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arXiv · 2602.13724

Instability of microbial droplets growing on viscous substrates

Vicente Gomez Herrera·Scott Weady
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Abstract

We develop and analyze a model for a flat microbial droplet growing on the surface of a three-dimensional 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 morphological stability. We find that growth forces stabilize the axisymmetric solution while buoyancy forces destabilize it. We connect these findings to experimental observations.

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Vicente Gomez Herrera, Scott Weady. 2026-02-14. Instability of microbial droplets growing on viscous substrates. https://doi.org/10.1017/jfm.2026.11721

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