# Volume 25 № 4 2023

**1. Larisa S. Goruleva, Evgenii Yu. Prosviryakov. A New Class of Exact Solutions for Magnetohydrodynamics Equations to Describe Convective Flows of Binary Liquids. Chemical Physics and Mesoscopy, 2023, vol. 25, no. 4, pp. 447-462. **Download

A new family of exact solutions for the equations of magnetohydrodynamics of an incompressible fluid is presented. The convective fluid flows in a rectangular Cartesian coordinate system are considered. Convection in a conducting fluid is induced by thermal factors and a solute. Thus, the announced exact solution describes thermal diffusion in magnetic fluids. Exact solutions are constructed taking into account the cross dissipative effects of Soret and Dufour. In the article, the Lin-Sidorov-Aristov class is used to construct the exact solution. The velocity field and the magnetic field are described by linear forms with respect to two spatial coordinates. The coefficients of linear forms depend on the third coordinate and time. Pressure, temperature and solute concentration are described by quadratic forms. A system of equations for finding unknown functions for hydrodynamic fields is given. This system is overridden. The article presents an exact solution for determining unknown functions for describing steady Stokes flows of convection of a binary conducting fluid. When constructing an exact solution in a nonlinear system of magnetohydrodynamics, all the terms for the convective derivative were assumed to be equal to zero (there is no convective and diffusive mixing of a continuous medium).

** Keywords: **exact solution, Lin-Sidorov-Aristov class, magnetohydrodynamics, thermal diffusion, Soret effect, Dufour effect, Stokes approximation.

**DOI:** https://doi.org/10.15350/17270529.2023.4.39

**2. Yuriy I. Dimitrienko, Andrey A. Zakharov, Mikhail N. Koryakov. Burnback Simulation of Fuel Grains with Dispersed-Reinforced Propellant Composition. Chemical Physics and Mesoscopy, 2023, vol. 25, no. 4, pp. 463-473.** Download

The article deals with fuel grains with dispersed-reinforced propellant composition. The aim of the study is the numerical simulation of such grain burnback. We consider the complexity of the geometric description of the change in the curvilinear multiply-connected burning surface of propellant grains, as well as a large number of different parameters that affect the burning rate. We develop a geometric model to predict the regression of the burning surface. The model is based on spline representations and a direct method for numerically solving the equation of motion of the phase separation surface. We formulate a cubic spline interpolation problem using the parametric geometry representation method. We describe the method of parameterizing the spline control points and the end conditions required to close the problem. We develop a method for removing burned sections produced during simulation of concave grain evolution. The propellant burning rate is variable and is determined by solving an internal ballistics problem. We give an algorithm for modeling the change in shape of the curvilinear burning surface of propellant grains. We describe the computer program developed to calculate and visualize the change in shape of the burning surface depending on time. We discuss three slotted grain configurations that differ in the geometric dimensions of the slot parameters. For each configuration, the time evolution of the burning area is calculated and the type of the thrust action is determined. The proposed methods have demonstrated their performance and effectiveness.

* Keywords:* fuel grain, energetic composition, radial slot configuration, solid fuel combustion, burning surface, numerical burnback analysis, natural cubic spline.

**DOI:** https://doi.org/10.15350/17270529.2023.4.40

**3. Stanislav A. Trubachev, Oleg P. Korobeinichev, Artem A. Shaklein, Albert R. Sagitov, Ilya V. Kulikov, Egor A. Sosnin. Fully Three-Dimensional Coupled Simulation of Flame Propagation over a Polymer Driven by Heat Flux. Chemical Physics and Mesoscopy, 2023, vol. 25, no. 4, pp. 474-489. **Download

