Characterization of biofilm through an inhibitive kinetic function

Several results have been obtained for biofilm under inhibitive substrate. The first result gives the conditions that the existence of protective effect in biofilm depends on the bulk liquid substrate concentration. The second adds one boundary condition to obtain a biofilm thickness such that the whole range of biofilm has higher substrate consumption rates than the rate in the bulk liquid. The third shows the maximum range of two intervals for both substrate concentration at the wall and biofilm thickness, and equations for two conservative biofilm thicknesses that may be useful for practical applications.