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Register a new userLattice Boltzmann simulations of spontaneous flow in active liquid crystals: the role of boundary conditions
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Active liquid crystals or active gels are soft materials which can be physically realised e.g. by preparing a solution of cytoskeletal filaments interacting with molecular motors. We study the hydrodynamics of an active liquid crystal in a slab-like geometry with various boundary conditions, by solving numerically its equations of motion via lattice Boltzmann simulations. In all cases we find that active liquid crystals can sustain spontaneous flow in steady state contrarily to their passive counterparts, and in agreement with recent theoretical predictions. We further find that conflicting anchoring conditions at the boundaries lead to spontaneous flow for any value of the activity parameter, while with unfrustrated anchoring at all boundaries spontaneous flow only occurs when the activity exceeds a critical threshold. We finally discuss the dynamic pathway leading to steady state in a few selected cases.
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We report hybrid lattice Boltzmann (HLB) simulations of the hydrodynamics of an active nematic liquid crystal sandwiched between confining walls with various anchoring conditions. We confirm the existence of a transition between a passive phase and an active phase, in which there is spontaneous flow in the steady state. This transition is attained for sufficiently ``extensile rods, in the case of flow-aligning liquid crystals, and for sufficiently ``contractile ones for flow-tumbling materials. In a quasi-1D geometry, deep in the active phase of flow-aligning materials, our simulations give evidence of hysteresis and history-dependent steady states, as well as of spontaneous banded flow. Flow-tumbling materials, in contrast, re-arrange themselves so that only the two boundary layers flow in steady state. Two-dimensional simulations, with periodic boundary conditions, show additional instabilities, with the spontaneous flow appearing as patterns made up of ``convection rolls. These results demonstrate a remarkable richness (including dependence on anchoring conditions) in the steady-state phase behaviour of active materials, even in the absence of external forcing; they have no counterpart for passive nematics. Our HLB methodology, which combines lattice Boltzmann for momentum transport with a finite difference scheme for the order parameter dynamics, offers a robust and efficient method for probing the complex hydrodynamic behaviour of active nematics.
Collective behaviour in suspensions of microswimmers is often dominated by the impact of long-ranged hydrodynamic interactions. These phenomena include active turbulence, where suspensions of pusher bacteria at sufficient densities exhibit large-scale, chaotic flows. To study this collective phenomenon, we use large-scale (up to $N=3times 10^6$) particle-resolved lattice Boltzmann simulations of model microswimmers described by extended stresslets. Such system sizes enable us to obtain quantitative information about both the transition to active turbulence and characteristic features of the turbulent state itself. In the dilute limit, we test analytical predictions for a number of static and dynamic properties against our simulation results. For higher swimmer densities, where swimmer-swimmer interactions become significant, we numerically show that the length- and timescales of the turbulent flows increase steeply near the predicted finite-system transition density.
Active matter describes materials whose constituents are driven out of equilibrium by continuous energy consumption, for instance from ATP. Due to the orientable character of the constituents, active suspensions can attain liquid crystalline order and can be theoretically described as active liquid crystals. Their inherently nonequilibrium dynamics causes a range of new striking effects, that in most cases have been characterized with numerical simulations, using lattice Boltzmann models (LB). In many active biological systems chirality plays an important role. Biomolecules such as DNA, actin, or microtubules form helical structures which, at sufficiently high density and in the absence of active forces, tend to self-assemble into twisted cholesteric phases. Understanding the outcome of the interplay between chirality and activity is therefore an important and timely question. Studying a droplet of chiral matter in 3D, we have found evidence of a new motility mode, where the rotational motion of surface topological defects, that arrange in a fan-like pattern. The resulting regular propulsive motion due to the underlying chirality is a striking phenomenon that can be also used in practical applications. The use of a parallel (MPI) implementation of lattice Boltzmann models, and available HPC resources, have been of fundamental importance in conducting the study. We have used different HPC clusters and among these RECAS. This allowed us to conduct a scaling test performed on different computational infrastructures.
Previous theoretical studies of calamitic (i.e., rod-like) ionic liquid crystals (ILCs) based on an effective one-species model led to indications of a novel smectic-A phase with a layer spacing being much larger than the length of the mesogenic (i.e., liquid-crystal forming) ions. In order to rule out the possibility that this wide smectic-A phase is merely an artifact caused by the one-species approximation, we investigate an extension which accounts explicitly for cations and anions in ILCs. Our present findings, obtained by grand canonical Monte Carlo simulations, show that the phase transitions between the isotropic and the smectic-A phases of the cation-anion system are in qualitative agreement with the effective one-species model used in the preceding studies. In particular, for ILCs with mesogenes (i.e., liquid-crystal forming species) carrying charged sites at their tips, the wide smectic-A phase forms, at low temperatures and within an intermediate density range, in between the isotropic and a hexagonal crystal phase. We find that in the ordinary smectic-A phase the spatial distribution of the counterions of the mesogens is approximately uniform, whereas in the wide smectic-A phase the small counterions accumulate in between the smectic layers. Due to this phenomenology the wide smectic-A phase could be interesting for applications which hinge on the presence of conductivity channels for mobile ions.
We consider an off-lattice liquid crystal pair potential in strictly two dimensions. The potential is purely repulsive and short-ranged. Nevertheless, by means of a single parameter in the potential, the system is shown to undergo a first-order phase transition. The transition is studied using mean-field density functional theory, and shown to be of the isotropic-to-nematic kind. In addition, the theory predicts a large density gap between the two coexisting phases. The first-order nature of the transition is confirmed using computer simulation and finite-size scaling. Also presented is an analysis of the interface between the coexisting domains, including estimates of the line tension, as well as an investigation of anchoring effects.
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