Inversion of Stabilized Large Droplet Clusters.

We investigate the spontaneous rearrangement of microdroplets in a self-assembled droplet cluster levitating over a thin locally heated water layer. The center-to-periphery droplet diameter ratio (the "inversion coefficient") controls the onset of the inversion. Larger droplets can squeeze between smaller ones due to increased drag force on them from the air-vapor flow. In smaller clusters, the rotation of the droplets plays an important role since larger droplets rotating with the same angular velocity (dependent on the rotor of the airflow field) have higher viscous friction force with the liquid layer. It is desirable to avoid cluster inversion in experiments where individual droplet positions should be traced.

Fluorescence profiles of water droplets in stable levitating droplet clusters.

Clusters of nearly identical water microdroplets levitating over a locally heated water layer are considered. The high-resolution and high-speed fluorescence microscopy showed that there is a universal brightness profile of single droplets, and this profile does not depend on the droplet temperature and size. We explain this universal profile using the theory of light scattering and propose a new method for determining the parameters of possible optical inhomogeneity of a droplet from its fluorescent image. In particular, we report for the first time and explain the anomalous fluorescence of some large droplets with initially high brightness at the periphery of the droplet. The disappearance of this effect after a few seconds is related to the diffusion of the fluorescent substance in water. Understanding the fluorescence profiles paves the way for the application of droplet clusters to the laboratory study of biochemical processes in individual microdroplets.

Survival of Virus Particles in Water Droplets: Hydrophobic Forces and Landauer's Principle.

Many small biological objects, such as viruses, survive in a water environment and cannot remain active in dry air without condensation of water vapor. From a physical point of view, these objects belong to the mesoscale, where small thermal fluctuations with the characteristic kinetic energy of kBT (where kB is the Boltzmann's constant and T is the absolute temperature) play a significant role. The self-assembly of viruses, including protein folding and the formation of a protein capsid and lipid bilayer membrane, is controlled by hydrophobic forces (i.e., the repulsing forces between hydrophobic particles and regions of molecules) in a water environment. Hydrophobic forces are entropic, and they are driven by a system's tendency to attain the maximum disordered state. On the other hand, in information systems, entropic forces are responsible for erasing information, if the energy barrier between two states of a switch is on the order of kBT, which is referred to as Landauer's principle. We treated hydrophobic interactions responsible for the self-assembly of viruses as an information-processing mechanism. We further showed a similarity of these submicron-scale processes with the self-assembly in colloidal crystals, droplet clusters, and liquid marbles.

Impact of Surfactants on the Formation and Properties of Droplet Clusters.

A levitating cluster of condensed microdroplets can form over the heated area of a water layer. The thermocapillary (TC) flow at the surface of the water layer combined with the convective flow in the layer often prevents a cluster's stability due to disturbances that it creates in the gas flow over the water surface. The TC flow can be suppressed by introducing small amounts of surfactants into the water layer. We conduct a systematic study of the effect of a surfactant on the cluster. We show experimentally that the introduction of the surfactant sodium laureth sulfate with concentrations of 0.05-0.5 g/L can suppress the TC convection. It is shown that the amount of surfactant does not affect the condensational growth of droplets and the structure of the cluster. In the absence of the surfactant, a ring-shaped cluster is formed, which is reported in this paper for the first time.

Clustering and self-organization in small-scale natural and artificial systems.

Physical properties of clusters, i.e. systems composed of a 'small' number of particles, are qualitatively different from those of infinite systems. The general approach to the problem of clustering is suggested. Clusters, as they are seen in the graphs theory, are discussed. Various physical mechanisms of clustering are reviewed. Dimensional properties of clusters are addressed. The dimensionality of clusters governs to a great extent their properties. Weakly and strongly coupled clusters are discussed. Hydrodynamic and capillary interactions giving rise to clusters formation are surveyed. Levitating droplet clusters, turbulent clusters and droplet clusters responsible for the breath-figures self-assembly are considered. Entropy factors influencing clustering are considered. Clustering in biological systems results in non-equilibrium multi-scale assembly, where at each scale, self-driven components come together by consuming energy in order to form the hierarchical structure. This article is part of the theme issue 'Bioinspired materials and surfaces for green science and technology (part 3)'.

