Similarity Solutions for Gravity-Dominated Spreading of a Lens of Organic Contaminant

摘要

In recent years it has become increasingly evident that numerous aquifers have become contaminated as a result of leaks from storage tanks and accidental spills of gasoline, aviation fuel, chlorinated solvents, and other organic liquids having low solubilities in water. Accordingly, it is important to develop a basic understanding of how an organic liquid (hereafter called oil for simplicity), which is largely immiscible with water, percolates through the soil until it reaches the water table and, in situations where its density is less than water, spreads there. Similarity solutions are developed for gravity-dominated spreading at the water table of a lens of organic liquid largely immiscible with water. Different solutions deal with different mechanisms by which the lens volume decreases with time: dissolution or evaporation, trapping as water invades the region beneath the central part of the lens, and uniform degradation. In the last case, the solution is a special case of the Barenblatt-Pattle solution. The same is true for the limiting case of a lens of constant volume. In all cases information is presented on variation of lens radius and thickness with time. All solutions except that involving trapping can be carried over with minor modifications to the case of a lens simultaneously spreading and translating along a slightly inclined water table.