In nature interactions between biopolymers and motor proteins give rise to biologically essential emergent behaviours. Besides cytoskeleton mechanics, active nematics arise from such interactions. Here we present a study on 3D active nematics made of microtubules, kinesin motors and depleting agent. It shows a rich behaviour evolving from a nematically ordered space-filling distribution of microtubule bundles toward a flattened and contracted 2D ribbon that undergoes a wrinkling instability and subsequently transitions into a 3D active turbulent state. The wrinkle wavelength is independent of the ATP concentration and our theoretical model describes its relation with the appearance time. We compare the experimental results with a numerical simulation that confirms the key role of kinesin motors in cross-linking and sliding the microtubules. Our results on the active contraction of the network and the independence of wrinkle wavelength on ATP concentration are important steps forward for the understanding of these 3D systems.
Nematic elastomers are rubbery solids which have liquid crystals incorporated into their polymer chains. These materials display many unusual mechanical properties, one such being the ability to form fine-scale microstructure. In this work, we explore the response of taut and appreciably stressed sheets made of nematic elastomer. Such sheets feature two potential instabilities -- the formation of fine-scale material microstructure and the formation of fine-scale wrinkles. We develop a theoretical framework to study these sheets that accounts for both instabilities, and we implement this framew…
Wrinkles commonly develop in a thin film deposited on a soft elastomer substrate when the film is subject to compression. Motivated by recent experiments [Agrawal et al., Soft Matter 8, 7138 (2012)] that show how wrinkle morphology can be controlled by using a nematic elastomer substrate, we develop the theory of small-amplitude wrinkles of an isotropic film atop a nematic elastomer. The directors of the nematic elastomer are assumed to lie in a plane parallel to the plane of the undeformed film. For uniaxial compression of the film along the direction perpendicular to the elastomer directors,…
Instabilities in thin elastic sheets, such as wrinkles, are of broad interest both from a fundamental viewpoint and also because of their potential for engineering applications. Nematic liquid crystal elastomers offer a new form of control of these instabilities through direct coupling between microscopic degrees of freedom, resulting from orientational ordering of rod-like molecules, and macroscopic strain. By a standard method of dimensional reduction, we construct a plate theory for thin sheets of nematic elastomer. We then apply this theory to the study of the formation of wrinkles due to …
We study the deflection by gravity of a circular elastic disk deposited on a rigid support. The axisymmetric deflection induces a compressive orthoradial stresses which leads to a wrinkling instability above a critical threshold of the dimensionless gravity force. We study this instability by a combination of experiments, numerical simulations and analytical tools, with a particular focus on the role of geometry. We show that aspect ratio is a crucial parameter that controls both the threshold of instability and the most unstable mode. The influence of this parameter on the threshold can be ca…
We consider the point-indentation of a pressurized elastic shell. It has previously been shown that such a shell is subject to a wrinkling instability as the indentation depth is quasi-statically increased. Here we present detailed analysis of this wrinkling instability using a combination of analytical techniques and finite element simulations. In particular, we study how the number of wrinkles observed at the onset of instability grows with increasing pressurization. We also study how, for fixed pressurization, the number of wrinkles changes both spatially and with increasing indentation dep…
We present experimental observations and numerical simulations of a wrinkling instability that occurs at sufficiently high strain rates in the trembling regime of vesicle dynamics in steady linear flow. Spectral and statistical analysis of the data shows similarities and differences with the wrinkling instability observed earlier for vesicles in transient elongation flow. The critical relevance of thermal fluctuations for this phenomenon is revealed by a simple model using coupled Langevin equations that reproduces the experimental observations quite well.
