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The bacterium {\em Bacilus subtilis} frequently forms biofilms at theinterface between the culture medium and the air. We develop a mathematicalmodel that couples a description of bacteria as individual discrete objects tothe standard advection-diffusion equations for the environment. The model takesinto account two different bacterial phenotypes. In the motile state, bacteriaswim and perform a run-and-tumble motion that is biased toward regions of highoxygen concentration (aerotaxis). In the matrix-producer state they excreteextracellular polymers, which allows them to connect to other bacteria and toform a biofilm. Bacteria are also advected by the fluid, and can triggerbioconvection. Numerical simulations of the model reproduce all the stages ofbiofilm formation observed in laboratory experiments. Finally, we study theinfluence of various model parameters on the dynamics and morphology ofbiofilms.

An individual-based model for biofilm formation at liquid surfaces