Spatiotemporal crystallization of an active fluid

Abstract

The emergence of long-range spatiotemporal order from intrinsic chaos is a central challenge in far-from-equilibrium physics. In active fluids, such as cytoskeletal networks driving cellular motion, self-generated flows typically produce "active turbulence", lacking translational symmetry. Here we show that a chaotic active nematic can self-organize into a spatiotemporal crystal, forming a regular lattice of density, orientation, and vorticity that breaks both spatial and temporal translational symmetry. Using a microtubule/kinesin active nematic interfaced with a lamellar liquid crystal and confined in microfluidic channels, we observe robust spatiotemporal lattices without external forcing. The ordering emerges from spontaneous synchronization of intrinsic flow instabilities, mediated by confinement and feedback between the active layer and the passive anisotropic interface. Continuum nematohydrodynamics simulations support our interpretation, highlighting how intrinsic length and time scales shape the active crystals. These results reconcile chaos and crystallinity in active matter and provide a strategy for engineering order in self-driven, far-from-equilibrium soft materials.

Figures (6)

• Figure 1: Experimental setup and self-organization of active flows. a Top view of experimental confined sample in an open cell. Lateral confinement is imposed with a series of polymeric walls. A layer of liquid crystal oil (8CB) is placed on top of the aqueous subphase. The AN layer forms at the water/oil interface. b Self-organization of the AN in density hot-spots and vortex lattices. ATP concentration is 1.37 mM. Scale bar, 200 $\mu$m. i) Fluorescence microscopy snapshot. ii) Time average of 240 fluorescence images obtained at a rate of 2 fps. iii) Map with the average vorticity of the active flow field. iv) Image in ii with a sketch of the vortex lattice shown in iii overlaid. c Time average of 240 fluorescence micrographs of the AN acquired at 2 fps. Three channels of different widths are observed simultaneously. Scale bar, 200 $\mu$m. d Time dependence of the space-averaged longitudinal component of the director field, $<n_x^2>$, for a channel of width 521 $\mu$m. The size of the averaging window is shown as an orange frame in panel b.ii. e Average Fourier transforms of time traces of $<n_x^2>$ for channels of different width, as specified.
• Figure 2: Intrinsic scales of the spatiotemporal patterns. a Transversal, $L_{trans} (\square)$, and longitudinal, $L_{long} (\circ)$, lattice parameters of the density hot-spot lattice as a function of channel width. Error bars are the standard deviation from the mean in repetitions. b Characteristic oscillation frequency of the orientational field in the spatiotemporal crystals as a function of the average speed, used as a proxy for activity. In the inset, the scaling proposal $L_{long} \sim \tau\,v_x$ is compared with the experimental value of $L_{long}$. The shaded region is the 99% confidence band of the weighted mean. Error bars indicate the 99% confidence interval of the parameters.
• Figure 3: Synchronized transversal instabilities trigger the formation of spatiotemporal crystals. a Fluorescence micrographs showing the self-organization of transversal instabilities of the antiparallel aligned flows in an unconfined AN layer. Elapsed times from the leftmost frame, and then top to bottom, are 4 s, 6 s, 8 s, 16 s, and 22 s (see also Movie \ref{['SMov:transversal_oscillations']}). Scale bars, 200 $\mu$m. The orientation of the magnetic field is indicated below the first frame. A sketch of the evolution of active filaments and topological defects is depicted below the images. b Map of the time averaged order parameter of the AN orientational field ($\psi = <2\sin^2(\theta)-1>$, under different conditions. Here, $\theta$ is the angle between the local director field of the AN and $\vec{B}$, and $<...>$ means time average). c Overlay, from bottom to top, of the time-averaged (479 frames at 2 fps) vorticity, transversal velocity, longitudinal velocity, and fluorescence image of a region within a channel of width 430 $\mu$m. Red and blue vertical rods are guides for the eye to highlight the position of vortices in the other images. d Sketch illustrating the synchronization of antiparallel aligned flows (blue arrows) and transversal flows (brown arrows) for the confined AN. Complementary lattices of vortices (blue and red circles) and stagnation regions (black crosses) emerge.
• Figure 4: Crostalk between active and passive phases. a Polarized microscopy image of the passive liquid crystal layer showing the SmA patterning. In the sketch, dashed lines indicate the orientation of the passive mesogens, solid lines indicate the arrangement of the SmA planes, and dotted lines are the curvature walls forced by geometry on the SmA planes. b Time average of 480 fluorescence micrographs of the AN layer acquired at 2 fps. Scalebar, 200 $\mu$m. c Images a and b are overlaid to highlight their spatial correlation.
• Figure 5: Scaling of spatiotemporal patterns in simulations (Model A). a Scaling for $L_{\text{trans}}$ length obtained from nematic simulations using a kinematic viscosity $\eta = 6.67$, and different values for $K \in (0.005-0.05)$ and $\zeta \in (0.005-0.05)$. b Scaling for $L_{\text{long}}$ length obtained from our simulations using a fixed value for $K = 0.015$ and different values for $\eta \in (6.67-22.7)$ and $\zeta \in (0.005-0.02)$. All parameter magnitudes are provided in simulation units although the characteristic spacings shown here can be dimensionalized by considering that a simulation length unit approximately corresponds to $1.25 \, \mu m$ (see Methods).