Instability of microbial droplets growing on viscous substrates

TL;DR

This paper presents a mathematical model for microbial droplet growth on viscous substrates, analyzing stability and the effects of growth and buoyancy forces, with connections to experimental results.

Contribution

It introduces a reformulated integro-differential model for microbial droplet growth and analyzes the stability of axisymmetric solutions under various forces.

Findings

Growth forces stabilize the droplet shape.

Buoyancy forces lead to instability.

Model aligns with experimental observations.

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.