  In this paper we derive a pore-scale model for permeable biofilm formation in
a two-dimensional pore. The pore is divided in two phases: water and biofilm.
The biofilm is assumed to consist of four components: water, extracellular
polymeric substances (EPS), active bacteria, and dead bacteria. The flow of
water is modeled by the Stokes equation whereas a diffusion-convection equation
is involved for the transport of nutrients. At the water/biofilm interface,
nutrient transport and shear forces due to the water flux are considered. In
the biofilm, the Brinkman equation for the water flow, transport of nutrients
due to diffusion and convection, displacement of the biofilm components due to
reproduction/dead of bacteria, and production of EPS are considered. A
segregated finite element algorithm is used to solve the mathematical
equations. Numerical simulations are performed based on experimentally
determined parameters. The stress coefficient is fitted to the experimental
data. To identify the critical model parameters, a sensitivity analysis is
performed. The Sobol sensitivity indices of the input parameters are computed
based on uniform perturbation by $\pm 10 \%$ of the nominal parameter values.
The sensitivity analysis confirms that the variability or uncertainty in none
of the parameters should be neglected.
