Speaker
Description
We develop and analyze a model for a flat microbial droplet growing on the surface of a viscous fluid. The model describes growth-induced stresses at the fluid surface, density variations in the bulk due to nutrient consumption, and the resulting fluid flows that arise. We reformulate this free boundary problem as a system of integro-differential equations defined solely on the microbial domain. From this formulation, we identify an axisymmetric solution corresponding to a radially expanding disk and analyze its stability. We find growth stabilizes the axisymmetric solution while buoyancy-driven flows destabilize it. Our analysis also leads to a spectral method for numerically solving the integro-differential equations on arbitrary smooth domains. We connect our findings to experimental observations of yeast growing on viscous substrates.