Confinement Effects in Droplet Formation on a Solid Particle.

Formation of a droplet around a spherical solid particle in supersaturated vapor is considered. The number and stability of equilibrium solutions in a closed small system are studied in the canonical ensemble in comparison to an open system in the grand canonical ensemble. Depending on the system's parameters, two modes exist in the canonical ensemble: the first one with only one solution and the second one with three solutions; the presence of the third solution is due to confinement.

Regularities of non-stationary diffusion growth of overcritical gas bubbles and kinetics of bubble distribution in presence of capillary and viscous forces.

The regularities of non-stationary diffusion growth of overcritical gas bubbles and kinetics of their distribution in sizes in a supersaturated-by-gas liquid solution on the nucleation stage have been analytically described by taking into account the full-scale influence of viscous and capillary forces on pressure in the overcritical bubbles. The results are general and not limited by values of gas supersaturation and gas solubility in the surrounding liquid solution. It is shown how the nonuniform concentration profile of the dissolved gas in supersaturated solution around the growing bubble changes with time and distance from the center of the overcritical bubble and gradually transforms into a stationary (at low solubility and moderate supersaturation of the dissolved gas) or self-similar profile (at large solubility and supersaturation of the dissolved gas).

Comment on "Size dependence of bubble wetting on surfaces: breakdown of contact angle match between small sized bubbles and droplets" by H. Zhang and X. Zhang, , 2019, , 2823.

The main result of the commented article is based on the use of an erroneous technique in the derivation of the equation for the contact angles of surface bubbles. A correct derivation gives the same Young equation as for sessile droplets, and therefore supplementary contact angles for bubbles and droplets. This cannot explain the presented results of simulations of nanosized droplets and bubbles where there are also several questions.

Multicomponent condensation on the nucleation stage.

A new analysis of evolution of an ensemble of supercritical (in size) droplets in the atmosphere of several condensing vapors has been presented. The analysis has been performed for the nucleation stage of formation and growth of the supercritical droplets in a closed system with a fixed amount of condensing species. The nucleation stage starts with appearance of supercritical droplets and finishes when nucleation rate of new critical droplets in the closed system ceases due to vapor depletion by the growing supercritical droplets.

Nucleation stage of multicomponent bubbles of gases dissolved in a decompressed liquid.

A new kinetic analysis of degassing and swelling of a decompressed liquid solution with several dissolved gases has been presented. The analysis has been performed for the nucleation stage of formation and growth of supercritical gas bubbles in a closed system under conditions of a limited availability of the dissolved species. The nucleation stage is an important stage of degassing, on which a certain size distribution of gas bubbles is formed, being the starting point for further growth.

Full-time kinetics of self-assembly and disassembly in micellar solution via the generalized Smoluchowski equation with fusion and fission of surfactant aggregates.

Full-time kinetics of self-assembly and disassembly of spherical micelles with their fusion and fission in non-ionic micellar solutions has been considered in detail on the basis of direct numerical solutions of the generalized Smoluchowski equations describing the evolution of the time-dependent concentrations of molecular aggregates for every aggregation number. The cases of instant increase of the monomer concentration up or dilution of a surfactant solution below the critical micelle concentration at large initial deviations from the final equilibrium state have been studied. Different stages in assembly or disassembly of micelles have been described and compared with the results of the stepwise mechanism of monomer attachment-detachment described by the Becker-Döring kinetic equations.

Relaxation times and modes of disturbed aggregate distribution in micellar solutions with fusion and fission of micelles.

We have performed direct numerical calculations of the kinetics of relaxation in the system of surfactant spherical micelles under joint action of the molecular mechanism with capture and emission of individual surfactant molecules by molecular aggregates and the mechanism of fusion and fission of the aggregates. As a basis, we have taken the difference equations of aggregation and fragmentation in the form of the generalized kinetic Smoluchowski equations for aggregate concentrations. The calculations have been made with using the droplet model of molecular surfactant aggregates and two modified Smoluchowski models for the coefficients of aggregate-monomer and aggregate-aggregate fusions which take into account the effects of the aggregate size and presence of hydrophobic spots on the aggregate surface.

Multi-scale times and modes of fast and slow relaxation in solutions with coexisting spherical and cylindrical micelles according to the difference Becker-Döring kinetic equations.

The eigenvalues and eigenvectors of the matrix of coefficients of the linearized kinetic equations applied to aggregation in surfactant solution determine the full spectrum of characteristic times and specific modes of micellar relaxation. The dependence of these relaxation times and modes on the total surfactant concentration has been analyzed for concentrations in the vicinity and well above the second critical micelle concentration (cmc2) for systems with coexisting spherical and cylindrical micelles. The analysis has been done on the basis of a discrete form of the Becker-Döring kinetic equations employing the Smoluchowsky diffusion model for the attachment rates of surfactant monomers to surfactant aggregates with matching the rates for spherical aggregates and the rates for large cylindrical micelles.

Thermodynamic and kinetic theory of nucleation, deliquescence and efflorescence transitions in the ensemble of droplets on soluble particles.

Thermodynamic and kinetic peculiarities of nucleation, deliquescence and efflorescence transitions in the ensemble of droplets formed on soluble condensation nuclei from a solvent vapor have been considered. The interplay of the effects of solubility and the size of condensation nuclei has been analyzed. Activation barriers for the deliquescence and phase transitions and for the reverse efflorescence transition have been determined as functions of the relative humidity of the vapor-gas atmosphere, initial size, and solubility of condensation nuclei.

Excess equimolar radius of liquid drops.

The curvature dependence of the surface tension is related to the excess equimolar radius of liquid drops, i.e., the deviation of the equimolar radius from the radius defined by the macroscopic capillarity approximation.

Nucleation stage with nonsteady growth of supercritical gas bubbles in a strongly supersaturated liquid solution and the effect of excluded volume.

An approach to the kinetics of barrier formation of supercritical gas bubbles in a strongly supersaturated liquid solution is presented. A common assumption of uniform reduction of a dissolved gas supersaturation in a liquid solution via stationary diffusion to nucleating gas bubbles is shown to be not applicable to the case of high gas supersaturations. The approach recognizes that the diffusion growth of supercritical bubbles at high gas supersaturation is essentially nonstationary.

Boltzmann distributions and slow relaxation in systems with spherical and cylindrical micelles.

Equilibrium and nonequilibrium distributions of molecular aggregates in a solution of a nonionic surfactant are investigated at the total surfactant concentration above the second critical micelle concentration (CMC2). The investigation is not limited by the choice of a specific micellar model. Expressions for the direct and reverse fluxes of molecular aggregates over the potential humps of the aggregation work are derived.