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The paper presents a fully three-dimensional coupled simulation of flame propagation over glass fiber reinforced epoxy resins under the influence of bilateral heat flux using the Fire Dynamic Simulator package. The model includes three-dimensional heat and mass transfer, diffusion of basic species in the gas phase, and diffusion transfer of pyrolysis products in the solid phase. The processes of pyrolysis and oxidation are represented by macro-reactions and take into account the effect of the phosphorus-containing flame retardant DDM-DOPO. The model predicts phenomena observed experimentally: absence of combustion in the case of zero external heat flux for fiberglass reinforced epoxy resin with the addition of 3% DDM-DOPO; flame propagation on both sides of the sample, self-sustaining combustion with a constant movement rate of the visible flame front. The values of the flame propagation rate over the samples obtained by the model are consistent with the experimental ones. In addition, the combustion rates are predicted beyond the limits of the experimental measurements. It has been found that the rate of flame propagation is sensitive to the reaction rate in the gas phase, which is a sign of the kinetic regime of flame propagation. An increase in the reaction rate leads to an increase in heat release in the gas phase, resulting in an increase in the total incident heat flux. The results obtained are an important step in establishing the requirements of the methodology for modeling the combustion of solid fuels under conditions of external thermal radiation that occur in real fires.

* Keywords:* combustion, numerical simulation, three-dimensional simulation, flame spread, polymers.

**DOI:** https://doi.org/10.15350/17270529.2023.4.41

**4. Artem A. Shaklein, Stanislav A. Trubachev, Gabriela Morar, Nikita A. Balobanov, Ekaterina A. Mitrukova. Numerical Study of Sensitivity of PMMA Burning Behavior in Counterflow to Input Data. Chemical Physics and Mesoscopy, 2023, vol. 25, no. 4, pp. 490-497. **Download

When some physical quantities, both general and particularly required for studying combustion of polymers, have to be measured, it is necessary to set some level of accuracy. The requirements here generally depend on a problem under consideration. Here we studied an effect of variation of input data values on the parameters of PMMA burning in the counterflow configuration. The mathematical model is set in a coupled "gas – solid" formulation to resolve heat and mass transfer between gas-phase flame and thermally degrading solid combustible. Gas-phase combustion was modeled in the open-source Cantera software in a one-dimensional counterflow flame configuration. The governing equations for solid fuel were solved in an in-house code in two-dimensional formulation. A skeletal chemical mechanism of MMA oxidation was employed to resolve gas-phase combustion. Variation of the distance between the burning surface and the air supply, density and thermal conductivity of PMMA, pre-exponent and activation energy of pyrolysis reaction rate and air mass inflow rate in the range of 10 % leads to a change in the temperature of the burning surface, the sample's mass loss rate and the molecular and radiative heat fluxes in the range of 20 %. It should be noted that despite the limited number of selected parameters and configurations of solid fuel combustion considered here, it can be concluded that for various combustion configurations the majority of thermal and physical quantities can be easily varied within 10 % without significantly (quantitatively and qualitatively) affecting the characteristics of a process under consideration.

** Keywords:** heat transfer, chemical mechanism, polymethylmethacrylate, counterflow flame, numerical simulation.

**DOI:** https://doi.org/10.15350/17270529.2023.4.42

**5. Andrey А. Shumikhin. The Use of Multicore Computing Systems for Numerical Simulation of Intrachamber Viscous Gas Flows. Chemical Physics and Mesoscopy, 2023, vol. 25, no. 4, pp. 498-506. ** Download

Numerical modeling of turbulent flows of compressible gas is important for the study of gas-dynamic processes occurring in solid-fuel rocket engines. The article presents a system of equations of hydromechanics describing the axisymmetric flow of compressible viscous gas. The system of basic equations is written in a cylindrical coordinate system. The use of parallel computing is currently an urgent tool for improving the computational performance of software and computer systems developed using computational fluid dynamics methods. Performing calculations on a multiprocessor computing computer system is associated with the need to develop software that performs several subtasks in parallel. Technically, this is achieved either by using computers with one or more multi-core central processors running under shared memory or by using a computer network working with distributed memory, respectively. Along with increasing the computing power of multiprocessor computer systems, it is important to develop appropriate algorithms and software. The use of multiprocessor computing technology imposes certain requirements on the construction of numerical algorithms for solving problems of hydro-gas dynamics. One of the main requirements is to minimize data exchange between processors during the calculation. Otherwise, the system will spend a significant part of its time on the information exchange, and not on the numerical calculations performed by processors. The basis of the proposed technique is an explicit modified Steger-Warming scheme of the 2nd order of accuracy in space. The developed program uses the proposed algorithm to perform parallel calculations on multiprocessor multicore computer systems with shared memory. Numerical studies of the flow of combustion products in a solid-fuel rocket engine using the developed parallel program have been performed. The results of modeling the in-chamber flow of a compressible viscous gas are presented and the dependence of the relative computational performance on the configuration of the computer system used in the calculations is analyzed.

