Multicomponent hydrodynamic model for heterogeneous biofilms: two-dimensional numerical simulations of growth and interaction with flows.

We develop a tricomponent (ternary) hydrodynamic model for multiphase flows of biomass and solvent mixtures, which we employ to simulate biofilm. In this model, the three predominant effective components in biofilms, which are the extracellular polymeric substance (EPS) network, the bacteria, and the effective solvent (consisting of the solvent and nutrient, etc.), are modeled explicitly. The tricomponent fluid mixture is assumed incompressible as a whole, while intercomponent mixing, dissipation, and conversion are allowed among the effective components. Bacterial growth and EPS production due to the growing bacterial population are modeled in the biomass transport equations. Bacterial decay due to starvation and natural causes is accounted for in the bacterial population dynamics to capture the possible bacterial population reduction due to the depletion of the nutrient. In the growth regime for biofilms, the mixture behaves like a multiphase viscous fluid, in which the molecular relaxation is negligible in the corresponding time scale. In this regime, the dynamics of biofilm growth in the solvent (water) are simulated using a two-dimensional finite difference solver that we developed, in which the distribution and evolution of the EPS and bacterial volume fractions are investigated. The hydrodynamic interaction between the biomass and the solvent flow field is also simulated in a shear cell environment, demonstrating the spatially and temporally heterogeneous distribution of the EPS and bacteria under shear. This model together with the numerical codes developed provides a predictive tool for studying biomass-flow interaction and other important biochemical interactions in the biofilm and solvent fluid mixture.