Biofilms are collections of microorganisms that aggregate using a self-produced matrix of extracellular polymeric substance. It has been broadly demonstrated that many microbial infections in the body, including dental plaque, involve biofilms. While studying experimental models of biofilms relevant to mechanical removal of oral biofilms, distinct ripple patterns have been observed. In this work, we describe a multiphase model used to approximate the dynamics of the biofilm removal process. We show that the fully nonlinear model provides a better representation of the experimental data than the linear stability analysis. In particular, we show that the full model more accurately reflects the relationship between the apparent wavelength and the external forcing velocities, especially at mid-to-low velocities at which the linear theory neglects important interactions. Finally, the model provides a framework by which the removal process (presumably governed by highly nonlinear behavior) can be studied.