A mathematical model of microbial growth for limiting nutrients in a full three dimensional flow reactor which accounts for the colonization of the reactor wail surface by the microbes is studied analytically. It can be viewed as a model of the large intestine or of the fouling of a commercial bioreactor or pipe flow. Two steady state regimes are identified, namely, the complete washout of the microbes from the reactor and the successful colonization of both the wall and bulk fluid by the microbes. Only one steady state is stable for any particular set of parameter values. Sharp and explicit conditions are given for the stability of each. The effects of adding an antimicrobial agent to the reactor are examined with and without wall growth.
- Bacterial wall growth
- Elliptic and parabolic boundary value problem
- Nonlinear boundary conditions
- Plug flow
ASJC Scopus subject areas
- Applied Mathematics