A continuum mathematical model with sharp interface is proposed for describing the occurrence of patterns in initially circular and homogeneous bacterial colonies. The mathematical model encapsulates the evolution of the chemical field characterized by a Monod-like uptake term, the chemotactic response of bacteria, the viscous interaction between the colony and the underlying culture medium and the effects of the surface tension at the boundary. The analytical analysis demonstrates that the front of the colony is linearly unstable for a proper choice of the parameters. The simulation of the model in the nonlinear regime confirms the development of fingers with typical wavelength controlled by the size parameters of the problem, whilst the emergence of branches is favored if the diffusion is dominant on the chemotaxis or for high values of the friction parameter. Such results provide new insights on pattern selection in bacterial colonies and may be applied for designing engineered patterns.

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