Microbial Competition for Nutrient and Wall Sites in Plug Flow

A mathematical model of microbial competition for limiting nutrients and for a limited set of available wall-attachment sites in an advection-dominated tubular reactor is formulated as a limiting case of the more general model considered in [M. Ballyk and H. L. Smith, A flow reactor with wall growth, in Mathematical Models in Medical and Health Sciences, M. Horn, G. Simonett, and G. Webb, eds., Vanderbilt University Press, Nashville, TN, 1998]. The model consists of a system of hyperbolic PDE. The existence and stability properties of its steady state solutions are investigated, both analytically and numerically. A surprising finding in the case of two-strain competition is the existence of a steady state solution characterized by the segregation of the two bacterial strains to separate nonoverlapping segments along the tubular reactor.