Fig 1. Schematic of the biofilm system.

The aqueous phase is the region without biomass present, Ω₁(t) = {(x, y) ∈ Ω:M(t;x, y) = 0}, the biofilm phase is the region with biomass present Ω₂(t) = {(x, y) ∈ Ω:M(t;x, y) > 0}. These regions change over time as the biofilm grows. Biofilm colonies form attached to the substratum, which is a part of the boundary of the domain.