A continuum model for the growth of bacterial colonies on a surface

A model for the spatio-temporal growth of a bacterial colony on the flat surface of a solid medium is introduced based on a reaction-diffusion equation with vertical and lateral growth components. If the colony height is restricted to some maximum value, the colony morphology corresponds to solitary wave propagation in the radial direction. However, if colony growth is flux limited by the diffusion of initially separated components into the colony, vertical colony growth results from a steady state, finite sized reaction zone within the colony. In the flux-limited growth regime a more general colony morphology is obtained with constant velocity propagation of the colony radius and central height in qualitative agreement with experiment.