Biofilms are colonies of bacteria attached to surfaces. They play a critical role in many engineering and medical applications. Scientists study biofilm growth in flow cells but often have limited direct knowledge of the environmental conditions in the apparatus. Using fully resolved, numerical simulations to estimate conditions within a flow cell is computationally expensive. In this paper, we use asymptotic analysis to create a simulation of a biofilm system that has one growth-limiting substrate, and we show that this method runs quickly while maintaining similar accuracy to prior models. These equations can provide a better understanding of the environmental conditions in experiments and can establish the boundary conditions for further smaller-scale numerical simulations.
Keywords: Asymptotic approximation; Biofilms; Flow cell.