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The main results of a completed cycle of complex studies of a strongly coupled dusty plasma conducted in the unique, experimental Plasma Crystal-3 Plus space laboratory that operated on the International Space Station are discussed. The experiments on the physics of phenomena in the dusty plasma are analyzed. A new state of dusty plasma, the electrorheological plasma, in which there is a transition from an isotropic plasma-dusty liquid to an anisotropic state, is studied. The study of the interpenetration of particles streams of various diameters, a nonequilibrium transition, is described. Experimental studies of the liquid–crystal phase transition in a three-dimensional dusty plasma system in which it is established that the dust component is compressed and crystallized upon a decrease in the neutral gas pressure are discussed. The nearly free motion of large particles in the volume of a plasma crystal, a nonviscous, irrotational flow about a large particle by a “liquid” of small dust particles, is analyzed. An experimental study of the dynamics of the crystallization of three-dimensional plasma-dust systems at a constant argon pressure under the effect of a low-frequency, alternating electric field and without its influence under microgravity conditions is described. The formation of the crystallization front and its propagation in the three-dimensional plasma-dust system with a velocity on the order of the average interparticle distance per second were discovered.

We have analyzed the data obtained at the PK-3 Plus Laboratory onboard the International Space Station from analysis of the crystallization front propagation in a dusty plasma. We have developed the “axial” algorithm for identifying “crystal-like” particles, which makes it possible to recognize different crystalline domains and their surface. We have proposed a method for determining the 3D front velocity, presuming the existence of a small region of the domain surface, which propagates along a certain line perpendicular to this region. It is shown that the front velocity is almost independent of time and amounts to about 60 μm/s. We have proposed a theory of the crystallization front propagation in the dust cloud under the assumption that the flux of particles being crystallized is proportional to the difference in the self-diffusion coefficients for the liquid and crystalline phases. The upper estimate of the front velocity correlates with the results of processing of experimental data.

Clusters of atoms in dense gold vapor are studied via atomistic simulation with the classical molecular dynamics method. For this purpose, we develop a new embedded atom model potential applicable to the lightest gold clusters and to the bulk gold. Simulation provides the equilibrium vapor phases at several subcritical temperatures, in which the clusters comprising up to 26 atoms are detected and analyzed. The cluster size distributions are found to match both the two-parameter model and the classical nucleation theory with the Tolman correction. For the gold liquid–vapor interface, the ratio of the Tolman length to the radius of a molecular cell in the liquid amounts to ∼0.16, almost exactly the value at which both models are identical. It is demonstrated that the lightest clusters have the chain-like structure, which is close to the freely jointed chain. Thus, the smallest clusters can be treated as the quasi-fractals with the fractal dimensionality close to two. Our analysis indicates that the cluster structural transition from the solid-like to chain-like geometry occurs in a wide temperature range around 2500 K.

Complex plasmas are low temperature plasmas that contain microparticles in addition to ions, electrons, and neutral particles. The microparticles acquire high charges, interact with each other and can be considered as model particles for effects in classical condensed matter systems, such as crystallization and fluid dynamics. In contrast to atoms in ordinary systems, their movement can be traced on the most basic level, that of individual particles. In order to avoid disturbances caused by gravity, experiments on complex plasmas are often performed under microgravity conditions. The PK-3 Plus Laboratory was operated on board the International Space Station from 2006 - 2013. Its heart consisted of a capacitively coupled radio-frequency plasma chamber. Microparticles were inserted into the low-temperature plasma, forming large, homogeneous complex plasma clouds. Here, we review the results obtained with recent analyses of PK-3 Plus data: We study the formation of crystallization fronts, as well as the microparticle motion in, and structure of crystalline complex plasmas. We investigate fluid effects such as wave transmission across an interface, and the development of the energy spectra during the onset of turbulent microparticle movement. We explore how abnormal particles move through, and how macroscopic spheres interact with the microparticle cloud. These examples demonstrate the versatility of the PK-3 Plus Laboratory.

