Instability of microbial droplets growing on viscous substrates
Fluid Dynamics
2026-05-20 v2 Biological Physics
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.
Keywords
Cite
@article{arxiv.2602.13724,
title = {Instability of microbial droplets growing on viscous substrates},
author = {Vicente Gomez Herrera and Scott Weady},
journal= {arXiv preprint arXiv:2602.13724},
year = {2026}
}