentration is proportional to the flow, is applied at the other boundary. A new time variable has been introduced to solve the unsteady flow problem. 1. INTRODUCTION Generally, the mixing of miscible fluids as they flow through porous media is referred to as hydrodynamical dispersion. With respect to the importance of dispersion processes studied in water quality management and pollution control, the dispersion has been referred to as a hydraulic mixing process, by which the waste concentrations are attenuated while the waste pollutants are being transported downstream. There are many occasions when waste pollutants from industrial plants, urban and agricultural areas, and other operations reach a natural water course. Interest in dispersion in porous media has also arisen because of seawater intrusion into coastal aquifers, the seepage from canals and streams into and through aquifers, the deliberate release of herbicides into canals to kill weeds, and the ion ex- change of cations in soils. Because of their importance, their problems have been of continual interest to researchers working in these areas. Quite a few investigations have been done concerning different aspects of these problems. A non-exhaustive list of references must include at least the works of Bastian and Lapidus (1956), Banks and Ali (1964), Ogata (1970), Lai and Jurinak (1971), and Mariflo (1974). Most of these works reveal a common assumption of a homogeneous porous medium with constant poros- ity, constant seepage flow velocity and dispersion coefficient. However, com- 0022-1694/83/$03.00 © 1983 Elsevier Science Publishers B.V.