Quantifying mixing in active fluids

Active matter consists of individual particles that consume energy and move collectively in bulk, forming emergent patterns. We study an active system composed of semi-flexible biopolymers (microtubules), and clustered molecular motors (kinesin) that self-mixes. In this system, microtubules are bundled together, and as kinesin clusters walk along the filaments, the bundles move relative to each other where they extend, bend, buckle, and fracture. When confined in 2D at an oil-water interface, the active network is an extensile active nematic, we can consider the defects to be virtual stirrers and the microtubules/kinesin system is the fluid. We quantify the quality of mixing, or topological entropy, in this self-mixing system, by coupling beads to the microtubule bundles and tracking their motion as it is mixed. Bead trajectories are used to measure the rate of separation in the material to calculate the topological entropy and these results are compared with a line-stretching method. We then change the rate of local extension, by varying the ATP concentration to see the effect on the topological entropy.