Coalescence of biphasic droplets embedded in free standing smectic A films.

We investigate micrometer-sized flat droplets consisting of an isotropic core surrounded by a nematic rim in freely suspended smectic A liquid-crystal films. In contrast to purely isotropic droplets which are characterized by a sharp edge and no long-range interactions, the nematic fringe introduces a continuous film thickness change resulting in long-range mutual attraction of droplets. The coalescence scenario is divided in two phases. The first one consists in the fusion of the nematic regions. The second phase involves the dissolution of a thin nematic film between the two isotropic cores. The latter has many similarities with the rupture of thin liquid films between droplets coalescing in an immiscible viscous liquid.

The structure of disintegrating defect clusters in smectic C freely suspended films.

Disclinations or disclination clusters in smectic C freely suspended films with topological charges larger than one are unstable. They disintegrate, preferably in a spatially symmetric fashion, into single defects with individual charges of +1, which is the smallest positive topological charge allowed in polar vector fields. While the opposite process of defect annihilation is well-defined by the initial defect positions, disintegration starts from a singular state and the following scenario including the emerging regular defect patterns must be selected by specific mechanisms. We analyze experimental data and compare them with a simple model where the defect clusters adiabatically pass quasi-equilibrium solutions in one-constant approximation. It is found that the defects arrange in geometrical patterns that correspond very closely to superimposed singular defect solutions, without additional director distortions. The patterns expand by affine transformations where all distances between individual defects scale with the same time-dependent scaling factor proportional to the square-root of time.

Fast-freezing kinetics inside a droplet impacting on a cold surface.

Freezing or solidification of impacting droplets is omnipresent in nature and technology, be it a rain droplet falling on a supercooled surface; in inkjet printing, where often molten wax is used; in additive manufacturing or metal-production processes; or in extreme ultraviolet lithography (EUV) for the chip production, where molten tin is used to generate the EUV radiation. For many of these industrial applications, a detailed understanding of the solidification process is essential. Here, by adopting an optical technique in the context of freezing-namely, total-internal reflection (TIR)-we elucidate the freezing kinetics during the solidification of a droplet while it impacts on an undercooled surface. We show that at sufficiently high undercooling, a peculiar freezing morphology exists that involves sequential advection of frozen fronts from the center of the droplet to its boundaries. This phenomenon is examined by combining elements of classical nucleation theory to the large-scale hydrodynamics on the droplet scale, bringing together two subfields which traditionally have been quite separated. Furthermore, we report a self-peeling phenomenon of a frozen splat that is driven by the existence of a transient crystalline state during solidification.

Shape instabilities of islands in smectic films under lateral compression.

Smectic liquid crystals are fluids, and in most rheological situations they behave as such. Nevertheless, when thin freely floating films of smectic A or smectic C materials are compressed quickly in-plane, they resist such stress by buckling similar to solid membranes under lateral stress. We report experimental observations of wrinkling and bulging of finite domains within the films, so-called islands, and give a qualitative explanation of different observed patterns. Depending on the external stress and their dimensions, the islands can expel a specifically shaped bulge in their center, form radial wrinkles or develop target-like wrinkle structures. When the external stress is relaxed, these patterns disappear reversibly.

Smectic free-standing films under fast lateral compression.

Smectic freely-suspended films can wrinkle like solid sheets. This has been demonstrated earlier with shape-fluctuating smectic bubbles. Here, we exploit the collapse of smectic catenoid films with a central equatorial film to expose the latter to rapid lateral compression. Wrinkle formation is observed in the planar film and the thickness dependence of the undulation wavelength is measured. In addition to the central film, its border undergoes an undulation instability as well.

Silo discharge of mixtures of soft and rigid grains.

We study the outflow dynamics and clogging phenomena of mixtures of soft, elastic low-friction spherical grains and hard frictional spheres of similar size in a quasi-two-dimensional (2D) silo with narrow orifice at the bottom. Previous work has demonstrated the crucial influence of elasticity and friction on silo discharge. We show that the addition of small amounts, even as low as 5%, of hard grains to an ensemble of soft, low-friction grains already has significant consequences. The mixtures allow a direct comparison of the probabilities of the different types of particles to clog the orifice. We analyze these probabilities for the hard, frictional and the soft, slippery grains on the basis of their participation in the blocking arches, and compare outflow velocities and durations of non-permanent clogs for different compositions of the mixtures. Experimental results are compared with numerical simulations. The latter strongly suggest a significant influence of the inter-species particle friction.

Self-Similar Liquid Lens Coalescence.

A basic feature of liquid drops is that they can merge upon contact to form a larger drop. In spite of its importance to various applications, drop coalescence on prewetted substrates has received little attention. Here, we experimentally and theoretically reveal the dynamics of drop coalescence on a thick layer of a low viscosity liquid. It is shown that these so-called "liquid lenses" merge by the self-similar vertical growth of a bridge connecting the two lenses. Using a slender analysis, we derive similarity solutions corresponding to the viscous and inertial limits. Excellent agreement is found with the experiments without any adjustable parameters, capturing both the spatial and temporal structures of the flow during coalescence. Finally, we consider the crossover between the two regimes and show that all data of different lens viscosities collapse on a single curve capturing the full range of the coalescence dynamics.

