Abstract
The motion of biofilm in aqueous environment is modeled as two-phase mixture flow which is governed by a generalized Novier-Stokes equation. Noticed that the propagation of bacteria colonies obeys the diffusion law with the similar instability mechanism in the coarsening of metallic grains during solidification, a thermodynamic framework has been derived which reveals the two competing mechanisms in biofilm growth: the absorption of nutrition from water phase that tends to maximize the contact area to environment and a loose-surface layer formation that tends to minimizes biofilm surface. Therefore an additional condition has been obtained which governs the formation of finger-shaped biofilm. 2D numerical simulation has been performed.