Symmetry of small clusters of levitating water droplets.

Self-assembled clusters of condensed water microdroplets can levitate over a locally heated layer of water. Large clusters form hexagonally ordered (honeycomb) structures similar to colloidal crystals, while small (from one to several dozens of droplets) clusters possess special symmetry properties. Small clusters may demonstrate 4-fold, 5-fold, and 7-fold symmetry which is absent from large clusters and crystals. The symmetry properties of small cluster configurations are universal, i.e., they do not depend on the size of the droplets and details of the interactions between the droplets. The small cluster configurations may be compared with other types of symmetric objects in geometry.

Self-Arranged Levitating Droplet Clusters: A Reversible Transition from Hexagonal to Chain Structure.

Water microdroplets condense over locally heated water-vapor interfaces and levitate in an ascending vapor-air flow forming self-assembled ordered monolayer clusters. The droplets do not coalesce due to complex aerodynamic interactions between them. The droplet cluster formation is governed by the condensation/evaporation balance and by coupling of heat flux and vapor flow with aerodynamic forces. Here, we report the observations of a reversible structural transition from the ordered hexagonal-structure cluster to the chain-like structure and provide an explanation of its mechanism and conditions under which the transition occurs. The phenomenon provides new insights on the fundamental physical and chemical processes with microdroplets including their role in reaction catalysis in nature and their potential for aerosol and microfluidic applications.

Droplet clusters: nature-inspired biological reactors and aerosols.

Condensed microdroplets play a prominent role in living nature, participating in various phenomena, from water harvesting by plants and insects to microorganism migration in bioaerosols. Microdroplets may also form regular self-organized patterns, such as the hexagonally ordered breath figures on a solid surface or levitating monolayer droplet clusters over a locally heated water layer. While the breath figures have been studied since the nineteenth century, they have found a recent application in polymer surface micropatterning (e.g. for superhydrophobicity). Droplet clusters were discovered in 2004, and they are the subject of active research. Methods to control and stabilize droplet clusters make them suitable for the in situ analysis of bioaerosols. Studying life in bioaerosols is important for understanding microorganism origins and migration; however, direct observation with traditional methods has not been possible. We report preliminary results on direct in situ observation of microorganisms in droplet clusters. We also present a newly observed transition between the hexagonally ordered and chain-like states of a droplet cluster. This article is part of the theme issue 'Bioinspired materials and surfaces for green science and technology (part 2)'.

Characterization of Self-Assembled 2D Patterns with Voronoi Entropy.

The Voronoi entropy is a mathematical tool for quantitative characterization of the orderliness of points distributed on a surface. The tool is useful to study various surface self-assembly processes. We provide the historical background, from Kepler and Descartes to our days, and discuss topological properties of the Voronoi tessellation, upon which the entropy concept is based, and its scaling properties, known as the Lewis and Aboav-Weaire laws. The Voronoi entropy has been successfully applied to recently discovered self-assembled structures, such as patterned microporous polymer surfaces obtained by the breath figure method and levitating ordered water microdroplet clusters.

Spectroscopic diagnostics of morphological changes arising in thermal processing of polypropylene.

Polypropylene is considered as a representative thermoplastic matrix for advanced composite materials that have some advantages in various engineering applications. Wide-range infrared optical properties of polypropylene are important for combined heat transfer modeling in these composite materials, which are semitransparent in a considerable part of the whole spectral range. This study is focused on optical properties of polypropylene in the visible and near-infrared ranges because the measurements in these ranges exhibit a stronger effect of the processing temperature used in the material manufacturing. The experimental study is based on spectral measurements of both the normal-hemispherical reflectance and transmittance of polypropylene samples. The main characteristics of volumetric absorption and scattering are identified using the inverse problem solution based on the modified two-flux approximation, which is sufficiently accurate to determine the hemispherical characteristics of the radiation field in the range of the problem parameters. In particular, the effect of a relatively strong scattering is observed at the absorption peaks in the near-infrared range. An approximate theoretical model based on spectroscopic data is developed to estimate morphological changes arising in thermal processing of polypropylene at different temperatures.

