Microtubule-based active nematics and the necessity of chaotic flows

Active nematics are fluids with local orientational order and an internal energy source driving fluid motion. Examples include dense swarms of motile bacteria, generating coherent flows, and dense 2D layers of rod-like microtubules cross-linked by molecular motors powered by ATP. We focus on the latter, microtubule system, for which experimental flows always exhibit chaotic advection. This is not the case for general active nematics. Theoretical models of the microtubule system can generate both chaotic flows and static flows that are not chaotic. We seek an explanation for why experiments always exhibit chaos. To this end, we propose a theoretical principle that guarantees chaotic advection. In particular, under reasonable physical assumptions we find that the Lyapunov exponent of the flow must be greater than the rate at which kinematic energy is dissipated by the system. This implies a strictly positive Lyapunov exponent and hence chaotic advection. The same argument does not hold for bacterial systems, which may explain why they can have non chaotic experimental states.