Chaotic Mixing in Simulations of Microtubule-based Active Nematics

Active nematics are non-equilibrium fluids composed of rod-like, self-driven units that can generate large-scale coherent flows. One of the most studied examples of active nematics is a bio-engineered fluid composed of densely packed extended microtubule (MT) bundles in 2D cross-linked by kinesin motors. Using energy from ATP, kinesin motors move along the MT bundles that generate extensile stress. The MT bundles deform due to the extensile stress, inducing high-curvature regions in the material domain. The local alignment of the densely packed MT bundles results in the formation of a nematic order. The orientational order breaks down in localized areas of zero density where the MT bundles fracture, creating pairs of topological defects. These mobile defects collectively develop a complex braiding pattern before annihilating in the fluid domain. Experimental observations suggest that these defects act like "virtual stirring rods", driving the self-mixing of the fluid. The chaotic self-mixing of the fluid can be quantified using topological entropy and the Lyapunov exponent. In this study, we explore the self-mixing of the microtubule-based active nematics using two numerical models: the traditional Beris-Edwards (BE) model and the more recently developed Beris-Edwards model with enhanced nematic locking (BENL). We employ several numerical methods to quantify both topological entropy and Lyapunov exponent, and compare the results between these two models.