Intermittent flow and transient congestions of soft spheres passing narrow orifices.

Soft, low-friction particles in silos show peculiar features during their discharge. The outflow velocity and the clogging probability both depend upon the momentary silo fill height, in sharp contrast to silos filled with hard particles. The reason is the fill-height dependence of the pressure at the orifice. We study the statistics of silo discharge of soft hydrogel spheres. The outflow is found to become increasingly fluctuating and even intermittent with decreasing orifice size, and with decreasing fill height. In orifices narrower than two particle diameters, outflow can stop completely, but in contrast to clogs formed by rigid particles, these congestions may dissolve spontaneously. We analyze such non-permanent congestions and attribute them to slow reorganization processes in the container, caused by viscoelasticity of the material.

Drop impact on hot plates: contact times, lift-off and the lamella rupture.

When a liquid drop impacts on a heated substrate, it can remain deposited, or violently boil in contact, or lift off with or without ever touching the surface. The latter is known as the Leidenfrost effect. The duration and area of the liquid-substrate contact are highly relevant for the heat transfer, as well as other effects such as corrosion. However, most experimental studies rely on side view imaging to determine contact times, and those are often mixed with the time until the drop lifts off from the substrate. Here, we develop and validate a reliable method of contact time determination using high-speed X-ray imaging and total internal reflection imaging. We exemplarily compare contact and lift-off times on flat silicon and sapphire substrates. We show that drops can rebound even without formation of a complete vapor layer, with a wide range of lift-off times. On sapphire, we find a local minimum of lift-off times that is much shorter than expected from capillary rebound in the comparatively low-temperature regime of transition boiling/thermal atomization. We elucidate the underlying mechanism related to spontaneous rupture of the lamella and receding of the contact area.

Dynamic wrinkling of freely floating smectic films.

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 behaving liquid-like with respect to flow in the film plane, they cannot quickly expand their thickness because that requires stacking of additional smectic layers. At short time scales, they therefore behave like quasi-incompressible membranes, very different from soap films. Smectic 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 reported. The characteristic wavelengths of the wrinkles are in the submillimeter range. We demonstrate the dynamic nature of the pattern formation mechanism and develop a basic model that explains the physical mechanism for the wavelength selection and wrinkle orientation.

Structure and dynamics of a two-dimensional colloid of liquid droplets.

Droplet arrays in thin, freely suspended liquid-crystalline smectic A films can form two-dimensional (2D) colloids. The droplets interact repulsively, arranging locally in a more or less hexagonal arrangement with only short-range spatial and orientational correlations and local lattice cell parameters that depend on droplet size. In contrast to quasi-2D colloids described earlier, there is no 3D bulk liquid subphase that affects the hydrodynamics. Although the films are surrounded by air, the droplet dynamics are genuinely 2D, the mobility of each droplet in its six-neighbor cage being determined by the ratio of cage and droplet sizes, rather than by the droplet size as in quasi-2D colloids. These experimental observations are described well by Saffman's model of a diffusing particle in a finite 2D membrane. The experiments were performed in microgravity, on the International Space Station.

From Bouncing to Floating: The Leidenfrost Effect with Hydrogel Spheres.

The Leidenfrost effect occurs when a liquid or stiff sublimable solid near a hot surface creates enough vapor beneath it to lift itself up and float. In contrast, vaporizable soft solids, e.g., hydrogels, have been shown to exhibit persistent bouncing-the elastic Leidenfrost effect. By carefully lowering hydrogel spheres towards a hot surface, we discover that they are also capable of floating. The bounce-to-float transition is controlled by the approach velocity and temperature, analogously to the "dynamic Leidenfrost effect." For the floating regime, we measure power-law scalings for the gap geometry, which we explain with a model that couples the vaporization rate to the spherical shape. Our results reveal that hydrogels are a promising pathway for controlling floating Leidenfrost objects through shape.

Free Cooling of a Granular Gas of Rodlike Particles in Microgravity.

Granular gases as dilute ensembles of particles in random motion are at the basis of elementary structure-forming processes in the Universe, involved in many industrial and natural phenomena, and also excellent models to study fundamental statistical dynamics. The essential difference to molecular gases is the energy dissipation in particle collisions. Its most striking manifestation is the so-called granular cooling, the gradual loss of mechanical energy E(t) in the absence of external excitation. We report an experimental study of homogeneous cooling of three-dimensional granular gases in microgravity. The asymptotic scaling E(t)∝t^{-2} obtained by Haff's minimal model [J. Fluid Mech. 134, 401 (1983)JFLSA70022-112010.1017/S0022112083003419] proves to be robust, despite the violation of several of its central assumptions. The shape anisotropy of the grains influences the characteristic time of energy loss quantitatively but not qualitatively. We compare kinetic energies in the individual degrees of freedom and find a slight predominance of translational motions. In addition, we observe a preferred rod alignment in the flight direction, as known from active matter or animal flocks.

