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A Statistical Method for Analysis of Diffusion in Soils¹

ABSTRACT

A special Monte Carlo method for use in investigating problems which involve random processes is developed. This approach differs from the usual Monte Carlo method for solution of differential equations in that the random process itself is constructed directly. The power of this approach is demonstrated by application of the method using two examples. In one case, the effect of thermal gradient on ionic diffusion through thin films of interfacial water in frozen clay is examined. The predicted ionic distribution is in agreement both with experimental data and with the result obtained by exact solution of the diffusion equation. In the second example, the distribution of acetone deposited in soil near the soil-atmosphere interface is calculated for a two-layer profile in which the adsorption coefficient and void-porosity vary between horizons.

¹ Contribution from the US Army Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire.

² Research Chemical Engineer and Research Chemist, respectively. USACRREL, Hanover, N.H.

Received for publication March 25, 1970. Accepted for publication December 22, 1970.