When a flexible filament is confined to a fluid interface, the balance between capillary attraction, bending resistance, and tension from an external source can lead to a self-buckling instability. We perform an analysis of this instability and provide analytical formulae that compare favorably with the results of detailed numerical computations. The stability and long-time dynamics of the filament are governed by a single dimensionless elastocapillary number quantifying the ratio between capillary to bending stresses. Complex, folded filament configurations such as loops, needles, and racquet…
We present experimental results on the relaxation dynamics of vesicles subjected to a time-dependent elongation flow. We observed and characterized a new instability, which results in the formation of higher order modes of the vesicle shape (wrinkles), after a switch in the direction of the gradient of the velocity. This surprising generation of membrane wrinkles can be explained by the appearance of a negative surface tension during the vesicle deflation, due to compression in a sign-switching transient. Moreover, the formation of buds in the vesicle membrane has been observed in the vicinity…
Motivated by the redrawing of hot glass into thin sheets, we investigate the shape and stability of a thin viscous sheet that is inhomogeneously stretched in an imposed non-uniform temperature field. We first determine the associated base flow by solving the long-timescale stretching flow of a flat sheet as a function of two dimensionless parameters: the normalized stretching velocity $α$, and a dimensionless width of the heating zone $β$. This allows us to determine the conditions for the onset of an out-of-plane wrinkling instability stated in terms of an eigenvalue problem for a linear part…
We investigate the theoretical nonlinear response, Hessian stability, and possible wrinkling behaviour of a voltage-activated dielectric plate immersed in a tank filled with silicone oil. Fixed rigid electrodes are placed on the top and bottom of the tank, and an electric field is generated by a potential difference between the electrodes. We solve the associated incremental boundary value problem of superimposed, inhomogeneous small-amplitude wrinkles, signalling the onset of instability. We decouple the resulting bifurcation equation into symmetric and antisymmetric modes. For a neo-Hookean …
We study theoretically the instabilities induced by a linearly polarized ordinary light wave incident at a small oblique angle on a thin layer of homeotropically oriented nematic liquid crystal with special emphasis on the dye-doped case. The spatially periodic Hopf bifurcation that occurs as the secondary instability after the stationary Freedericksz transition is analyzed.
We study theoretically the formation of long-wavelength instability patterns observed at spreading of nematic droplets on liquid substrates. The role of surface-like elastic terms such as saddle-splay and anchoring in nematic films of submicron thickness is (re)examined by extending our previous work [Manyuhina et al EPL, 92, 16005 (2010)] to hybrid aligned nematics. We identify the upper threshold for the formation of stripes and compare our results with experimental observations. We find that the wavelength and the amplitude of the in-plane director undulations can be related to the small bu…
Motivated by recent experimental observations [U. Delabre et al, Langmuir 24, 3998, 2008] we reconsider an instability of ultrathin nematic films, spread on liquid substrates. Within a continuum elastic theory of liquid crystals, in the harmonic approximation, we find an analytical expressions for the critical thickness as well as for the critical wavenumber, characterizing the onset of instability towards the stripe phase. Comparing theoretical predictions with experimental observations, we establish the utility of surface-like term such as an azimuthal anchoring.
We show that the dominant mode of alignment plays an important role in dry active nematics,leading to two dynamical sub-classes defined by the nature of the instability of the nematic bands that characterize, in these systems, the coexistence phase separating the isotropic and fluctuating nematic states. In addition to the well-known instability inducing long undulations along the band, another stronger instability leading to the break-up of the band in many transversal segments may arise. We elucidate the origin of this strong instability for a realistic model of self-propelled rods and deter…
An important aspect of molecular fluids is the relation between orientation and translation parts of the two-particle correlations. Especially the detailed knowledge of the influence of orientation correlations is needed to explain and calculate in detail the occurrence of a nematic phase. The simplest model system which shows both orientation and translation correlations is a system of hard ellipsoids. We investigate an isotropic fluid formed of hard ellipsoids with Percus-Yevick theory. Solving the Percus-Yevick equations self-consistently in the high density regime gives a clear criterion f…
Surface wrinkling is an instability mode that is often observed in a wide variety of multilayer tubes under bending deformation. When the degree of applied bending exceeds a critical value, wrinkles appear at the intrados of the tube and release a large amount of in-plane strain energy stored by bending deformation. In the present work, we propose a simple theoretical model for evaluating the critical curvature and critical bending moment for the occurrence of wrinkling in multilayer tubes and apply the model to carbon nanotubes in a case study. Results indicate an inverse proportional relatio…
We consider a phenomenological continuum model for an active nematic fluid and show a universal, model independent, instability which renders the homogeneous nematic state unstable to order fluctuations. Using numerical and analytic tools we show that, for low energy excitations in the vicinity of a critical point, this instability leads to a phase separation in which the ordered regions form bands with the direction of nematic order being perpendicular to the direction of density gradient. We argue that this mechanism of phase separation, which we term self-regulation, is a universal feature …
A surface instability is reported in thin nematic films of 5CB and 8CB, occurring near the nematic--isotropic phase transition. Although this instability leads to patterns reminiscent of spinodal dewetting, we show that it is actually based on a nucleation mechanism. Its characteristic wavelength does not depend markedly on film thickness, but strongly on the heating rate.
