Sedimentation dynamics of passive particles in dilute bacterial suspensions: emergence of bioconvection

Microorganisms are ubiquitous in nature and technology. They inhabit diverse environments ranging from small river tributaries and lakes to oceans, as well as wastewater treatment plants and food manufacturing. In many of these environments, microorganisms coexist with settling particles. Here, we investigate the effects of microbial activity (swimming \textit{E. coli}) on the settling dynamics of passive colloidal particles using particle tracking methods. Our results reveal the existence of two distinct regimes in the correlation length scale ($L_u$) and the effective diffusivity of the colloidal particles ($D_{e\!f\!f}$), with increasing bacterial concentration ($\phi_b$). At low $\phi_b$, the parameters $L_u$ and $D_{e\!f\!f}$ monotonically increases with increasing $\phi_b$. Beyond a critical $\phi_b$, second regime is found in which both $D_{e\!f\!f}$ and $L_u$ are independent of $\phi_b$. We demonstrate that the transition between these regimes is characterized by the emergence of bioconvection. We use experimentally-measured particle-scale quantities ($L_u$, $D_{e\!f\!f}$) to predict the critical bacterial concentration for the diffusion-bioconvection transition.