A model of microbial growth in a plug flow reactor with wall attachment

Mary Ballyk, Hal Smith

Research output: Contribution to journalArticlepeer-review

67 Scopus citations


A mathematical model of microbial growth for limiting nutrient in a plug flow reactor which accounts for the colonization of the reactor wall surface by the microbes is formulated and studied analytically and numerically. It can be viewed as a model of the large intestine or of the fouling of a commercial bio-reactor 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, and for the long term persistence of the bacteria in the reactor.

Original languageEnglish (US)
Pages (from-to)95-126
Number of pages32
JournalMathematical Biosciences
Issue number2
StatePublished - May 1999


  • Bacterial wall growth
  • Gut
  • Plug flow

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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