A transient surface instability is reported in thin nematic films of 5CB and 8CB, occurring near the nematic-isotropic phase transition. Although this instability leads to patterns reminiscent of spinodal dewetting, we show that it is actually based on a nucleation mechanism. Its characteristic wavelength does not depend markedly on film thickness, but strongly on the heating rate.
Coupled magneto-mechanical wrinkling has appeared in many scenarios of engineering and biology. Hence, soft magneto-active (SMA) plates buckle when subject to critical uniform magnetic field normal to their wide surface. Here, we provide a systematic analysis of the wrinkling of SMA plates subject to an in-plane mechanical load and a transverse magnetic field?. We consider two loading modes: plane-strain loading and uni-axial loading, and two models of magneto-sensitive plates: the neo-Hookean ideal magneto-elastic model and the neo-Hookean magnetization saturation Langevin model. Our analysis…
We theoretically investigate the threshold for the director reorientation from the homeotropic state to the hybrid homeotropic-planar state and vice versa in a cell filled with a flexoelectric nematic liquid crystal (NLC) subjected to an electric field. The liquid crystal is doped by a CTAB-like substance, a part of molecules of which dissociates into positive and negative ions. The anchoring on one of the cell surfaces is assumed to be strong and homeotropic, while the other surface can adsorb positive ions which play the role of an orienting surfactant for NLC molecules on this surface. At c…
Substrates which are chemically or topographically patterned induce a variety of liquid crystal textures. The response of the liquid crystal to competing surface orientations, typical of patterned substrates, is determined by the anisotropy of the elastic constants and the interplay of the relevant lengths scales, such as the correlation length and the surface geometrical parameters. Transitions between different textures, usually with different symmetries, may occur under a wide range of conditions. We use the Landau-de Gennes free energy to investigate the texture of nematics in sinusoidal c…
Pattern formation in nonlinear dynamics of nematic liquid crystals above the flexoelectric instability threshold
Landau Institute for Theoretical Physics, RAS（朗道理论物理研究所，俄罗斯科学院）；Institute for Oil and Gas Research, RAS（油气研究所，俄罗斯科学院）；NRU Higher School of Economics（国立研究大学高等经济大学）
From the mitotic spindle up to tissues and biofilms, many biological systems behave as active droplets, which often break symmetry and change shape spontaneously. Here, I show that active nematic droplets can experience a fingering instability. I consider an active fluid that acquires nematic order through anchoring at the droplet interface, and I predict its morphological stability in terms of three dimensionless parameters: the anchoring angle, the penetration length of nematic order compared to droplet size, and an active capillary number. Droplets with extensile (contractile) stresses and …
Partially wetting nematic liquid crystal (NLC) films on substrates are unstable to dewetting-type instabilities due to destablizing solid/NLC interaction forces. These instabilities are modified by the nematic nature of the films, which influences the effective solid/NLC interaction. In this work, we focus on the influence of imposed substrate anchoring on the instability development. The analysis is carried out within a long-wave formulation based on the Leslie-Ericksen description of NLC films. Linear stability analysis of the resulting equations shows that some features of the instability, …
The stability of the equilibrium configurations of a nematic liquid crystal confined between two coaxial cylinders is analysed when a radial electric field is applied and the flexoelectric effect is taken into account. The threshold for perturbations depending only on the radius r in the cylindrical coordinate system and strong boundary conditions is studied. A new type of orientational transition caused by pure flexoelectric effect is found.
