Since the bacterial growth changes the size of the pores, at the next time step we have a different flow region. To avoid the complication and expense of regridding the region, we implement a perturbation procedure. The disadvantage is that the boundary conditions are more complicated, but the simplicity of a regular domain outweighs this problem. A comparison with some experimental results using Pseudomonas aeruginosa in a straight tube, and using oxygen as the limiting nutrient was done in Cunningham, et al. Microscopic models, such as the one described above, help understand the basic biofilm growth processes, help determine parameters that are hard or impossible to measure, and complement experiments.
More complete models are in development.
Homogenization Porous media are very complicated. It is not possible to simulate the flow at each pore. In order to obtain results at the macroscopic scale, some sort of averaging needs to be done. Homogenization consists of assuming that the problem has two different length scales, a short and a long one. The resulting equations are then averaged to eliminate the small scale.