We report observation of the dust ionization waves (DIWs) excited by an external oscillating electric field on the Plasma Kristall-4 facility under microgravity conditions. It is shown that at the smallest excitation amplitude, the waves are linear, and the dispersion relation can be deduced from the experimental data. The microparticle oscillations are represented as a superposition of two longitudinal waves propagating in the opposite directions. In the investigated range of excitation frequency, the wavenumber is not directly proportional to the frequency, and the phase velocity is almost proportional to the frequency. We propose an interpretation of DIW assuming that the microparticle effect on the recombination rate rather than the microparticle subsystem compressibility is responsible for the wave propagation. The calculated phase velocity of DIW is compatible with the experimental one.

The ionization equation of state (IEOS) for a cloud of the dust particles in the low-pressure gas discharge under microgravity conditions is proposed. IEOS relates pairs of the parameters specific for the charged components of dusty plasma. It is based on the modified collision enhance collection model adapted for the Wigner--Seitz cell model of the dust cloud. This model takes into account the effect of ion--atom collisions on the ion current to the dust particles and assumes that the screening length for the ion--particle interaction is of the same order of magnitude as the radius of the Wigner--Seitz cell. Included effect leads to a noticeable decrease of the particle charge as compared to the previously developed IEOS based on the orbital motion limited model. Assuming that the Havnes parameter of the dusty plasma is moderate one can reproduce the dust particle number density measured in experiments and, in particular, its dependence on the gas pressure. Although IEOS includes no fitting parameters, it can ensure a satisfactory precision in a wide range of dusty plasma parameters. Based on the developed IEOS, the threshold relation between the dusty plasma parameters for onset of the lane formation in binary dusty plasmas is deduced., 12 pages, 9 figures

We analyze stability of a three-dimensional cloud of the dust particles in the low-pressure radio frequency discharge under microgravity conditions. The parameters of such complex plasma are assumed to conform to the recently developed ionization equation of state that includes the effects of the ion–atom collisions on the particle charge and of the ion–particle collisions on the ion mean free path. Propagation of the particle number density perturbation in a cloud is treated using the fluid approach. The equation for dust cloud dynamics allows for the electric and ion drag forces that are not compensated in a nonstationary state and yields the wave equation for the dust acoustic waves with either a positive or negative effective friction coefficient. The resulting dispersion relation defines a condition of the instability onset, which is written for the maximum ambipolar field and dust number density gradient. Analysis of the available experimental data reveals a satisfactory correspondence with the theory. In particular, it is demonstrated that the maximum dust density gradient in the cloud increases with the increase in the particle diameter and in the pressure of plasma-forming gas.

Complex (dusty) plasmas are composed of weakly ionised gas and charged microparticles and represent the plasma state of soft matter. Due to the ”heavy” component — the microparticles — and the low density of the surrounding medium, the rarefied gas and plasma, it is necessary to perform experiments under microgravity conditions to cover a broad range of experimental parameters which are not available on ground. The investigations have been performed onboard the International Space Station (ISS) with the help of the ”Plasma Crystal-3 Plus” (PK-3 Plus) laboratory. It was perfectly suited for the formation of large stable liquid and crystalline Systems and provided interesting insights into processes like crystallisation and melting, laning in binary mixtures, electrorheological effects due to ac electric fields and projectile interaction with a strongly coupled complex plasma cloud.

The PK-3 Plus laboratory onboard the International Space Station is used to form complex plasma with a liquidlike particle subsystem in metastable state and to observe the propagation of crystallization fronts corresponding to the surfaces of crystal domains. We propose the "axis" algorithm of solidlike particles identification, which makes it possible to isolate different domains and their surfaces as well. Determination of the three-dimensional front velocity is based on its definition implying that there exists a small area of the domain surface propagating along some line perpendicularly to it. The velocity measured in this way is an important characteristic of the plasma crystallization kinetics. It proves to be almost independent of time and the direction of front propagation and amounts to ca. 60--80 micron per second., Comment: 10 pages, 8 fidures

