Resumen
We derive a set of phase field models for biofilms using the one-fluid two-component formulation in which the combination of extracellular polymeric substances (EPS, or polymer networks) and the bacteria is effectively modeled as one fluid component, while the collective ensemble of nutrient substrates and the solvent are modeled as the other. The biofilm is assumed to be an incompressible continuum, in which the motion of the polymer network and the solvent relative to the average velocity is accounted for by binary mixing kinetics. Various constitutive stress models are proposed for the effective polymer network component according to the property of the polymer network. Steady states are identified, their stability is analyzed (where two long wave growth modes are identified), and numerical solutions of different variations of the model in one space dimension are discussed and compared.