2.1 The phase field model
The PF model for two-phase flow was applied to simulate biofilm deformation under fluid flow. This two-dimensional continuum biofilm model was implemented using COMSOL Multiphysics (COMSOL v5.4, Comsol Inc, Burlington, MA) with finite element method. COMSOL has computational fluid dynamics and phase field modeling as built-in features, and we implemented the constitutive equation (i.e., Oldroyd-B viscoelastic model) for the biofilm viscoelastic behavior using partial differential equation (PDE) module. The biofilm was considered an incompressible viscoelastic liquid.