Auto-chemotactic micro-swimmer suspensions: modeling, analysis and simulations

Abstract: Microorganisms can preferentially orient and move along gradients of a chemo-attractant (i.e., chemotax) while colonies of many microorganisms can collectively undergo complex dynamics in response to chemo-attractants that they themselves produce. For colonies or groups of micro-swimmers we investigate how an "auto-chemotactic" response that should lead to swimmer aggregation is affected by the non-trivial fluid flows that are generated by collective swimming. For this, we consider chemotaxis models based upon a hydrodynamic theory of motile suspensions that are fully coupled to chemo-attractant production, transport, and diffusion. Linear analysis of isotropically ordered suspensions reveals both an aggregative instability due to chemotaxis that occurs independently of swimmer type, and a hydrodynamic instability when the swimmers are "pushers". Nonlinear simulations show nonetheless that hydrodynamic interactions can significantly modify the chemotactically-driven aggregation dynamics in suspensions of "pushers" or "pullers". Different states of the dynamics resulting from these coupled interactions in the colony are discussed.