Colloquium
3:30 p.m., Friday
Math 100
John Chadam
University of Pittsburg
A mathematical model of bioremediation in a porous medium
A simplified model for bacterial remediation of wastes in a porous
medium is proposed. The mathematical model consists of a coupled set of
nonlinear partial differential equations and an ordinary differential
equation. Basic existence, uniqueness and regularity of the system can
be proved in three space dimensions, globally in time. The existence of
travelling waves can also be established. In a physically relevant limit,
a free boundary problem can be formally derived. In this sharp interface
limit the shape stability of the moving reaction fronts can be studied
using elementary bifurcation analysis. In agreement with industrial
observations, these reaction fronts are stable in the early phases of
remediation, becoming unstable as the concentration of bacteria becomes
high. This could lead to undesirable fingering which would result in
some of the waste being inaccessible to the bacteria, greatly reducing the effectiveness of this type of remediation process. (Joint work with
Changsheng Chen, Manulife Insurance, Toronto, Cananda)