Plasmonic "pump-probe" method to study semi-transparent nanofluids.

Nanofluids have been increasingly used in a wide range of thermal applications. Although these applications can benefit greatly from investigating the behavior of nanoparticles under different heating scenarios, there is a lack of experiments that can achieve this. To overcome this challenge, an optical "pump-probe"-type experiment is suggested in this paper. In experiments of this type, a set of "pumping" nanoparticles are specifically selected to absorb laser radiation. These particles represent a flexible tool for volumetric heating. A second set of "probing" nanoparticles can be tailored to scatter a separate optical probing signal. This work presents a selection procedure for nanoparticles of both types. The selection procedure is then demonstrated for a specific example where the pump and probe wavelengths are of 980 and 532 nm, respectively. Gold nanorods with diameters of 10 and a length of 58 nm are selected as the "most suitable" absorbing particles, while silver nanospheres with a diameter of 110 nm are selected as the "most suitable" scattering particles. These particles are synthesized and shown to experimentally match the desired optical properties. Overall, this paper proposes and demonstrates an approach by which it is possible to design and fabricate particles for a wide range of optical studies in semi-transparent nanofluids.

Apple-like Shape of Freezing Paraffin Wax Droplets and Its Origin.

Paraffin wax stores energy in the form of latent heat at a nearly constant temperature during melting and releases this energy during solidification. This effect is used in industrial energy storage. At the same time, the possible deformation of even small volumes of material as a result of phase change is insufficiently studied. In this paper, the physical nature of such deformation, probably for the first time, is studied on the example of a droplet of paraffin wax. An unusual change in the shape of a melted droplet of paraffin wax placed on a relatively cold glass plate was observed in the laboratory experiments. As the droplet solidifies, its upper surface becomes nearly flat, and a dimple is formed in the center of this surface, making the droplet look like a fruit (pumpkins are more commonly shaped like this, but the authors prefer apples). A series of experiments, as well as physical and numerical modeling of the droplet's thermal state, taking into account the formation of a mushy zone between liquidus and solidus, made it possible to understand the role of gravity and gradual increase in viscosity and density of paraffin wax on changing the droplet shape and, in particular, to clarify the mechanism of formation of the dimple on its upper. It was shown that the mushy zone between the liquidus and solidus of the paraffin wax is responsible for the dimple formation.

Branched droplet clusters and the Kramers theorem.

Scaling laws inherent for polymer molecules are checked for the linear and branched chains constituting two-dimensional (2D) levitating microdroplet clusters condensed above the locally heated layer of water. We demonstrate that the dimensionless averaged end-to-end distance of the droplet chain r[over ¯] normalized by the averaged distance between centers of the adjacent droplets l[over ¯] scales as r[over ¯]/l[over ¯]∼n^{0.76}, where n is the number of links in the chain, which is close to the power exponent ¾, predicted for 2D polymer chains with excluded volume in the dilution limit. The values of the dimensionless Kuhn length b[over ̃]≅2.12±0.015 and of the averaged absolute value of the bond angle of the droplet chains |θ|[over ¯]=22.0±0.5^{0} are determined. Using these values we demonstrate that the predictions of the Kramers theorem for the gyration radius of branched polymers are valid also for the branched droplets' chains. We discuss physical interactions that explain both the high value of the power exponent and the applicability of the Kramers theorem including the effects of the excluded volume, surrounding droplet monomers, and the prohibition of extreme values of the bond angle.

Hierarchical liquid marbles formed using floating hydrophobic powder and levitating water droplets.

