Biofilm is a collection of microbial cells which stick together within a protective gel-like substance that they produce, and which adhere to a surface. In the talk we will report on recently published collaborative research in which we studied the evolution of biofilm in porous media.
The first step was to use X-ray microtomography images from the lab of Dorthe Wildenschild. The images inspired the construction of a new mathematical model for biofilm evolution, which uses a variational inequality to satisfy the maximum volume constraint observed by experimentalists. The mathematical model is a doubly nonlinear PDE system, and has solutions of very low regularity, thus it requires delicate numerical schemes. Further challenges include time-stepping but our computations are able to reproduce the biofilm morphologies similar to those seen in the images.
The images also provide the detailed geometry of the porous medium at porescale, and this geometry changes due to the biomass clogging the pores. We simulate these effects with a coupled hydrodynamics model which is in turn upscaled; the calculated conductivities compare very well to those obtained experimentally, at various flow rates. The modeling and computational efforts are joint work with Anna Trykozko (University of Warsaw). The project shares some similarities with hydrate modeling, and has been/is supported by NSF-DMS 1115827 and NSF-DMS 1522734.