When in a laboratory small populations of bacteria are put on an agar surface, they begin to develop very distinct patterns depending on the strain of bacteria, the thickness of the agar and the level of nutrients available.

In our research we are working on the mathematical description of the process in which a population of Staphylococcus aureus bacteria develops a distinct pattern structure on an agar plate. A novel approach in this context is that the interplay between the pressure distribution on the agar plate and the growth of the bacteria population is considered.

Our model setting of a population of bacteria multiplying on an agar plate resembles the situation in a Hele-Shaw-cell. The governing equation of Hele-Shaw-flow is the same as for the flow of a fluid through a porous medium governed by Darcy's law. Thus the propagation velocity of the cells is assumed to depend on the gradient of the pressure. We will study how patterns emerge from both the pressure distribution that results from the growth of the bacteria population as well as bacterial regulation mechanisms.