The processing of thin-structured materials in a fluidic environment, from nearly inextensible but flexible graphene sheets to highly extensible polymer films, arises in many applications. So far, little is known about the dynamics of such thin sheets freely suspended in fluid. In this work, we study the dynamics of freely suspended soft sheets in uniaxial extensional flow. Elastic sheets are modeled with a continuum model that accounts for in-plane deformation and out-of-plane bending, and the fluid motion is computed using the method of regularized Stokeslets. We explore two types of sheets:…
We perform dynamical simulations of a two-dimensional active nematic fluid in coexistence with an isotropic fluid. Drops of active nematic become elongated, and an effective anchoring develops at the nematic-isotropic interface. The activity also causes an undulatory instability of the interface. This results in defects of positive topological charge being ejected into the nematic, leaving the interface with a diffuse negative charge. Quenching the active lyotropic fluid results in a steady state in which phase-separating domains are elongated and then torn apart by active stirring.
Systems involving nematic liquid crystals subjected to magnetic fields or electric fields are modeled using the Oseen-Frank macroscopic continuum theory, and general criteria are developed to assess the local stability of equilibrium solutions. The criteria take into account the inhomogeneity of the electric field and the mutual influence of the electric field and the liquid-crystal director field on each other. The criteria show that formulas for the instability thresholds of electric-field Freedericksz transitions cannot in all cases be obtained from those for the analogous magnetic-field tr…
Toroidal nematics are nematic liquid crystals confined within a circular torus and subject to planar degenerate anchoring on the boundary of the torus. They may be droplets floating in an isotropic environment or cavities carved out of a solid substrate. A universal solution of Frank's elastic free energy is an equilibrium configuration for the nematic director field, irrespective of the values of the elastic constants, whose vector lines are the coaxial parallels of the torus. We explore the local stability of this configuration and identify a range of parameters where the main drive towards …
We consider a phenomenological continuum theory for an extensile, overdamped active nematic liquid crystal, applicable in the dense regime. Constructed from general principles, the theory is universal, with parameters independent of any particular microscopic realization. We show that it exhibits a bend instability similar to that seen in active suspensions, that leads to the proliferation of defects. We find three distinct nonequilibrium steady states: a defect-ordered nematic in which $+\frac{1}{2}$ disclinations develop polar ordering, an undulating nematic state with no defects, and a turb…
Recent experiments by Kantsler et. al. (2007) have shown that the relaxational dynamics of a vesicle in external elongation flow is accompanied by the formation of wrinkles on a membrane. Motivated by these experiments we present a theory describing the dynamics of a wrinkled membrane. Formation of wrinkles is related to the dynamical instability induced by negative surface tension of the membrane. For quasi-spherical vesicles we perform analytical study of the wrinkle structure dynamics. We derive the expression for the instability threshold and identify three stages of the dynamics. The scal…
We analyze the buckling of a rigid thin membrane floating on a dense fluid substrate. The interplay of curvature and substrate energy is known to create wrinkling at a characteristic wavelength $λ$, which localizes into a fold at sufficient buckling displacement $Δ$. By analyzing the regime $Δ<<λ$, we show that wrinkles are unstable to localized folding for {\em arbitrarily small} $Δ$. After observing that evanescent waves at the boundaries can be energetically favored over uniform wrinkles, we construct a localized Ansatz state far from boundaries that is also energetically favored. The resul…
We use linear stability analysis to show that an isotropic phase of elongated particles with dipolar flow fields can develop nematic order as a result of their activity. We argue that ordering is favoured if the particles are flow-aligning and is strongest if the wavevector of the order perturbation is neither parallel nor perpendicular to the nematic director. Numerical solutions of the hydrodynamic equations of motion of an active nematic confirm the results. The instability is contrasted to the well-known hydrodynamic instability of an ordered active nematic.