An example of the non-equilibrium phase transition is the formation of lanes when one kind of particles is driven against the other. According to experimental observation, lane formation in binary complex plasmas occurs when the smaller particles are driven through the stationary dust cloud of the larger particles. We calculate the driving force acting on a probe particle that finds itself in a quiescent cloud of particles in complex plasma of the low-pressure radio frequency discharge under microgravity conditions. It is shown that the nonzero driving force is a result of the dependence of the ion mean free path on the particle number density. If this effect is properly included in the model of similar complex plasmas then one arrives at the driving force that changes its sign at the point where the probe and the dust particles have equal radii. If the probe is smaller than the dust particle then the driving force is directed toward the discharge center and vice versa, in accordance with experiment. Obtained results can serve as the ansatz for future investigation of the lane formation in complex plasmas., Comment: 8 pages, 5 figures

Oscillation of particles in a dust crystal formed in a low-pressure radio-frequency gas discharge under microgravity conditions is studied. Analysis of experimental data obtained in our previous study shows that the oscillations are highly isotropic and nearly homogeneous in the bulk of a dust crystal; oscillations of the neighboring particles are significantly correlated. We demonstrate that the standard deviation of the particle radius-vector along with the local particle number density fully define the coupling parameter of the particle subsystem. The latter proves to be of the order of 100, which is two orders of magnitude lower than the coupling parameter estimated for the Brownian diffusion of particles with the gas temperature. This means significant kinetic overheating of particles under stationary conditions. A theoretical interpretation of the large amplitude of oscillation implies the increase of particle charge fluctuations in the dust crystal. The theoretical estimates are based on the ionization equation of state for the complex plasma and the equation for the plasma perturbation evolution. They are shown to match the results of experimental data processing. Estimated order of magnitude of the coupling parameter accounts for the existence of the solid-liquid phase transition observed for similar systems in experiments., Comment: 12 pages, 11 figures, 1 table

Thermal fluctuations of the surface of argon-like cluster are considered. Data obtained by molecular dynamics method are used to find effective surface tension for the capillary component of fluctuations, which characterizes the deviation of Fourier spectrum observed in numerical experiment from the spectrum of macroscopic capillary waves. The variational method was used to solve the problem. It is revealed that effective surface tension is close to constant value within a rather wide wavelength range. At the boundary of this range in the region of large wave numbers, the obtained value quickly tends to infinity, while spectral amplitudes decay thus corresponding to the theory proposed previously. The width of damping region is estimated for different temperatures and cluster sizes.

We propose a novel method of determination of the dust particle spatial distribution in dust clouds that form in three-dimensional (3D) complex plasmas under microgravity conditions. The method utilizes the data obtained during the 3D scanning of a cloud and provides a reasonably good accuracy. Based on this method, we investigate the particle density in a dust cloud realized in gas discharge plasma in the PK-3 Plus setup onboard the International Space Station. We find that the treated dust clouds are both anisotropic and inhomogeneous. One can isolate two regimes, in which a stationary dust cloud can be observed. At low pressures, the particle density decreases monotonically with the increase of the distance from the discharge center; at higher pressures, the density distribution has a shallow minimum. Regardless of the regime, we detect a cusp of the distribution at the void boundary and a slowly varying density at larger distances (in the foot region). A theoretical interpretation of obtained results is developed that leads to reasonable estimates of the densities for both the cusp and foot. The modified ionization equation of state, which allows for violation of the local quasineutrality in the cusp region, predicts the spatial distributions of ion and electron densities to be measured in future experiments., Comment: 37 pages, 13 figures

Dust acoustic waves in the bulk of a dust cloud in complex plasma of low-pressure gas discharge under microgravity conditions are considered. The complex plasma is assumed to conform to the ionization equation of state (IEOS) developed in our previous study. This equation implies the ionization similarity of plasmas. We find singular points of IEOS that determine the behavior of the sound velocity in different regions of the cloud. The fluid approach is utilized to deduce the wave equation that includes the neutral drag term. It is shown that the sound velocity is fully defined by the particle compressibility, which is calculated on the basis of the used IEOS. The sound velocities and damping rates calculated for different three-dimensional complex plasmas both in ac and dc discharges demonstrate a good correlation with experimental data that are within the limits of validity of the theory. The theory provides interpretation for the observed independence of the sound velocity on the coordinate and for a weak dependence on the particle diameter and gas pressure. Predictive estimates are made for the ongoing PK-4 experiment., Comment: 11 pages, 4 figures, and 1 table