** Keywords:** parallel calculations, turbulence, unsteady flow, computational hydro-gas dynamics.

**DOI:** https://doi.org/10.15350/17270529.2023.4.43

**6. Valentin A. Tenenev, Maria R. Koroleva. Statement of the Riemann Problem for Polytropic Gases Described by Complex Equations of State. Chemical Physics and Mesoscopy, 2023, vol. 25, no. 4, pp. 507-514. **Download

A statement of the Riemann problem for polytropic gases with arbitrary equations of state is presented. The characteristic form of the Euler system of equations is described. The eigenvalues of the Jacobian matrix and the corresponding eigenvectors of the gas dynamics equation system are given. Their effect on the structure of the Riemann problem solution is determined based on the nonlinearity factor. As consequence, the solution can be constructed in the form of a combination of simple waves - rarefaction waves, shock waves and contact discontinuities. The main analytical relationships for determining entropy, internal energy, pressure, temperature and speed of sound in a gas are given for two equations of state of real gases – van der Waals equation and Soave-Redlich-Kwong equation,. These relations underlie the procedure for constructing an exact Riemann problem solution and can be used to implement the Godunov method for solving multidimensional non-stationary problems of gas dynamics.

*Keywords:** *Riemann problem, exact solution, characteristic form, equations of state, van der Waals equation, Soave-Redlich-Kwong equation.

**DOI:** https://doi.org/10.15350/17270529.2023.4.44

**7. Mikhail S. Smakovskiy, Svetlana A. Atroshenko, Evgeny V. Kharanzhevskiy, Sergey N. Kostenkov, Valery I. Borodulin, Georgy G. Savenkov. Laser Modification of Aluminum Bronze. Chemical Physics and Mesoscopy, 2023, vol. 25, no. 4, pp. 515-523. **Download

The properties and microstructure of the surface of aluminum bronze BrAZhNMts 9-4-4-1 after laser quenching and laser alloying with molybdenum carbide were investigated. A short-pulse laser with a wavelength of 1064 nm and a pulse duration of 40 ns was used for processing. After laser treatment the modified layers were evaluated with the help of different techniques. The phase composition of the treated surfaces was analyzed on a multifunctional X-ray diffractometer Rigaku Ultima IV. Microstructural studies were carried out using an Axio-Observer Z1M optical microscope in a bright field. To measure the microhardness, an Affri microhardness tester was used. The load on the indenter was from 50 g to 2 kg, the scanning step was 100 μm. The statistical evaluation of the symmetry of binary objects in the microstructure was performed taking into account their mutual arrangement. The hidden ordering of the structure before and after laser treatment was assessed. After laser alloying, in the surface structure a chemically homogeneous layer with a doubled hardness was found converting into quenched structures with the dispersion of microstructure elements and martensite precipitation. Deeper from the surface, elongated grains were observed located along the boundaries after laser doping with eutectoid precipitates. In addition, twins and a large amount of martensite were found in the heat-affected zone. The maximum increase in hardness up to 410 HV was found in the laser-alloyed sample. The results of the study are necessary for improving the operational characteristics of shut-off elements of hydraulic equipment made of aluminum bronze.

** Keywords: **laser alloying, aluminum bronze, microstructure, microhardness.

**DOI:** https://doi.org/10.15350/17270529.2023.4.45

**8. Mikhail G. Vasin, Vladimir G. Lebedev, Vladimir E. Ankudinov, Konstantin Y. Shklyaev. The Phase-Field Model of the Glass Transition. Chemical Physics and Mesoscopy, 2023, vol. 25, no. 4, pp. 524-537.**Download