We investigate the effects of extrinsic curvature on the turbulent behavior of a 2D active nematic confined to the surface of a cylinder. The surface of a cylinder has no intrinsic curvatrue and only extrinsic curvature. A nematic field reacts to the extrinsic curvature by trying to align with the lowest principle curvature, in this case parallel to the long axis of the cylinder. When nematics are sufficiently active, there is a proliferation of defects arising from a bend or splay instability depending on the nature of the active stress. The extrinsic curvature of the cylinder beaks the rotat…
We analyze stability of the planar orientational structure in a nematic liquid crystal (NLC) cell with planar anchoring conditions at both substrates. Specifically, we study the instabilities of the ground state caused by surface elasticity at large saddle-splay elastic constant, $K_{24}$. For relatively small $K_{24}$ violating the Ericksen inequalities the theory predicts that the critical fluctuation mode of the wavelength, $λ_c$, will render the structure unstable when the thickness of the cell is below its critical value, $d_c$. The parity of the critical mode changes as the twist-splay r…
In experiments, an individual chemically active liquid crystal (LC) droplet submerged in the bulk of a surfactant solution may self-propel along a straight, helical, or random trajectory. In this paper, we develop a minimal model capturing all three types of self-propulsion trajectories of a drop in the case of a nematic LC with homeotropic anchoring at LC-fluid interface. We emulate the director field within the drop by a single preferred polarization vector that is subject of two reorientation mechanisms, namely, the internal flow-induced displacement of the hedgehog defect and the droplet's…
Strong effects of the Faraday instability on suspensions of rodlike colloidal particles are reported through measurements of the critical acceleration and of the surface wave amplitude. We show that the transition to parametrically excited surface waves displays discontinuous and hysteretic features. This subcritical behaviour is attributed to the shear-thinning properties of our colloidal suspensions thanks to a phenomenological model based on rheological data under large amplitude oscillatory shear. Birefringence measurements provide direct evidence that Faraday waves induce local nematic or…
We present in this paper a detailed analysis of the flexoelectric instability of a planar nematic layer in the presence of an alternating electric field (frequency $ω$), which leads to stripe patterns (flexodomains) in the plane of the layer. This equilibrium transition is governed by the free energy of the nematic which describes the elasticity with respects to the orientational degrees of freedom supplemented by an electric part. Surprisingly the limit $ω\to 0$ is highly singular. In distinct contrast to the dc-case, where the patterns are stationary and time-independent, they appear at fini…
Using novel micro-printing techniques, we develop a versatile experimental setup that allows us to study how lateral confinement tames the active flows and defect properties of the microtubule/kinesin active nematic system. We demonstrate that the active length scale that determines the self-organization of this system in unconstrained geometries loses its relevance under strong lateral confinement. Dramatic transitions are observed from chaotic to vortex lattices and defect-free unidirectional flows. Defects, which determine the active flow behavior, are created and annihilated on the channel…
There is now growing evidence of the emergence and biological functionality of liquid crystal features, including nematic order and topological defects, in cellular tissues. However, how such features that intrinsically rely on particle elongation, emerge in monolayers of cells with isotropic shapes is an outstanding question. In this article we present a minimal model of cellular monolayers based on cell deformation and force transmission at the cell-cell interface that explains the formation of topological defects and captures the flow-field and stress patterns around them. By including mech…
We propose a simple deterministic dynamic equation and reveal the mechanism of large-scale endless evolvement of spatial density inhomogeneity in active nematic. We determine the phase regions analytically. The interplay of density, magnitude of nematic order, and nematic director is crucial for the long-wave-length instability and the emergence of seemingly fluctuated collective motions. Ordered nematic domains can absorb particles, grow and divide endlessly. The present finding extends our understanding of the large-scale and seemingly fluctuated organization in active fluids.
We study a continuum model of an extensile active nematic to show that mesoscale turbulence develops in two stages: (i) ordered regions undergo an intrinsic hydrodynamic instability generating walls, lines of stong bend deformations, (ii) the walls relax by forming oppositely charged pairs of defects. Both creation and annihilation of defect pairs reinstate nematic regions which undergo further instabilities, leading to a dynamic steady state. We compare this with the development of active turbulence in a contractile active nematic.