We explore thermodynamic properties of a vapor in the range of state parameters where the contribution to thermodynamic functions from bound states of atoms (clusters) dominates over the interaction between the components of the vapor in free states. The clusters are assumed to be light and sufficiently "hot" for the number of bonds to be minimized. We use the technique of calculation of the cluster partition function for the cluster with a minimum number of interatomic bonds to calculate the caloric properties (heat capacity and velocity of sound) for an ideal mixture of the lightest clusters. The problem proves to be exactly solvable and resulting formulas are functions solely of the equilibrium constant of the dimer formation. These formulas ensure a satisfactory correlation with the reference data for the vapors of cesium, mercury, and argon up to moderate densities in both the sub- and supercritical regions. For cesium, we extend the model to the densities close to the critical one by inclusion of the clusters of arbitrary size. Knowledge of the cluster composition of the cesium vapor makes it possible to treat nonequilibrium phenomena such as nucleation of the supersaturated vapor, for which the effect of the cluster structural transition is likely to be significant.

The potential of the interaction of an alkali metal with a planar metal surface was calculated by solving a two-dimensional Schrodinger equation. The potential energy of the valence electron of the atom was derived from a model pseudopotential based on the image potential. It was demonstrated that the potential energy curve for the interaction of an alkali metal atom with the surface of a heavier alkali metal has a minimum at a certain distance from the surface, a feature that gives rise to equilibrium states of levitating atoms.

As is known, the two-photon annihilation of positron‐electron pair constituting ortho-positronium atom is prohibited by the angular momentum conservation law. Therefore, when the ortho-positronium gets into a liquid, its lifetime becomes shorter due to the annihilation of positronium with an electron of liquid molecule. However, in the majority of cases, this effect is not so pronounced, because a vacuum bubble arises in a liquid around positronium that lowers the probability of annihilation. The reason for the appearance of the bubble (the autolocalization of positronium) is the Pauli repulsion between positronium electron and electrons of a liquid. The size of this steadily metastable formation is determined by the balance between the energy of Pauli repulsion and the surface energy of the bubble: as the size of bubble increases, its repulsive energy lowers and surface energy rises. The autolocalization of positronium was first observed in experiments reported in [1, 2]; in subsequent studies (for the detailed bibliography see [3, 4]), the bubble radii and the lifetime of positronium in the bubble were determined. Bubble radii vary from the unity to several tens of a distance between molecules in a liquid. The shape of such a supersmall bubble can differ profoundly from spherical in each moment; hence, the term “nanocavity” is frequently met in the literature and will be used hereafter.

Stationary states of molecular negative ions (anions) near the surface of a solid are investigated. The lone electron is assumed to interact with a diatomic molecule and the surface of the solid. The energies of elec- tron levels are determined by solving the 2D Schrodinger equation. It is shown that its stable solutions exist at distances from the surface greater than some critical distance, otherwise the electron is detached from the anion. In the case of attraction between the electron and the solid, the interaction potential between the anion and the solid appears to have the Lennard-Jones form and the ion is separated from the surface by some equilibrium distance. © 2003 MAIK "Nauka/Interperiodica".

Based on the division of particles into internal and surface particles, the expression is derived closing the system of equations of classical thermodynamics for curvature-dependent surface tension, equimolar radius, and radius of tension surface. A solution to this system allows one to find the surface tension of new phase nucleus of any size (including minimal) and any sign of surface curvature. The obtained results indicate the weak size dependence of thermodynamic parameters that are the functions of surface tension; it is shown that Tolman's length cannot be determined using experimental determination of these parameters. It is shown that the work of nucleus formation strongly depends on its size and is the function of effective rather than true surface tension. Numerical simulation of clusters by the molecular dynamics method indicates that the pressure inside a fairly small cluster is described by Laplace's formula with the coefficient of surface tension for the plane surface of a liquid that agrees with the proposed theory.

