Spatio-temporal patterns in growing bacterial suspensions.

We present a theoretical model to explore the dynamics and phase evolution of growing bacterial suspensions. The model described by the hydrodynamic evolution of bacterial density, orientation, and fluid velocity, incorporating birth and death terms to account for colony growth. Starting from a low-density regime, the system undergoes structural and dynamical transitions driven by bacterial proliferation, leading to the emergence of distinct phases: dilute, turbulent, and heterogenous. At low density, bacteria show local ordering, which transitions to clustering and eventually to a turbulent phase with spatiotemporal vortices of varying scales, as observed in dense suspensions. As density increases, orientation becomes increasingly inhomogeneous and random, indicating heterogeneity. Our findings emphasize the critical role of growth in emergence of phases, illustrating how a single system can sequentially transit through different phases over time. We provide a comprehensive understanding of the evolving patterns and behaviors within growing bacterial colonies, which makes our work different from previous studies on dense bacterial suspensions. Since the growth is generic to active system hence the current work bridges theory and experiment, offering insights into the self-organization and emergent phases in active matter systems driven by growth.