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Levitating cluster of fluorescent droplets.

Synthetic calcium silicates and phosphates are promising compounds for targeted drug delivery for the effective treatment of cancerous tumors, and for minimizing toxic effects on the patient’s entire body. This work presents an original synthesis of a composite based on crystalline wollastonite CaSiO3 and combeite Na4Ca4(Si6O18), using a sea urchin Mesocentrotus nudus skeleton by microwave heating under hydrothermal conditions. The phase and elemental composition and structure of the obtained composite were studied by XRF, REM, BET, and EDS methods, depending on the microwave heating time of 30 or 60 min, respectively, and the influence of thermo-oxidative post-treatment of samples. The role of the sea urchin skeleton in the synthesis was shown. First, it provides a raw material base (source of Ca2+) for the formation of the calcium silicate composite. Second, it is a matrix for the formation of its porous inorganic framework. The sorption capacity of the composite, with respect to 5-fluorouracil, was estimated, the value of which was 12.3 mg/L. The resulting composite is a promising carrier for the targeted delivery of chemotherapeutic drugs. The mechanism of drug release from an inorganic natural matrix was also evaluated by fitting its release profile to various mathematical models.

Symmetry and orderliness of two-dimensional (2D) levitating microdroplet clusters are quantified with the Voronoi entropy (VE) and the continuous symmetry measure (CSM). The time evolution of both ...

Received: 18.02.2022. Revised: 13.05.2022. Accepted: 01.06.2022. Available online: 14.06.2022. In this work, we obtained polycalciumphenylsiloxane (PCPS) by the interaction of calcium bis (acetylacetonate) with polyphenylsiloxane. The first method consisted in boiling the starting reagents in toluene for several hours; the second was as follows: the mixture of the starting reagents was preliminarily treated mechanically in a ball mill, followed by boiling in toluene for several hours. Two fractions, soluble and insoluble, were isolated in both syntheses. They were investigated using IR, NMR spectroscopy, thermogravimetric analysis, and gel permeation chromatography. It was shown that the insoluble fraction is a mixture of calcium acetylacetonate and polyphenylsiloxane with a small calcium ion content. The soluble fraction is polycalciumphenylsiloxane. The yield of the soluble fraction is higher in the second synthesis method. The polymers obtained in the first and second synthesis methods are similar in composition and structure, which was confirmed by physicochemical methods. Next, the skeleton of the sea urchin Strongylocentrotus intermedius was treated with a soluble fraction in toluene. In this case, a composite was obtained, which was treated with 2–3% hydrochloric acid and then calcined at a temperature of 600 °C. At each stage, the composition of the composites was investigated using elemental analysis and IR spectroscopy. The morphology was investigated using scanning electron microscopy.

The condensational growth of water droplets in technical and natural systems varies with environmental conditions such as droplet size, droplet composition, air humidity, temperature, and turbulenc...

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.

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.

A new type of a levitating droplet clusters composed of often transforming small aggregates of water droplets is described for the first time. Unlike earlier observed droplet clusters controlled by aerodynamic forces, which formed either an ordered hexagonal structure or a chain structure, the cluster under consideration has a hierarchical organization. Small groups of closely spaced or packed droplets with interactions controlled by the electrostatic force are combined into larger structures controlled by aerodynamic forces. Since charged droplets in the nucleus of the cluster do not have dynamically stable configurations, droplet aggregates keep continuously restructuring. However, droplets with lower charge in external layers of the cluster form a stable hexagonal structure.

Horizontal oscillations of small droplet clusters (from one to four droplets) levitating over a locally heated water layer in upward vapor–air flow are investigated experimentally. These oscillatio...

The condensational growth of spherical water microdroplets is studied in a laboratory setup and with a mathematical model. In the experiment, droplet clusters are kept in a freely levitated state within an upward-oriented flow of water vapor. In the presence of an electrostatic field of 1.5 * 10^5 V / m, droplet growth is accelerated by factors 1.5 to 2.0 as compared to conditions without any external electric field. Presumably water molecules in the ambient air are accelerated through the presence of the electric field. A kinetic model to predict the acceleration of condensational growth confirms this hypothesis to be feasible. The droplets themselves are polarized so that the deposition of steam molecules is facilitated in the electric field. The simplifications and limitations of the model are discussed., accepted manuscript

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.