Complex (dusty) plasmas are composed of weakly ionized gas and charged micro-particles and represent the plasma state of soft matter. Due to the "heavy" component, microparticles, and the low density of the surrounding medium, the rarefied gas and plasma, it is necessary to perform experiments under microgravity conditions to cover a broad range of experimental parameters which are not available on ground. The investigations have been performed onboard the International Space Station with the help of the PK-3 Plus laboratory. This laboratory was mainly built to investigate the crystalline state of complex plasma, the so-called plasma crystal, its phase transitions and processes in multi-particle mixtures. Due to the manipulation of the interaction potential between the microparticles it is possible to initiate a phase transition from isotropic plasma into electrorheological plasma. The crystal–liquid phase transition was obtained in large three-dimensional isotropic dusty plasma system. First observations of a transition of the dusty plasma system state due to variations of the plasma component density are presented.

We report the first observation of the Mach cones excited by a larger microparticle (projectile) moving through a cloud of smaller microparticles (dust) in a complex plasma with neon as a buffer gas under microgravity conditions. A collective motion of the dust particles occurs as propagation of the contact discontinuity. The corresponding speed of sound was measured by a special method of the Mach cone visualization. The measurement results are incompatible with the theory of ion acoustic waves. The estimate for the pressure in a strongly coupled Coulomb system and a scaling law for the complex plasma make it possible to derive an evaluation for the speed of sound, which is in a reasonable agreement with the experiments in complex plasmas., 5 pages, 2 figures, 1 table

Numerical experiments showed that the number-of-bonds distribution of particles that form a fairly large molten argon-like cluster was bimodal. This result was interpreted as a consequence of the formation of two “phases, ” namely, particles inside the cluster and a monolayer of particles lying above the others. Particle chains were shown to be formed near the surface of the cluster. Splitting off of separate particles from them was the most probable mechanism of vaporization. Model concepts that described the dependences observed in numerical experiments were developed.

Complex (dusty) plasmas are composed of weakly ionized gas and charged microparticles and represent the plasma state of soft matter. Due to the "heavy" component, microparticles, and the low density of the surrounding medium, the rarefied gas and plasma, it is necessary to perform experiments under microgravity conditions to cover a broad range of experimental parameters which are not available on ground. The investigations have been performed onboard the International Space Station (ISS) with the help of the PK-3 Plus laboratory. This laboratory was mainly built to investigate the crystalline state of complex plasma, the so-called plasma crystal, its phase transitions and processes in multi-particle mixtures. The crystal–liquid phase transition was obtained in large three-dimensional isotropic dusty plasma system. Observations of a transition of the dusty plasma system state due to the particle charge reduction and due to variations of the plasma component density are presented.

We employ the approximation of overlapped scattering potentials of charged dust particles exposed to streaming ions to deduce the "equation of state" for a stationary dust cloud in the radio frequency discharge apart from the void dust boundary. The obtained equation defines the potential of a dust particle as a function of the ion number density, the mass of a carrier gas atom, and the electron temperature. A scaling law that relates the particle number density to the particle radius and electron temperature in different systems is formulated. Based on the proposed approach the radius of a cavity around a large particle in the bulk of a cloud is estimated. The results of calculation are in a reasonable agreement with the experimental data available in literature., 10 pages, 7 figures, and 1 table

At relatively high temperatures (higher than the melting temperature of a liquid), clusters existing in the supersaturated vapor are characterized by an intense internal motion of molecules. The virtual chains model of small “hot” clusters is proposed, which assumes that the number of bonds in small clusters is minimal, and that their structure is chainlike. Interpolation formulas for extensive thermodynamic functions of a cluster containing arbitrary number of atoms are found. Validity of model assumptions are verified by the molecular dynamics simulation for the ensemble with constant temperature and pressure. Simulation results are discussed, among which are the average potential energy of a cluster, the radial distribution function, and topological structure of clusters. Numerical results validate the basic assumption of proposed model.

We propose a model, which is an alternative to the droplet model and presumes that the number of bonds between the atoms is a minimum, to describe highly excited clusters containing a small number of atoms. It is shown that at sufficiently high temperatures such a structure, which has the form of a system of spontaneously appearing chains of atoms (virtual chains),is realized with a greater probability than the close-packed structure. Analytic estimates are supported by the results of numerical molecular-dynamics simulations.