Smectic C to smectic A transition induced mechanically by the rupture of freely suspended liquid crystal films.

The tilt angle of smectic C phases can be controlled by external forces of very different nature. In particular near a smectic A-smectic C transition, it is susceptible to temperature changes. It can be influenced with electric fields (electroclinic effect), and even mechanically by intra-layer stresses in elastomers. We show that capillary forces that act during the rupture of a free-standing smectic C film can trigger a smectic C to smectic A transition, which rapidly reduces the surface area of the films, concurrently increasing the film thickness. The effect occurs on the sub-millisecond scale, practically independent of film thickness and temperature. We propose that this mechanical effect could even trigger a ferroelectric to paraelectric transition in chiral phases.

Dynamic interface tension of a smectic liquid crystal in anionic surfactant solutions.

The interface tension of a smectic liquid crystal with respect to a surrounding ionic surfactant solution is investigated at concentrations above and below the critical micelle concentration (cmc). A simple measurement technique has been developed recently [Phys. Chem. Chem. Phys., 2013, 15, 7204], based on the geometrical analysis of the shape of smectic bubbles in water that are deformed by the buoyancy of trapped air bubbles. After preparation of the smectic membranes in the solution, we measure both the time dependence of their dynamic interface tension as well as the asymptotically reached static tension values. These are established about 15 minutes after the membrane preparation. At large enough concentrations of the surfactant (above the critical micelle concentration), the interface tension drops to 6 mN m(-1). At the lowest possible surfactant concentrations in our experiment, the equilibrium tension reaches 20 mN m(-1), which is almost equal to the smectic surface tension respective to air. The tension of a freshly drawn film exceeds this value by far.

Freely floating smectic films.

We have investigated the dynamics of freely floating smectic bubbles using high-speed optical imaging. Bubbles in the size range from a few hundred micrometers to several centimeters were prepared from collapsing catenoids. They represent ideal model systems for the study of thin-film fluid dynamics under well-controlled conditions. Owing to the internal smectic layer structure, the bubbles combine features of both soap films and vesicles in their unique shape dynamics. From a strongly elongated initial shape after pinch-off, they relax towards the spherical equilibrium, first by a slow redistribution of the smectic layers, and finally by weak, damped shape oscillations. In addition, we describe the rupture of freely floating smectic bubbles, and the formation and stability of smectic filaments.

Impact and embedding of picoliter droplets into freely suspended smectic films.

We study the impact of liquid microdroplets on thin freely suspended smectic films. Such films are very thin but robust objects that can serve as model systems for quasi-two-dimensional liquids. Droplet velocities and sizes determine the character of the collisions. The dynamics of the integration of droplets into the film can be divided into three phases, starting with the impact and a dissipation of the kinetic energy, followed by a balancing of capillary forces within fractions of a second. The analysis of the droplet shape evolution with high-speed imaging allows us to study the dynamics of this process. The final phase, formation of a meniscus of smectic material, takes several seconds up to minutes.

Rotational and translational motions in a homogeneously cooling granular gas.

A granular gas composed of monodisperse spherical particles was studied in microgravity experiments in a drop tower. Translations and rotations of the particles were extracted from optical video data. Equipartition is violated, the rotational degrees of freedom were excited only to roughly 2/3 of the translational ones. After stopping the mechanical excitation, we observed granular cooling of the ensemble for a period of three times the Haff time, where the kinetic energy dropped to about 5% of its initial value. The cooling rates of all observable degrees of freedom were comparable, and the ratio of rotational and translational kinetic energies fluctuated around a constant value. The distributions of translational and rotational velocity components showed slight but systematic deviations from Gaussians at the start of cooling.

Cooling of a granular gas mixture in microgravity.

Granular gases are fascinating non-equilibrium systems with interesting features such as spontaneous clustering and non-Gaussian velocity distributions. Mixtures of different components represent a much more natural composition than monodisperse ensembles but attracted comparably little attention so far. We present the observation and characterization of a mixture of rod-like particles with different sizes and masses in a drop tower experiment. Kinetic energy decay rates during granular cooling and collision rates were determined and Haff's law for homogeneous granular cooling was confirmed. Thereby, energy equipartition between the mixture components and between individual degrees of freedom is violated. Heavier particles keep a slightly higher average kinetic energy than lighter ones. Experimental results are supported by numerical simulations.

Measurement of the interface tension of smectic membranes in water.

A simple method is proposed to measure the interfacial tension of a smectic liquid crystal (LC) in freely suspended film geometry in aqueous environment. The method is based upon the evaluation of the deformation of smectic bubbles by the buoyancy of a trapped air volume. The advantages over classical suspended smectic droplet experiments in water are the considerably shorter equilibration times, and most important, the much larger density differences between the fluids. The latter allow a much more accurate force determination. Bulk elastic force contributions can be practically neglected in the thin smectic films. Values for a smectic C mixture of two disubstituted phenylpyrimidines are reported.