To study the material based on the binary system Ti + Cu (50% atm), samples were produced from powders of commercially pure metals and additionally ground in a ball mill (final size about 12 µm) by spark plasma sintering. The following intermetallic phases were obtained in the materials: CuTi2, TiCu, and Ti3Cu4. The materials have a hardness of 363 and 385 HV (800 and 900 °C), a microhardness of 393 and 397 µHV, a density of 4.24 and 5.23 kg/m3, and resistance to corrosion in acids (weight gain + 0.002% after 24 h of testing according to ISO 16151 for a sample with 900 °C—the best result in comparison with steel 308, AA2024, CuA110Fe3Mn2). The hardness value varies due to the presence of pure metal agglomerates. The relationship between the temperature of spark plasma sintering and the characteristics of the material (material parameters improve with increasing temperature, segregation is reduced) is revealed.

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.

The paper describes the method for producing WC-10wt%Co hard alloy with 99.6% of the theoretical density and a Vickers hardness of ~1400 HV 0.5. Experimental data on densification dynamics, phase composition, morphology, mechanical properties, and grain size distribution of WC-10%wtCo using spark plasma sintering (SPS) within the range of 1000–1200 °C are presented. The high quality of the product is provided by the advanced method of high-speed powder mixture SPS-consolidation at achieving a high degree of densification with minimal calculated grain growth at 1200 °C.

The relatively stable clusters of regularly positioned small droplets formed over the locally heated water surface have been studied starting from the early paper by the first author. The life of a cluster appeared to be not long because of growing of droplets due to condensation of steam and the final coalescence of large droplets with the substrate layer of water. However, further laboratory studies of biochemical processes in single droplets will be possible only in the case of their longer life. One way to stabilize the cluster suggested recently by the authors is an external infrared heating which prevents growing of droplets. The present paper is focused on another way to stabilize the cluster. This is an expected rebuilding of droplet clusters at periodic changes in power of the heating laser beam. The frequency of these oscillations is more important than their amplitude because of the resonance nature of the phenomenon. The experiments showed that in the simplest variant of alternating constant power values with the same duration of heating, the droplet growth rate is approximately twice reduced with a power modulation period of about 0.9 s. It means that such a “rejuvenescence” procedure can be used at laboratory conditions to prolong the life of levitating droplet clusters.

The structure of electrolytically deposited nanocrystalline alloys of the CoP-CoNiP systems under low-temperature heating was investigated by means of high-resolution transmission electron microscopy (HRTEM), high-angle annular dark-field scanning transmission electron microscopy (HAADF STEM), and analytical methods such as energy dispersive x-ray spectroscopy (EDS) and electron energy loss spectroscopy (EELS). Structural relaxation and crystallization were investigated at temperatures from 150°C to 300°C. Structural and compositional inhomogeneities were found in the CoP-CoNiP alloys, while the local changes in composition were found to reach 15 at.%. Nanocrystals in the alloys grew most intensely in the presence of a free surface. It was determined that the local diffusion coefficient ranged from 1.2 to 2.4 10−18 m2/s, which could be explained by the surface diffusion prevalence. The data gathered in these investigations can be further used to predict the thermal stability of CoP-CoNiP alloys.

The aberration corrected transmission electron microscopy era inspires the development of new research methods. Due to small aberration many of HRTEM applications have become more precise and reliable. The research presented in this paper is devoted to developing a new method for revealing the 3D structure of thin films by focal series processing. We have obtained the sum of the Fourie power spectra in the sliding window of focal series images. Relative defocus value for the minimum of the power spectra is a target function depending on the thin film roughness. For amorphous CoNiP alloy films the new method shows roughness of up to 8 nm for site 65*65 nm in X, Y planes.

Polyethyleneimine (PEI) cryogels have been fabricated using poly(ethylene glycol) diglycidyl ether (DGE-PEG), 1,4-butanediol diglycidyl ether (DGE-1,4-BD), and glutaric aldehyde (GA) as cross-linking agents. The rate of PEI cross-linking changes in the order GA > DGE-1,4-BD > DGE-PEG. The established correlations between the modification degree, swelling, and static ion-exchange capacity revealed a tendency of diglycidyl ethers, especially DGE-1,4-BD, to graft as a side chain to PEI in alkaline media. Low reactivity of cross-linkers at temperatures below zero resulted in lower modification degree and higher sorption capacities of PEI cryogels in comparison with PEI cross-linked at room temperature. Due to the difference in mechanisms of sorption of metal cations and anions, PEI cryogels cross-linked with DGE-1,4-BD and DGE-PEG were the most efficient for sorption of Hg(II) as [HgCl4]2− complex and Cu(II) ions, respectively. The morphology of PEI cryogels depends on the type of the cross-linking agent, cross-linker/PEI molar ratio, and concentration of PEI solution; the pore volume of cryogels obtained under the same conditions decreased in the order GA > DGE-1,4-BD > DGE-PEG.

