We study experimentally and theoretically the hydrodynamic interaction of pairs of circular inclusions in two-dimensional, fluid smectic membranes suspended in air. By analyzing their Brownian motion, we find that the radial mutual mobilities of identical inclusions are independent of their size but that the angular coupling becomes strongly size-dependent when their radius exceeds a characteristic hydrodynamic length. The observed dependence of the mutual mobilities on inclusion size is described well for arbitrary separations by a model that generalizes the Levine/MacKintosh theory of point-force response functions and uses a boundary-element approach to calculate the mobility matrix.
Ring patterns of concentric 2pi-solitons in molecular orientation, form in freely suspended chiral smectic-C films in response to an in-plane rotating electric field. We present measurements of the zero-field relaxation of ring patterns and of the driven dynamics of ring formation under conditions of synchronous winding, and a simple model which enables their quantitative description in low polarization DOBAMBC. In smectic C_A* TFMHPOBC we observe an odd-even layer number effect, with odd number layer films exhibiting order of magnitude slower relaxation rates than even layer films. We show th…
In this Letter we discuss theoretically the instabilities of thermotropic freely standing smectic-A films under shear flow\cite{re:wu}. We show that, in Couette geometry, the centrifugal force pushes the liquid crystal toward the outer boundary and induces smectic layer dilation close to the outer boundary. Under strong shear, this effect induces a layer buckling instability. The critical shear rate is proportional to $1/\sqrt{d}$, where $d$ is the thickness of the film.
A theoretical analysis of surface fluctuations of a freely standing thermotropic smectic-A liquid crystal film is provided, including the effects of viscous hydrodynamics. We find two surface dynamic modes (undulation and peristaltic). For long wavelengths and small frequencies in a thin film, the undulation mode is the dominant mode. Permeation enters the theory only through the boundary conditions. The resulting power spectrum is compared with existing experiments. It is also shown that feasible light scattering experiments on a freely standing smectic-A film can reveal viscosity and elastic…
We study the hydrodynamics of a freely-standing smectic-A film in the isothermal, incompressible limit theoretically by analyzing the linearized hydrodynamic equations of motion with proper boundary conditions. The dynamic properties for the system can be obtained from the response functions for the free surfaces. Permeation is included and its importance near the free surfaces is discussed. The hydrodynamic mode structure for the dynamics of the system is compared with that of bulk systems. We show that to describe the dynamic correlation functions for the system, in general, it is necessary …
Smectic liquid crystal films a few molecular layers thick that are freely suspended in air are used as a model system to study the coalescence of fluids in two dimensions. High-speed video microscopy is used to observe the coalescence of islands, which are thicker, disk-shaped regions of the film, in a process driven by the line tension associated with edge dislocations along the island boundaries and limited by viscous dissipation in the liquid crystal and in the surrounding air. The early time growth of the bridge connecting the merging islands reveals much slower dynamics than predicted by …
We study a horizontal streaming excited by means of a low frequency and intensity acoustic wave in 2D freely suspended film of thermotropic smectic liquid crystal. Acoustic pressure induces fast periodic transverse oscillations of the film, which produce in-plane stationary couples of vortices slowly rotating in opposite directions owing to hydrodynamic nonlinearity. The parameters of vortices are measured using a new method, based on tracking disk-shaped island defects. The horizontal motion occurs only when the amplitude of acoustic pressure exceeds threshold value, which can be explained by…
We demonstrate spontaneous wrinkling as a transient dynamical pattern in thin freely floating smectic liquid-crystalline films. The peculiarity of such films is that, while flowing liquid-like in the film plane, they cannot quickly expand in the direction perpendicular to that plane. At short time scales they therefore behave in two dimensions like quasi-incompressible membranes. Such films can develop a transient undulation instability or form bulges in response to lateral compression. Optical experiments with freely floating bubbles on parabolic flights and in ground lab experiments are repo…
Bubbles made of smectic liquid crystals (LC) can display buckling and wrinkling. These deformations are induced in the course of the relaxation of an elongated bubble towards a sphere. The bubbles are created through the collapse of a catenoid LC film. Two mechanisms leading to wrinkles are reported: (a) Compression of the smectic film by outer forces, and (b) Invagination of the bubble shortly after formation. The flow on the bubble surface is analyzed, providing insight into how the outer forces act on the bubble and induce local surface deformation. It is found that the orientation of the w…
Experimental and theoretical studies of a smectic-hexatic transition in freely suspended films of 54COOBC compound are presented. X-ray investigations revealed a discontinuous first-order transition into the hexatic phase. Moreover, the temperature region of two phase coexistence near the phase transition point diminishes with film thickness. The coexistence width dependence on film thickness was derived on the basis of the Landau mean-field theory in the vicinity of the tricritical point (TCP). Close to TCP the surface hexatic ordering penetrates anomalously deep into the film interior.