We employ a model, in which the density fluctuations in a bulk liquid are represented as presence of the clusters of molecules with the lowered number of nearest neighbors (number of bonds). The nanobubble size distribution is calculated on the basis of a close analogy between the surface part of the work of formation for a cluster and for a nanobubble. The pre-exponential factor for this distribution is related to the fluid compressibility. Estimates made for different liquids show that it can be noticeably different from that adopted in the classical nucleation theory (CNT). Molecular dynamics (MD) simulation is performed for a liquid inside a macroscopic droplet of molecules interacting via the Lennard-Jones potential plus a long-range tail. The nanobubbles are identified by clusters of bond-deficient particles with the optimum number of bonds that provide the maximum nanobubble number density and maximum resolvable nanobubble equimolar size. The results of MD simulation are in qualitatively better agreement with proposed theory than with CNT.

Behavior of an argonlike cluster in supersaturated vapor at constant temperature and pressure is simulated. In contrast to the results of conventional microcanonical ensemble simulations, instability of cluster size is observed (unlimited growth or complete evaporation). This defines cluster critical size, which is noticeably larger than that predicted by the classical nucleation theory. Analysis of cluster collective vibrational spectra shows that its evaporation is intimately connected with spontaneous emergence of the lowest modes of breathing vibrations. The cluster phonon spectrum resembles that of a strange attractor.

The vapor-liquid nucleation in a dense Lennard-Jones system is studied analytically and numerically. A solution of the nucleation kinetic equations, which includes the elementary processes of condensation/evaporation involving the lightest clusters, is obtained, and the nucleation rate is calculated. Based on the equation of state for the cluster vapor, the pre-exponential factor is obtained. The latter diverges as a spinodal is reached, which results in the nucleation enhancement. The work of critical cluster formation is calculated using the previously developed two-parameter model (TPM) of small clusters. A simple expression for the nucleation rate is deduced and it is shown that the work of cluster formation is reduced for a dense vapor. This results in the nucleation enhancement as well. To verify the TPM, a simulation is performed that mimics a steady-state nucleation experiments in the thermal diffusion cloud chamber. The nucleating vapor with and without a carrier gas is simulated using two different thermostats for the monomers and clusters. The TPM proves to match the simulation results of this work and of other studies.

Subsonic motion of a large particle moving through the bulk of a dust crystal formed by negatively charged small particles is investigated using the PK-3 Plus laboratory onboard the International Space Station. Tracing the particle trajectories show that the large particle moves almost freely through the bulk of plasma crystal, while dust particles move along characteristic alpha-shaped pathways near the large particle. In the hydrodynamic approximation, we develop a theory of nonviscous dust particles motion about a large particle and calculate particle trajectories. A good agreement with experiment validates our approach., Comment: 14 pages, 5 figures

A size‐corrected thermodynamic model for clusters is proposed which implies that cluster chemical potential is a linear function of the number of molecules at its surface and the total number of molecules. The model is free from the introduction of the surface tension for small clusters and therefore has no limitation in this size range. The expressions for homogeneous nucleation rates have been obtained in the approximations of small and large critical sizes. Calculated nucleation rates are slightly lower than predicted by the classical theory for water vapor and much higher for mercury vapor, in agreement with the experiments.

Analysis of surface fluctuation spectra is performed for a large cluster of particles interacting via a sum of the short-range Lennard-Jones potential and long-range ±1/r potential, where the positive sign corresponds to the gravity, and negative corresponds to the electrostatic interaction. The spectral amplitudes of thermally driven capillary modes in a self-consistent field induced by cluster particles including the modes with no axial symmetry are derived in the approximation of small amplitudes. It is demonstrated that within used approximation, the surface tension is independent of the field strength. The low wave vector amplitudes are damped by attracting field that compresses the cluster and magnified by repulsing field leading to cluster fission. The fission threshold is found to be different from that found by Bohr and Wheeler and Frenkel due to the replacement of the ordinary surface tension by the bare one. Molecular dynamics study of a cluster with the long-range interaction in the vapor environment is performed using a novel integrator for a multiscale system. Simulation scheme implies rotation of the long-range components of forces acting on cluster particles thus vanishing an artificial torque. Simulation results justify theoretical conclusion of modes damping and independence of the surface tension of the field strength. Fission threshold evaluated from simulation data is in a good agreement with theory.

