Emergence of Radial Tree of Bend Stripes in Active Nematics

Abstract

Living liquid crystals, a realization of active nematics where a lyotropic liquid crystal is combined with active bacteria, exhibit a plethora of out-of-equilibrium phenomena that range from active turbulence and dynamic spatiotemporal patterns to the creation and annihilation of motile topological defects. Experiments and hydrodynamic simulations are used here to report on the emergence of bend stripes, which arise as spontaneous undulations of the director field in circularly aligned lyotropic liquid crystals doped with bacteria. The interplay between bacterial-induced hydrodynamic flows and elastic forces in the material induces remarkable deformation patterns consisting of branched, radially elongated bands of a high curvature of the director field. The average number of such branches increases with the distance from the center of the circular alignment, leading to the formation of a radial tree of bands that is reminiscent of a snowflake structure. Hydrodynamic simulations, which are in agreement with the experiments, are used to explain the origin of such structures and to provide additional insights into regimes that are beyond the limit of experimental measurements. In particular, it is found that when activity is switched off in the early stages of pattern formation, a pronounced decay of bend-distortion energy ensues, with little change of the splay energy, serving to confirm that the bend stripes are an outcome of activity-driven bend-instability phenomena. Taken together, experiments and simulations demonstrate a system in which strain and geometry can be combined to dynamically manipulate pattern formation in active matter, paving the way to a deeper understanding and finer control of active colloidal systems.

Machine learning active-nematic hydrodynamics

“…Active Nematohydrodynamics and Lattice Boltzmann Simulation. Simulation data for training and testing were generated using a hybrid lattice Boltzmann method which has been used in prior studies of different types of active nematics (18,27,60,61). The symmetric and traceless tensorial order parameter of the nematic is defined as Q = S(nn − I/3) [8] with S being the scalar order parameter, n being the unit vector describing the local nematic orientation, and I being an identity tensor.…”

Interplay of Active Stress and Driven Flow in Self-Assembled, Tumbling Active Nematics

“…Specifically, the Ericksen number is defined as Er = γ 1 u 0 L z /K 1 for the Couette flow and Er = GL 2 z /K 1 for the pressure-driven flow. We employ a hybrid lattice Boltzmann method to solve the coupled governing partial differential equations (Equations ( 1) and ( 3)) [31,57,58]. The simulation box size was [L x , L y , L z ] = [51,101,51], with periodic boundary coditions in the xdirection and y-direction.…”

“…In some types of active nematic LCs, their constituents can selfpropel, as is the case for two-dimensional sheets of microtubule and kinesin [26], or actin and myosin [27] and dense bacteria suspensions [28]. Another class of active nematics is often called "living nematic" in which bacteria are swimming in a nontoxic, lyotropic chromonic LC [29][30][31][32]. An analogous system consists of active biopolymers suspended in a passive colloidal nematic LC [33].…”

A Discrete Multi-Physics Model to Simulate Fluid Structure Interaction and Breakage of Capsules Filled with Liquid under Coaxial Load

“…In order to analyse the influence of these parameters on the deformability, strength, and type of fracture of the capsule, the main simulation, fitted to the experimental force-displacement curve, was assessed in 9 different simulations modifying kb (1.56, 4.67, and 14 N m −1 ) and rmax (1.03•r0, 1.2•r0, and 1.27•r0) values. Many other authors have applied similar methodologies in order to perform sensitivity analysis in different fields [39][40][41][42].…”