Mathematical Theory of a Kinetic Model for Dispersion of Previously Distributed Chemicals in a Sorbing Porous Medium

Authors:
  • FLF. T. Lindstorm
    F. T. Lindstorm
  • MNM. N. Narasimham
    M. N. Narasimham
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Abstract
The problem of mass transport and dispersion of materials through porous media has been increasingly becoming important in industry, agriculture, biophysical and biochemical studies. The existing mathematical treatment of these problems consists in assuming simple distribution laws relating the free phase chemical concentration in the medium and the resulting field equations are generally solved numerically. In the present investigation we have developed a physically realistic dynamic model for the free and sorbed phase distributions and we have obtained exact solutions of the field equations by analytical means using operational and repeated contour integration methods involving convolutions. This is an important step in the development of this direction of study since these analytical models and mass transport predictions pave the way for a better and more complete understanding of the dispersion phenomena than what the numerical techniques alone can provide. Furthermore, many interesting new results have been found. The behavior of the free and sorbed phase profiles for a range of values of a certain parameter measuring the speed of exchange between the two phases is examined and the interesting phenomenon of “tailing” is studied in detail. Physical examples and graphical solutions are given to illustrate the model developed obtaining results in very good agreement with those of recent experiments.