HYPOTHESIS: Liquid marbles i.e. droplets coated by hydrophobic particles may be formed not only on the solid substrates but also on the floating layers of hydrophobic powders such as fluorinated fumed silica or polytetrafluoroethylene. EXPERIMENTS: Formation and growth of liquid marbles on fluorinated fumed silica or polytetrafluoroethylene powder floating on a heated water-vapor interface is reported. Marbles emerge from condensation of water droplets levitating above the powder layer. FINDINGS: The kinetics of the growth of droplets is reported. Growth of droplets results from three main mechanisms: water condensation, absorption of small droplets and merging of droplets with neighboring ones. Growing droplets are coated with the hydrophobic powder, eventually giving rise to the formation of stable liquid marbles. Formation of hierarchical liquid marbles is reported. Growth of liquid marbles emerging from water condensation follows the linear temporal dependence. A phenomenological model of the liquid marble growth is suggested.

Effect of asymmetric cooling of sessile droplets on orientation of the freezing tip.

HYPOTHESIS: The shape of the "freezing tip" formed by the crystallization of water droplets demonstrated remarkable universality - no dependence on the cooling rate and physico-chemical properties of the substrate has been observed. At the same time, the spatial orientation of the freezing cone may be varied. We hypothesized that the orientation of the freezing tip is determined by the direction of heat flux at the base of the sessile droplet. This direction is expected to be changed when the substrate with a low thermal diffusivity is not cooled uniformly. EXPERIMENTS: We studied the freezing of water droplets placed on the inclined surface of wedges made from a variety of materials (polymers: Polymethylmethacrylate, Polytetrafluoroethylene, Polyurethane and metal: Titanium), which were cooled from below. The shape of the frozen droplets was controlled in situ. COMPUTATIONS: The computational model was suggested for the transient temperature field in the polymer wedge to determine a time variation of the local heat flux under the droplets. A comparison of numerical results and the measurements enabled us to confirm the aforementioned hypothesis relating the orientation of the freezing tips to the direction of the heat flux. FINDINGS: It was established that the orientation of the freezing cone axis depends on the location of the frozen droplet on the inclined surface of the wedge. Calculations of the transient temperature field of the wedge confirmed our hypothesis about the physical reason of the various spatial orientations of the freezing cones.

Osmotic evolution of composite liquid marbles.

HYPOTHESIS: We hypothesized that the reported evolution (growth) of composite water marbles filled with saline water and coated with lycopodium dispersed in a thin layer of silicone oil is due to the osmotic mass transfer. The hypothesis is supported by the semi-empirical model of osmotic growth of small liquid marbles floating on distilled water. EXPERIMENTS: Saline composite, silicone oil-coated marbles floating on distilled water grew with time; whereas, composite marbles filled with distilled water floating on aqueous solutions of NaCl lost mass with time and shrunk. However, composite liquid marbles filled with saline water and floating on aqueous solutions of NaCl remained stable during 25 h of the laboratory experiment. FINDINGS: The reported findings are reasonably attributed to osmotic mass transport through the thin silicon layer filled with lycopodium particles coating the marbles, acting as an osmotic membrane. This is supported by the suggested model for the osmotic growth of marbles.

Self-assembled levitating clusters of water droplets: pattern-formation and stability.

Water forms ordered hexagonally symmetric structures (snow crystals) in its solid state, however not as liquid. Typically, mists and clouds are composed of randomly moving small droplets lacking any ordered structure. Self-organized hexagonally patterned microdroplet clusters over locally heated water surfaces have been recently observed. However, many aspects of the phenomenon are far from being well understood including what determines droplets size, arrangement, and the distance between them. Here we show that the Voronoi entropy of the cluster tends to decrease indicating to their self-organization, while coupling of thermal effects and mechanical forces controls the stability of the clusters. We explain the balance of the long-range attraction and repulsion forces which stabilizes the cluster patterns and established the range of parameters, for which the clusters are stable. The cluster is a dissipative structure similar to self-organized Rayleigh-Bénard convective cells. Microdroplet formation plays a role in a variety effects from mist and clouds to aerosols. We anticipate that the discovery of the droplet cluster phenomenon and its explanation will provide new insights on the fundamental physical and chemical processes such as microdroplet role in reaction catalysis in nature as well as new tools for aerosol analysis and microfluidic applications.