A method is proposed for the neural network based analysis of the existence and stability of grain boundary complexions formed at high-symmetry tilt boundaries Σ3 (111) and Σ5 (210) in a polycrystalline Ni(Bi) solid solution. This method is based on the use of reference interparticle interaction potentials constructed within the framework of the density functional theory in combination with the structural capabilities of an artificial two-level self-learning neural network. The absolute error in determining potential energy by the neurosystem analysis is 0.012 eV/atom. The values of the formation enthalpy of grain boundary complexions for Σ3 and Σ5 boundaries are in rather good agreement with the published results of simulating this system and experimental data.

Very simple and strict equations thoroughly characterizing the effect of capillary self-retardation of a droplet in the process of its detachment from the continuous part of a disintegrating jet, this effect having been revealed earlier and then confirmed experimentally, are derived from Newton’s laws of momentum and energy variations. Equations describe four total (over the time of disintegration) losses of the momentum, translational energy, total energy, and internal energy per unit mass of a liquid. As the rate of an initial cylindrical jet rises, the loss of momentum and internal energy unlimitedly decreases, the loss of translational energy limitedly rises, and the loss of total energy remains unchanged.

The distribution of a liquid over the height of a vertical column (with the lower part immersed in a wetting liquid) of close-packed solid spherical particles is studied. For such a system, the equilibrium distribution of the liquid in the three-phase region with a high expansion ratio is shown to be described by the same formulas as for a two-phase disperse system (high-expansion monodisperse foam), but the radius of spherical particles is used in the three-phase case instead of the radius of polyhedral foam cells of equivalent volume. Linear, surface, and bulk capillary forces acting in model three-phase systems with liquid “collars” between close-packed spherical particles are considered. Specific forces of capillary adhesion are shown to be independent of the specific volume of the liquid if it is small enough, but they increase with decreasing size of the particles. In the two-dimensional case with hexagonal packing of particles, these forces are also independent of the particle size.

The expression for the film elasticity modulus is deduced including both the Gibbs elasticity and disjoining pressure contributions and explaining a peak of foam stability near the critical micelle concentration discovered earlier in experiments.

Rigorous formulas for the heat conductivity, electrical conductivity, and hydraulic conductivity of polydisperse polyhedral foams and highly concentrated emulsions are derived on the basis of the ideas recently formulated by one of the authors, with the structure of Plateau borders and films represented in the form of hierarchic series.

The transversal elasticity modulus and the film thickness have been measured in an equilibrium foam by an optical method to verify the theoretical prediction of the behaviour of these properties near the critical micelle concentration.

The elasticity of multicomponent closed and partially open thin films is analyzed. The elastic modulus of a completely closed film is shown to be additive with respect to contributions that are due to the Gibbs elasticity and disjoining pressure. In the case of only one closed component (e.g., a surfactant), both contributions are inseparably related to each other and may be expressed one through the other. For films of surfactant solutions, the resultant expressions make it possible to explain the marked maximum (observed in many experiments) of the foaming capacity of solutions and stability of foams in the vicinity of the critical micellization concentration.

The theory of transverse elasticity of thin foam films is formulated under the conditions when the action of Gibbs elasticity is excluded. The theory predicts the presence of maxima of the modulus of transverse elasticity and film thickness near the critical micellization concentration as functions of the content of surfactant at a given disjoining pressure. Theoretical conclusions are confirmed experimentally by measuring film thickness at various heights of equilibrium foam column.

The elasticity of open and closed thin foam films is analyzed. The elasticity modulus of a closed film is shown to be additive with respect to contributions from Gibbs elasticity and disjoining pressure. A detailed expression for the film elasticity modulus explains the pronounced maxima of foaminess and foam stability near the critical micelle concentration observed earlier in many experiments. A theory of transversal elasticity of thin foam films is formulated under conditions excluding the action of Gibbs elasticity. Near the critical micelle concentration, the theory predicts maxima of the transversal elasticity modulus and of the films thickness as functions of concentration at a given disjoining pressure. The prediction has been verified experimentally by measuring the film thickness in equilibrium foam as a function of height.

The indicatrix of light scattering by a polyhedral foam is calculated. The theoretical and experimental data for the specific differential cross section of scattering are shown to coincide. The effect of the foam film thickness and the spectral sensitivity function of the measuring instrument on the shape of the scattering indicatrix is considered.

A new method is proposed for studying the foaminess of surfactant solutions. The method is based on the determination of the stability of the foam monolayer in contact with the solution surface. Data on the foaminess of an aqueous sodium dodecyl sulfate solution are reported.

A new method of studying the foam stability based on the determination of the evolution time of foam cell at a given level of foam column is developed. The method is based on optical measurements that allow one to determine the main structural parameters of a foam. Experimental results are reported for sodium dodecyl sulfate solutions.

The method that consists in representing a surface by an infinite hierarchy of nonintersecting circles (and representing the surface area by an infinite series of sums) whose diameters are small compared to radii of curvature is proposed. As a simple example, the total cross-sectional area of a convex body is found—the area of its orthogonal projection (geometrical shadow) averaged over all three angular degrees of freedom of a solid body. This cross-sectional area turned out to be equal to a quarter of the surface area of the body. For disperse systems, the method provides a direct procedure for finding some average statistical regularities of structural properties that are the same for monodisperse and polydisperse systems.

On the basis of the mass, energy, and momentum conservation laws formulated for capillary continua, formulas describing postrelaxation results of merging of jets from slitlike sources were obtained. The effect of inelastic interaction between stationary jets in the noncapillary limit was revealed, as well as specific effects of capillary continua, which have no analogs in inelastic collision of isolated bodies.

On the basis of the energy and momentum conservation laws for the process of disintegration of a rotating cylindrical jet as a capillary continuum, rigorous and outstandingly simple universal equations of disintegration are derived. The Bernoulli equation for a steady-state “stream tube” is shown to have the same form for jet disintegration as well. The effect of capillary–centrifugal self-retardation of a disintegrating jet is revealed, as well as the effect of the drop in its internal energy, which takes place in the process. The seemingly paradoxical relationship between these effects is established; they are proved to be completely independent of the surface area formed during disintegration under the conditions of fixed parameters of the initial unperturbed jet. The law of conservation of the angular momentum flux during disintegration of a rotating jet is mathematically formulated and studied.