The paper presents a mathematical model describing the transition of a substance from a liquid state to a solid in the process of its uniform cooling. Two theoretical approaches were used to formulate the model: the gauge theory of glass transition, which describes this process as a topological phase transition in an elastic medium; and the phase field method, which describes the ordering process. As a parameter of the transition of a substance from the liquid state to the glassy state, it is proposed to use the curl of the gauge field characterizing the topological distortions of the locally ordered structure. The numerical calculation of the system of differential equations obtained within the framework of the proposed approach made it possible to simulate the competition between the crystallization and glass transition processes occurring during rapid cooling of the liquid. The model qualitatively describes the glass-crystal competition during quenching at finite cooling speed. In this case, the mobility of vortices is a defining property in the competition between glass and crystal formation. It is shown that the nucleation of the crystalline phase at slow cooling speeds and low undercoolings proceeds by a fluctuation mechanism; the majority of vortices have time to annihilate, and the remaining part is arranged in energetically favorable chains and quadrupoles, forming boundaries of ordered (crystalline) grains. The increase in the cooling rate leads to the increase in the glazing of the final structure.

* Keywords: i*ntermetallic alloys, relaxation, melts, viscosity.

**DOI:**https://doi.org/10.15350/17270529.2023.4.46

**9. Elena B. Dolgusheva, Еvgenii I. Salamatov. Changes in the Vibrational Spectrum of an Ultrathin Film Associated with the Loss of Symmetry when Adding One Atomic Layer. Chemical Physics and Mesoscopy, 2023, vol. 25, no. 4, pp. 538-543.** Download

The paper shows that the use of the molecular dynamics method, taking into account the atomic structure, to study the dynamic properties of crystalline ultrathin films consisting of several atomic layers can lead to a new interesting result - a qualitative change in the low-frequency region of the vibrational spectrum, which always occurs when one atomic layer is added or removed. In the elastic theory, changes in the vibrational spectrum with a change in the thickness of the film occur monotonically, because in an elastic film a plane parallel to the surface and passing through the middle of its thickness is always an element of the symmetry. This makes it possible to describe the dynamics of the system using the theory of elasticity in terms of bending waves and compression waves. The low-frequency vibrational spectra obtained by molecular dynamics for an aluminum film consisting of five, six and seven atomic layers show that in the case of a film consisting of an even number (6) of atomic layers, bending vibrations corresponding to the maximum wavelength are practically absent. In films with an odd (5,7) number of atomic layers, bending vibrations with the same wavelength have a significant amplitude. It is shown that the frequencies of these oscillations have a linear dependence on the number of atomic layers of the film, which is a sign of bending vibrations. The analysis of the atomic structure of the films under consideration has shown that a plane parallel to the surface and passing through the middle of its thickness is an element of symmetry only for films consisting of an odd number (5,7) atomic layers. When one atomic layer is added of removed, a change in the symmetry of the system leads to a qualitative change in the vibrational spectrum. This circumstance will affect the properties of the system such as, for example, the low-temperature heat capacity of thin films, thermal conductivity, etc., which are mainly determined by the behavior of the low-frequency region of the vibrational spectrum. Knowledge of the fundamental characteristics of ultrathin films will allow us to determine the scope of their application in modern nanotechnology.

* Keywords:* molecular dynamics method, low-frequency vibrational spectrum, ultrathin films, symmetric analysis, bending vibrations.

**DOI:** https://doi.org/10.15350/17270529.2023.4.47

**10. Tatyana S. Kartapova, Vasily L. Vorob’ev, Faat Z. Gil’mutdinov. The Influence of the Chemical Activity of Implanted Ions and Preliminary Irradiation of the Target with Low-Energy Ions on the Introduction Profile of the Implanted Impurity. Chemical Physics and Mesoscopy, 2023, vol. 25, no. 4, pp. 544-553. **Download

This work compares the results of implantation of inert (Ar) and chemically active element (N) ions into thin carbon films on the surface of iron, and also shows the effect of the preliminary implantation of low-energy (3 keV) argon ions on the result of the subsequent nitrogen implantation into armco iron samples. It has been revealed that the experimental distribution profiles of implanted N^{+} ions in the surface layers of iron differ from the calculated distribution profiles. It has been shown that the introduction and accumulation of nitrogen is largely determined by its chemical interaction with iron atoms. Preliminary irradiation of Armco iron samples with Ar^{+} ions with doses not exceeding 10^{17}
ions/cm^{2} promotes a more significant saturation of the thin surface layer with nitrogen during the subsequent implantation of N^{+} ions, which is most likely due to the creation of various types of radiation defects.

* Keywords:* carbon films, ion implantation, XPS, software package SRIM, chemical interaction.

