Power, chaos, and energy extraction in active nematics

Active nematics are an important class of fluids with both

orientational (i.e. nematic) order and an internal energy source

(i.e. activity). This energy source can drive complex fluid motion,

including chaotic advection. A prototypical example of an active

nematic consists of long filamentous bundles of microtubules

crosslinked by molecular motors which are powered by ATP. Here, we

explore the relationship between the power injected via the ATP and

the resulting chaotic mixing of the system, as measured by the

Lyapunov exponent. We see that the power and Lyapunov exponent are

proportional to one another, which helps explain why these systems

always exhibit chaotic advection in the laboratory. We also discuss

how extracting work from such a system should lower the amount of

chaotic mixing. We address these questions via theoretical

arguments, numerical simulation, and analysis of experimental data.