Surface interactions can cause freely suspended thin liquid crystalline films to form phases different from the bulk material, but it is not known what happens at the surface of thick films. Edge dislocations can be used as a marker for the boundary between the bulk center and the reconstructed surface. We use noncontact mode atomic force microscopy to determine the depth of edge dislocations below the surface of freely suspended thick films of 4-n-heptyloxybenzylidene-4-n-heptylaniline (7O.7) in the crystalline B phase. 3.0 +/- 0.1 nm high steps are found with a width that varies with tempera…
Using computer simulations, we studied the diffusion and structural relaxation in equilibrium smectic liquid crystal bulk phases of parallel hard spherocylinders. These systems exhibit a non-Gaussian layer-to-layer diffusion due to the presence of periodic barriers and transient cages, and show remarkable similarities with the behavior of out-of-equilibrium supercooled liquids. We detect a very slow inter-layer relaxation dynamics over the whole density range of the stable smectic phase which spans a time interval of four time decades. The intrinsic nature of the layered structure yields a hop…
We study the annihilation of topological defect pairs in the quasi-twodimensional (2D) geometry of freely suspended smectic films. This elementary process is at the basis of all models describing the statistics of complex defect patterns. We prepare pairs with opposite topological charges and retrieve the interaction mechanisms from their trajectories. The square-root dependence of the defect separation on the time until annihilation and the asymmetry in propagation velocities of the opponents predicted by theory are confirmed. The importance of defect orientations is demonstrated. Trajectorie…
Long-scale dynamic fluctuation phenomena in freely suspended films is analyzed. We consider isotropic films that, say, can be pulled from bulk smectic A liquid crystals. The key feature of such objects is possibility of bending deformations of the film. The bending (also known as flexular) mode turns out to be anomalously weakly attenuated. In the harmonic approximation there is no viscous-like damping of the bending mode, proportional to q^2 (q is the wave vector of the mode), since it is forbidden by the rotational symmetry. Therefore the bending mode is strongly affected by non-linear dynam…
We present a modified version of our "sliding model", where chain arcs, between two contacts at the surface, may move if all the barriers along the arc are weaker than a certain threshold.An important advance of the revised model is that the high limiting chain lengths N* observed in the experiments are naturally accoundted for. In this model, a film of thickness h, smaller than the coil size, can show either a "sandwich" structure with two mobile sublayers (at low temperatures T<T(h)), or a single mobile layer at T>T(h). But the accident occurring at T=T(h), does not necessarily coincide with…
We report a detailed theoretical analysis of novel quadrupolar interactions observed between islands, which are disk-like inclusions of extra layers, floating in thin, freely suspended smectic C liquid crystal films. Strong tangential anchoring at the island boundaries result in a strength +1 chiral defect in each island and a companion -1 defect in the film, these forming a topological dipole. While islands of the same handedness form linear chains with the topological dipoles pointing in the same direction, as reported in the literature, islands with different handedness form compact quadrup…
Two dimensional (2D) laminar jet-----a stream of fluid that projected into a surrounding medium with the flow confined in 2D-----has both theoretical and experimental significance. We carried out 2D laminar jet experiments in freely suspended liquid crystal films (FSLCFs) of nanometers thick and centimeters in size, in which individual molecules are confined to single layers thus enable film flows with two degrees of freedom. The experimental observations are found in good agreement with the classic 2D laminar jet theory of ideal cases that assume no external coupling effects, even in fact the…
Freely suspended films of smectic liquid crystals are unique examples of quasi two-dimensional fluids. Mechanically stable and with quantized thickness of the order of only a few molecular layers, smectic films are ideal systems for studying fundamental fluid physics, such as collective molecular ordering, defect and fluctuation phenomena, hydrodynamics, and nonequilibrium behavior in two dimensions (2D), including serving as models of complex biological membranes. Smectic films can be drawn across openings in planar supports resulting in thin, meniscus-bounded membranes, and can also be prepa…
