Keywords: biofilm modelling, heterogeneous biofilms, dispersion, volume averaging, transport equations
Effective dispersion in channelled biofilms
Heterogeneous biofilms may arise because of non-uniform biofilm growth. When considering multiple-scale problems involving biofilms, a direct simulation of the flow in the heterogeneous biofilm is not tractable. This calls for an averaged description of the flow and transport in such heterogeneous biofilms. This paper presents a theoretical derivation of the transport equations in such structures. The averaged equations are obtained from an averaging procedure applied to the small-scale transport equations. The resulting macro-scale equations involve effective properties (permeability, dispersion, etc), which are connected to the small-scale structure through several closure problems. These closure problems were solved for simple representative unit cells of columnar and channelled biofilms, and numerical results are presented.