Small clusters of condensed microdroplets can levitate above a heated water surface. Vertical oscillations of small clusters (one, two, and three droplets) in the frequency range below 90 Hz are studied and compared with recently reported horizontal oscillations. Two reproducible peak frequencies are at 41.6 ± 0.4 Hz and at 49.5 ± 0.2 Hz. These frequencies are much higher than those for horizontal oscillations (between 1.61 Hz and 5.96 Hz); however, corresponding amplitudes are much smaller, which suggests equal energy distributions between the degrees of freedom. The values of effective stiffness constants are obtained from the data on equilibrium height of levitation of droplets of different sizes, and possible sources of oscillations are discussed. The oscillations are caused by aerodynamic forces, and these are same forces which are responsible for the stability of the droplet cluster.

The effect of temperature profile of the water layer surface on the formation and structure of a levitating droplet cluster is studied in the paper. The laboratory experiments indicate that a local temperature maximum of water is a necessary condition for the formation of a cluster. A quantitative criterium of transformation of a monolayer of randomly positioned microdroplets to a self-assembled cluster of relatively large droplets is obtained.

A wide range of possible temperatures of levitating water droplets is interesting for the upcoming laboratory studies of biochemical processes in the droplets. The previously obtained temperature of droplets levitating above the locally heated water of room temperature appeared to be too high for some important biochemical experiments. At the same time, it was not obvious that one can generate much colder droplets. Fortunately, this problem is solved experimentally in the present study with the use of a strong cooling water layer and ambient air. The modified experimental configuration which includes a separate volume of cold air just above the central part of water layer is designed to work at quite different temperature conditions. It is shown that even moderate local heating of water surface is the most important factor to produce sufficiently large self-assembled levitating clusters of water droplets which are similar to those observed at normal temperature conditions. The effect of ambient temperature on both the generation process and characteristics of droplet clusters is studied in the paper.

A modified laboratory installation to generate levitating clusters of droplets above the locally heated water surface is presented. The laser-heated sitall plate with an opaque graphite coating is used as a substrate for the water layer which produces a levitating droplet cluster. The cluster is stabilized with the use of infrared heating as was recently demonstrated by the authors. A combined experimental and computational method is developed to obtain the axisymmetric quasi-steady temperature field in sitall plate and water and also to calculate the radial profile of heat flux at the water surface. Both the temperature and heat flux at the water surface are important boundary conditions for the upcoming computational modeling of cluster formation. The correlations between the laser power, the measured overall flow rate of steam at the water surface, and other important parameters of the problem are also examined.

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.

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)’.

New experimental results and their physical analysis are presented to clarify the behavior of a relatively stable self-arranged droplet cluster levitating over the locally heated water surface. An external electric field of both opposite directions leads to a significant increase in the rate of a condensational growth of droplets in the cluster. The experimental data are used to estimate a small electrical charge of single droplets and the attraction force of polarized droplets to the water layer. It is confirmed that the interaction between the droplets is governed by aerodynamic forces., 13 pages, 9 figures

A horizontal water layer of 0.29-0.44 mm thickness, locally heated from the substrate, is investigated. The value of thermocapillary deformation occurring at local heating is measured by an inverted laser scanning confocal microscope Zeiss LSM 510 Meta. The heater in the form of strip of 0.5-mm width, 40-mm length, and 0.5-mm height made of indium oxide is sputtered on a sapphire substrate. The water temperature from the side of the substrate is measured using the infrared scanner Titanium 570M. We studied in detail the effect of the initial layer thickness and heating power on the value of thermocapillary deformation and temperature field. It is shown that deformation increases with an increase in thermal capacity and decrease in the layer thickness. Results of numerical simulation are in good qualitative agreement with the measurement results.

Theoretical estimates based on the Mie solution for single droplets show that infrared irradiation of droplet clusters levitating over the heated water surface prevents the ordinary growth of droplets and subsequent coalescence of the droplet cluster with water layer. As a result, this irradiation can be used to stabilize the levitating clusters for a long time. This prediction is confirmed in the paper by a series of experiments with obtaining the required power of infrared irradiation. The resulting stable droplet clusters are considered as an appropriate laboratory model of atmospheric droplets to study biochemical processes in the droplets of natural mists and clouds. Possible use of sub-millimeter electromagnetic radiation to reach a similar stabilization effect is also analyzed in the paper.