We analyze a solenoidal motion in a vertically vibrated freely suspended thin smectic film. We demonstrate analytically that transverse oscillations of the film generate two-dimensional vortices in the plane of the film owing to hydrodynamic nonlinearity. An explicit expression for the vorticity of the in-plane film motion in terms of the film displacement is obtained. The air around the film is proven to play a crucial role, since it changes the dispersion relation of transverse oscillations and transmits viscous stresses to the film, modifying its bending motion. We propose possible experime…
We report on X-ray studies of freely suspended hexatic films of three different liquid crystal compounds. By applying angular X-ray cross-correlation analysis (XCCA) to the measured diffraction patterns the parameters of the bond-orientational (BO) order in the hexatic phase were directly determined. The temperature evolution of the BO order parameters was analyzed on the basis of the multicritical scaling theory (MCST). Our results confirmed the validity of the MCST in the whole temperature range of existence of the hexatic phase for all three compounds. The temperature dependence of the BO o…
We investigate theoretically the elliptical shapes of soft colloids in freely standing smectic C films, that have been reported recently. The colloids favour parallel alignment of the liquid crystal molecules at their surfaces and, for sufficiently strong anchoring, will generate a pair of defects at the poles of the colloidal particles. The elastic free energy of the liquid crystal matrix will, in turn, affect the shape of the colloids. In this study we will focus on elliptical soft colloids and determine how their equilibrium shapes depend on the elastic constants of the liquid crystal, the …
In a theoretical analysis, we generalise well known asymptotic results to obtain expressions for the rate of transfer of material from the surface of an arbitrary, rigid particle suspended in an open pathline flow at large Péclet number, $\textrm{Pe}$. The flow may be steady or periodic in time. We apply this result to numerically evaluate expressions for the surface flux to a freely suspended, axisymmetric ellipsoid (spheroid) in Stokes flow driven by a steady linear shear. We complement these analytical predictions with numerical simulations conducted over a range of $\textrm{Pe} = 10^1 - 10…
Machine learning techniques have been developed to identify inclusions on the surface of freely suspended smectic liquid crystal films imaged by reflected light microscopy. The experimental images are preprocessed using Canny edge detection and then passed to a radial kernel support vector machine (SVM) trained to recognize circular islands and droplets. The SVM is able to identify these objects of interest with an accuracy that far exceeds that of conventional tracking software, especially when the background image is non-uniform or when the target features are in close proximity to one anoth…
Coalescence of droplets is an ubiquitous phenomenon in chemical, physical and biolog-ical systems. The process of merging of liquid objects has been studied during the pastyears experimentally and theoretically in different geometries. We introduce a uniquesystem that allows a quasi two-dimensional description of the coalescence process,micrometer-sized flat droplets in freely suspended smectic liquid-crystal films. We findthat the bridge connecting the droplets grows linearly in time during the initial stage ofcoalescence, both with respect to its height and lateral width. We also verify self…
We present an x-ray study of freely suspended hexatic films of the liquid crystal 3(10)OBC. Our results reveal spatial inhomogeneities of the bond-orientational (BO) order in the vicinity of the hexatic-smectic phase transition and the formation of large scale hexatic domains at lower temperatures. Deep in the hexatic phase up to 25 successive sixfold BO order parameters have been directly determined by means of angular x-ray cross-correlation analysis (XCCA). Such strongly developed hexatic order allowed us to determine higher order correction terms in the scaling relation predicted by the mu…
Finite difference method in prolate spheroidal coordinates for freely suspended spheroidal particles in linear flows of viscous and viscoelastic fluids
