On the validity of a perturbation flow solution for mass transport calculations in 2D biofilm growth simulations
Pressure difference driven (Poiseuille) flow through a 2D channel with biofilm growing on one or both of the channel walls is a common setup used in the mesoscale biofilm growth studies. These studies require the repeated solution of Navier Stokes equations for the fluid flow and the transport equations for the substrate concentration in addition to the equations governing the growth and spreading of biomass. These calculations are time consuming and require large grid sizes to resolve the flow features and substrate concentration gradients arising due to substrate consumption inside the biofilm. Due to these constraints, the simulation studies are often done in narrow channels where biofilm thickness is of the same order of magnitude as the width of the channel. This setup in long term growth simulation studies however suffers from problems arising due to bioclogging. In my talk, I will introduce a fast, computationally inexpensive way to compute an approximate flow solution in wider channels using a Boundary Perturbation Method (BPM). I will present the results of our study where we investigated how the inaccuracies in the flow solution affects the numerical solution of the substrate transport equation calculated using it.