**DOI:**https://doi.org/10.15350/17270529.2023.4.48

**11. Nikolai M. Barbin, Marina A. Shumilova, Dmitriy I. Terentiev, Mikhail Yu. Karpukhin. Thermodynamic Modeling of Gas-Phase Combustion of Tetrachlorodibenzo-p-dioxin in an Air Atmosphere. Chemical Physics and Mesoscopy, 2023, vol. 25, no. 4, pp. 554-561.**Download

Dioxins refer to the most dangerous technogenic superecotoxicants for the formation of which three conditions are necessary: the presence of organic matter, chlorine- or bromine-containing components, and high temperature. Consequently, almost all thermal processes are a serious problem since they are accompanied by the formation of environmentally hazardous amounts of dioxins. The aim of the work is to study the process of combustion of tetrachlorodibenzo-p-dioxin in air by the method of thermodynamic modeling to create new technologies. The process of tetrachlorodibenzo-p-dioxin combustion in the air atmosphere with different ratios of the system components has been studied by thermodynamic modeling. It has been established that with an increase in the air content in the system, the temperature interval for the existence of dioxin and its concentration decrease. An increase in the amount of air in the system leads to an increase in the concentration of N_{2}, CO, HCl in the gas phase over the entire temperature range, while the concentrations of dioxin and other compounds decrease. In each of the studied systems, the presence of compounds characteristic only of one of the systems and absent in the other was recorded. Thus, the combustion of dioxin should be carried out in the presence of a large amount of air, which reduces the amount of harmful substances formed.

* Keywords: *thermodynamic modeling, dioxins, air, maximum concentration, temperature range.

**DOI:** https://doi.org/10.15350/17270529.2023.4.49

**12. Lyudmila I. Zhdanova, Dmitriy S. Rybin, Alla A. Zhygalova. Electronic Structure and Biological Activity of Some Halogen Derivatives of Diethylenetriamides of Phosphoric Acid. Chemical Physics and Mesoscopy, 2023, vol. 25, no. 4, pp. 562-569.**Download

The paper examines how halogen substitution in the benzene ring of benzoteph affects its molecular and electronic structure and biological activity. X-ray diffraction and quantum chemistry simulation were used to analyze halogen derivatives and their impact on the molecular electronic structure. The paper focuses on the antiblastic activity of N-benzoyl-N', N', N'', N''-diethylenetriamide of phosphoric acid (I), as well as its halogen derivatives: N-para-fluorobenzoyl-N', N', N'', N''-diethylenetriamide phosphoric acid (II), N-meta-fluorobenzoyl-N', N', N'', N''-diethylenetriamide phosphoric acid (III), N-para-chlorobenzoyl-N', N', N'', N''-diethylenetriamide phosphoric acid (IV), and N-meta-iodobenzoyl-N', N', N'', N''-diethylenetriamide phosphoric acid (V). It was found that HOMO and HOMO-1 in molecules I-IV are formed with slightly different energies due to the oxygen atoms of the carbonyl group, the nitrogen of the ethylenimine ring and the phosphoryl oxygen atom. In molecule V, the HOMO is mainly localized on the substituent in the benzene ring, specifically the iodine atom, which differs from molecules I-IV. The differences in the activity and toxicity of the studied compounds result from the changes in their membrane permeability, which are caused by deviations in the dipole moment during stereochemical transformations of the molecules during the synthesis of halogenated benzoteph derivatives. The most active molecules have a trans-orientation of the O=P and N-C bonds in the urea fragment. In contrast, the less active meta-fluoro and para-chloro derivatives of benzoteph have a gauche orientation characterized by a change in the relative position of the phosphoryl and carbonyl oxygen atoms.