In search for novel nematic materials, a laterally linked H-shaped liquid crystal dimer have been synthesized and characterized. The distinct feature of the material is a very broad temperature range (about 50 oC) of the nematic phase, which is in contrast with other reported H-dimers that show predominantly smectic phases. The material exhibits interesting textural features at the scale of nanometers (presence of smectic clusters) and at the macroscopic scales. Namely, at a certain temperature, the flat samples of the material show occurrence of domain walls. These domain walls are caused by …
The Brownian diffusion of micron-scale inclusions in freely suspended smectic A liquid crystal films a few nanometers thick and several millimeters in diameter depends strongly on the air surrounding the film. Near atmospheric pressure, the three-dimensionally coupled film/gas system is well described by Hughes/Pailthorpe/White hydrodynamic theory but at lower pressure (p < 70 torr), the diffusion coefficient increases substantially, tending in high vacuum toward the two-dimensional limit where it is determined by film size. In the absence of air, the films are found to be a nearly ideal physi…
A thermal colloid suspended in a liquid will transition from a short time ballistic motion to a long time diffusive motion. However, the transition between ballistic and diffusive motion is highly dependent on the properties and structure of the particular liquid. We directly observe a free floating tracer particle's ballistic motion and its transition to the long time regime in both a Newtonian fluid and a viscoelastic Maxwell fluid. We examine the motion of the free particle in a Newtonian fluid and demonstrate a high degree of agreement with the accepted Clercx-Schram model for motion in a …
We study hydrodynamic interactions of spherical particles in incident Poiseuille flow in a channel with infinite planar walls. The particles are suspended in a Newtonian fluid, and creeping-flow conditions are assumed. Numerical results, obtained using our highly accurate Cartesian-representation algorithm [Physica A xxx, {\bf xx}, 2005], are presented for a single sphere, two spheres, and arrays of many spheres. We consider the motion of freely suspended particles as well as the forces and torques acting on particles adsorbed at a wall. We find that the pair hydrodynamic interactions in this …
It is well known that electro-hydrodynamical effects in freely suspended liquid films can flow the liquid. Here we report a purely electrically driven rotation in water and some other liquid suspended films with full control on the velocity and the chirality of the rotating vortices. The device, which is called ``film motor'', consists of a quasi two-dimensional electrolysis cell in an external in-plane electric field, crossing the mean electrolysis current density. If either the external field or the electrolysis voltage exceeds some threshold (while the other one is not zero), the liquid fil…
Colloidal inclusions suspended in a bath of smaller particles experience an effective bath-mediated attraction at small intersurface separations, which is known as the depletion interaction. In an active bath of nonchiral self-propelled particles, the effective force changes from attraction to repulsion; an effect that is suppressed, when the active bath particles are chiral. Using Brownian Dynamics simulations, we study the effects of channel confinement and bath chirality on the effective forces and torques that are mediated between two inclusions that may be fixed within the channel or may …
Motivated by a freely suspended graphene and polymerized membranes in soft and biological matter we present a detailed study of a tensionless elastic sheet in the presence of thermal fluctuations and quenched disorder. The manuscript is based on an extensive draft dating back to 1993, that was circulated privately. It presents the general theoretical framework and calculational details of numerous results, partial forms of which have been published in brief Letters (Le Doussal and Radzihovsky 1992). The experimental realization of atom-thin graphene sheets has driven a resurgence in this fasci…
A magnetorheological fluid, which consists of magnetic particles suspended in a viscous fluid, flows freely with well-dispersed particles in a the absence of a magnetic field, but particle aggregation results in flow cessation when a field is applied. The mechanism of dynamical arrest is examined by analysing interactions between magnetic particles in a magnetic field subject to a shear flow. An isolated spherical magnetic particle undergoes a transition between a rotating state at low magnetic field and a static orientation at high magnetic field. The effect of interactions for spherical dipo…