Infrared irradiation of a droplet cluster has been used during several years as the main method of preventing coalescence of the cluster with a layer of water. The desired effect is achieved by suppressing the condensational growth of large droplets. In new experiments, it was first discovered that prolonged exposure to infrared radiation leads to asymptotic equalization of radii of various droplets. A theoretical analysis of the experimental results was carried out on the basis of the developed model for transient heat transfer. The suggested model includes the thermal effect of infrared radiation, the dynamics of the combined process of evaporation and condensation, as well as convective heat transfer with the surrounding humid air. When calculating the infrared heating of semi-transparent water droplets, the spectral composition of the external radiation is taken into account. The evaporation and condensation of water droplets is considered taking into account the kinetics of the process in the Knudsen layer and the vapor diffusion in the outer part of the boundary layer. Simple analytical relations are obtained for the asymptotic equilibrium parameters of small droplets. The numerical data for the time variation in the size of cluster droplets streamlined by a mixture of air and supersaturated water vapor are in good agreement with the results of laboratory measurements.

The self-assembled clusters of regularly positioned small droplets were observed for the first time in 2004 by Alexander Fedorets. The recent results on stabilization of droplet clusters enable the laboratory study of specific parameters of chemical and biochemical reactions in the microdroplets. However, the analysis of the cluster behavior under the action of external factors is also continued. Some new experimental findings concerning behavior of a cluster of water droplets levitating over the locally heated water surface are reported in the present paper. It is shown that an external electric field leads not only to an increase in the rate of a condensational growth of droplets but also to a relatively early coalescence of small droplets with water layer. The latter is partially explained by the attraction force arising due to polarization of droplets closely spaced to the water surface. The effect of electric field on size of droplets before their coalescence with water layer is used to estimate an electrical charge of single droplets at the experimental conditions. It is shown that this electric charge does not change the aerodynamic nature of the main forces responsible for both the self-arranging and levitation of small water droplets. The results obtained are expected to be useful for further theoretical modeling of the phenomenon of levitating droplets clusters.

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)’.

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 micro-porous polymer surfaces obtained by the breath figure method and levitating ordered water micro-droplet clusters.

A self-assembled cluster of microdroplets levitating over a heated water surface is a fascinating phenomenon with potential applications for microreactors and for chemical and biological analysis of small volumes of liquids. Recently, we suggested a method to synthesize a cluster with an arbitrary number of small monodisperse droplets. However, the interactions, which control the structure of the cluster, are still not well understood. Here we propose a Langevin computational model considering the aerodynamic forces between the droplets and random diffusion-like fluctuations. Characteristic length and time scales and scaling relationships of interactions are discussed. The model shows excellent agreement with experimental observations for a small number of droplets.

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.

Levitating small water droplets formed from the upward flow of steam and entrained air above the heated water surface are studied. The case of relatively large droplets in the middle of a droplet cluster which is practically immobile at a small distance from the water surface is considered. The close-up infrared measurements in the spectral absorption band of water are used to identify temperature of the upper surface of the droplet. Both the directional spectral emittance of water surface and the spectral sensitivity of the device are taken into account to formulate an inverse problem for the integral equation. The numerical solution of this problem showed that temperature is minimal at the top of droplet and increases sharply towards the droplet equator. This temperature difference increases almost linearly with the droplet size. The results obtained are expected to be useful for more detailed physical analysis and possible modeling of complex behavior of the levitating droplet clusters.

A method to generate levitating monodisperse microdroplet clusters with an arbitrary number of identical droplets is presented. Clusters with 1–28 droplets levitate over a locally heated water layer in an ascending vapor-air jet. Due to the attraction to the center of the heated area combined with aerodynamic repulsion between the droplets, the clusters form structures that are quite diverse and different from densest packing of hard spheres. The clusters self-organize into stable and reproducible configurations dependent on the number of droplets while independent of the droplets’ size. The central parts of larger clusters reproduce the shape of smaller clusters. The ability to synthesize stable clusters with a given number of droplets is important for tracing droplets, which is crucial for potential applications such as microreactors and for chemical analysis of small volumes of liquid.

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.

Packets of capillary waves on the surface of a horizontal water layer generated at coalescence with a layer of microdroplets (with a characteristic diameter of 50–100 μm) of the dissipative structure “droplet cluster” have been detected by high-speed video recording and the schlieren method. The shortest experimentally observed waves have a length of about 130 μm and their phase velocity exceeds 1.8 m/s. It has been found that the coalescence of a single drop initiates a self-sustained wave process, which induces the coalescence of hundreds of droplets in a time shorter than 1 ms, which form a cluster.

It has been found experimentally that the infrared irradiation of a droplet cluster levitating over the surface of water reduces the rate of the condensation growth of droplets until the stabilization of the size of droplets and even until possibly its decrease. The revealed effect is proportional to the power of a source of radiation. The appropriate choice of the infrared radiation flux makes it possible to prevent the collapse of the cluster and to significantly increase the duration of its stable levitation.