Steady, Diffusive-Reactive Transport in Shallow Triangular Domain
Publication: Journal of Engineering Mechanics
Volume 124, Issue 10
Abstract
Diffusion of a substance accompanied by a first-order reaction in a shallow triangular domain of bottom slope S is examined as a model for environmental problems such as diffusion of toxic substances in landfills or dissolved gas diffusion in coastal waters. The substance is introduced by a constant flux along the surface of the domain, while all other boundaries are insulated. The length and concentration scales of the resulting concentration field are examined in detail. It is found that in a region near the pointed end of the domain, a balance between the horizontal diffusion and the reaction develops. If the length scale of this region is smaller than the length of the domain, then a region where the vertical diffusion balances reaction develops. Using the pertinent scales, the equations and boundary conditions are rendered nondimensional and the asymptotic limit as S→ 0 is examined. This limit can be approached either by letting h→ 0 while keeping constant or by letting l→∞ while keeping constant. The former leads to a regular perturbation problem; the latter, to a singular perturbation problem. Analytical solutions to both problems are found and compared with full numerical solutions. It is concluded that, as a result of the sloping bottom, the diffusion in the vertical leads to horizontal fluxes that can be important in specific physical situations.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 124 • Issue 10 • October 1998
Pages: 1135 - 1141
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Oct 1, 1998
Published in print: Oct 1998
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