Using the PK-3 Plus laboratory onboard the International Space Station motion of a large projectile in the bulk of a dust crystal formed by negatively charged small particles was investigated. It is demonstrated that a subsonic projectile moves almost freely inside the dust crystal. A hydrodynamic theory of projectile nonviscous motion confirms the experimental data.

Spectra of the cluster surface equilibrium fluctuations are treated by decomposition into the bulk and net capillary ones. The bulk fluctuations without capillary ones are simulated by the surface of a cluster truncated by a sphere. The bulk fluctuation spectrum is shown to be generated primarily by the discontinuity in the spatial distribution of cluster internal particles. The net capillary fluctuation slice spectrum is obtained in molecular dynamics simulation by subtraction of the bulk fluctuation spectrum from the total one. This net spectrum is in the best agreement with a theoretical estimation if we assume the intrinsic surface tension to be independent of the wave number. The wave number cutoff is brought in balance with the intrinsic surface tension and excess surface area induced by the capillary fluctuations. It is shown that the ratio of the ordinary surface tension to the intrinsic one can be considered as a universal constant independent of the temperature and cluster size.

We discuss the inductively heated plasma generator (IPG) facility in application to the generation of the thermal dusty plasma formed by the positively charged dust particles and the electrons emitted by them. We develop a theoretical model for the calculation of plasma electrical conductivity under typical conditions of the IPG. We show that the electrical conductivity of dusty plasma is defined by collisions with the neutral gas molecules and by the electron number density. The latter is calculated in the approximations of an ideal and strongly coupled particle system and in the regime of weak and strong screening of the particle charge. The maximum attainable electron number density and corresponding maximum plasma electrical conductivity prove to be independent of the particle emissivity. Analysis of available experiments is performed, in particular, of our recent experiment with plasma formed by the combustion products of a propane–air mixture and the CeO2 particles injected into it. A good correlation between the theory and experimental data points to the adequacy of our approach. Our main conclusion is that a level of the electrical conductivity due to the thermal ionization of the dust particles is sufficiently high to compete with that of the potassium-doped plasmas.

Classification of cluster particles is proposed that introduces three particle types: the internal particles, surface particles, and virtual chains of particles. Thermal fluctuations of a surface passing through the surface particles of a Lennard-Jones liquid cluster are studied using a molecular dynamics simulation. It is shown that for large clusters, the Fourier spectral amplitude of these fluctuations decays faster than 1q, where q is the wave number. The frequency Fourier spectrum shows an overdamped system behavior, which is the evidence for the absence of thermal capillary waves for clusters comprising less than 10(5) particles. The time-averaged cluster density profile is given by an error function with the width parameter diverging as the logarithm of the cluster size.

At relatively high temperatures (higher than the melting temperature of a liquid), clusters that are present in the supersaturated vapor are characterized by an intense internal motion of molecules. Investigation of clusters in such states is within the scope of this Chapter. The virtual chains model is proposed, which assumes that the number of bonds in small clusters is minimal, and their structure is chainlike. The thermodynamic model describing cluster properties for an arbitrary law of the interaction between molecules and the size-corrected nucleation theory are developed on this basis. Validity of model assumptions are verified by the numerical simulations using molecular dynamics in an ensemble with constant average temperature and pressure. Simulation results are discussed, among which are the cluster critical size, internal energy, radial distribution function, and topological structure of clusters. Numerical results validate the main assumptions of proposed model.

The incompressible Navier-Stokes equation is employed to describe a subsonic particle flow induced in complex plasmas by a moving projectile. Drag forces acting on the projectile in different flow regimes are calculated. It is shown that, along with the regular neutral gas drag, there is an additional force exerted on the projectile due to dissipation in the surrounding particle fluid. This additional force provides significant contribution to the total drag.