** Keywords:** organophosphorus compounds, molecular structure, density functional theory (DFT), biological activity.

**DOI:**https://doi.org/10.15350/17270529.2023.4.50

**13. ****Vladimir**** I. Lad’yanov, Maksim S. Konovalov, ****Marina**** I. Mokrushina, Andrey I. Shilyaev, Darya P. Ardasheva. The Influence of the Cooling Rate of the Melt during Spinning on the Structure of the Contact and Free Sides of the Fe**_{77}**Ni**_{1}**Si**_{9}**B**_{13}**
Alloy Tapes. Chemical Physics and Mesoscopy, 2023, vol. 25, no. 4, pp. 570-576.** Download

Using the melt spinning method, fast-quenched tapes with different thicknesses were obtained: 200, 50, 30, 20 μm at a quenching disk rotation speed of 500, 1500, 2500, 3500 rpm, respectively. The chemical composition of the ribbons was determined by atomic emission spectroscopy on a Spectroflame Module S installation. The X-ray patterns of the ribbons were obtained on a DRON-6 diffractometer in CuKα-radiation (graphite monochromator). The influence of the melt cooling rate on the structural state of the contact and free sides of Fe_{77}Ni_{1}Si_{9}B_{13}
alloy ribbons is considered. It has been established that increasing the cooling rate of the melt makes it possible to obtain rapidly quenched ribbons of the Fe_{77}Ni_{1}Si_{9}B_{13} alloy with different structures: X-ray amorphous at 3500, 2500 and 1500 rpm, crystalline at 500 rpm. In this case, cooling the melt at a rotation speed of the quenching disk of 500 rpm makes it possible to obtain ribbons of the Fe_{77}Ni_{1}Si_{9}B_{13}
alloy with three types of crystallographic structures, namely A2, C16 and D0_{3} (A2 corresponds to the α-Fe(Si) phase, C16 – to the Fe_{2}B phase, and D0_{3} – Fe_{3}Si phase). At the same time, texturing of the Fe_{3}Si phase was detected in the near-surface layers on the free side of the tape. It is noted that the crystal structure of the ribbons obtained by cooling the melt on a quenching disk with a rotation speed of 500 rpm differs from the structure of the ribbons of this alloy after their crystallization from the amorphous state during annealing.

** **** Keywords:** structure, amorphous tape, spinning method, cooling rate, Fe

_{77}Ni

_{1}Si

_{9}B

_{13}alloy.

**DOI:** https://doi.org/10.15350/17270529.2023.4.51

**14. Andrey V. Rychkov, Maksim D. Tokarev, Alena A. Chernova. Corrosion Protection System for Tank Equipment Adapted for Climatic Conditions of Middle Latitudes. Chemical Physics and Mesoscopy, 2023, vol. 25, no. 4, pp. 577-586. **Download

The work is devoted to the issues of the anticorrosion protection of oil equipment, namely the development and testing of the system of anticorrosion protection for oil gathering tanks and oil storage tanks in the climatic conditions of middle latitudes with the increase of the period of works on anticorrosion protection of the inner and outer surface of capacitive equipment in the conditions of subzero temperatures. The types of corrosion, main mechanism of corrosion formation and methods for corrosion control were analyzed. It is shown that complex influence of different mechanisms of the corrosion formation is characteristic of external capacitive equipment, and the most employed and effective methods are contact methods. An innovative system is offered for the treatment of the inner and outer surface of capacitive equipment in the conditions of subzero temperatures. The peculiarities of the standardization and norming for the systems of anticorrosion protection as well as the methods for testing the adhesion strength of coatings were considered. It is offered to use the anticorrosion protection system based on epoxy resins with inclusion of polyamine hardener for the equipment operating at subzero temperatures. The offered coating consists of epoxy resin (primer) with high dry residue and amine hardeners (polyethylene polyamine, hexamethylenediamine, metaphenylene-diamine and 2,4,6 triaminomethylphenol). Curing with amines (except trietanolamine, dicyandiamide, etc.) took place at normal temperature or at low heating (70-80 °C), i.e. in the conditions of cold curing. Durability tests were carried out for a number of anticorrosion coatings. It is demonstrated that widely spread systems of anticorrosion protection do not provide required durability that is not less than 2 years of service in the industrial atmosphere of macroclimatic zones of temperate and cold climate). Two types of coatings (the offered coating and widely-spread Jotum) were experimentally studied for durability using adhesion tests. The series of the adhesion tests confirmed the protective efficiency of the offered anticorrosion system and the possibility of increasing the life-time in the conditions of sub-zero temperatures.

** Keywords:** anti-corrosion treatment, tear-off method, chemical process, corrosion, application.

**DOI:** https://doi.org/10.15350/17270529.2023.4.52