#### Volume 89, №4

**DYNAMICS OF A "TWO-PHASE" BUBBLE IN COMPRESSION WAVES**

The behavior of a vapor envelope around a heated solid particle in a variable pressure fi eld has been studied. Problems of this kind arise in propagation of shock waves in three-phase systems ″liquid–hot solid particles surrounded by vapor envelopes.″ The behavior of the system in the vicinity of the forward shock wave front on a linear rise in pressure in the system has been studied analytically. A simple formula describing the change in the radius of the vapor layer in time has been obtained.

**Author:**
N. S. Khabeev

**Keywords:**
shock wave, heated particle, vapor envelope.

**Page:**
795

**INFLUENCE OF THE "SELF-RADIATION" OF COMBUSTION PRODUCTS ON THE INTENSITY OF EVAPORATION OF AN INHOMOGENEOUS WATER DROPLET IN THE FLAME**

The processes of heat transfer during the heating, evaporation, and boiling of an inhomogeneous (with a solid inclusion) droplet of a liquid (water) in a high-temperature (800–1500 K) gas medium have been modeled numerically. The inclusion (carbonaceous particle) in the shape of a disk of height and diameter 2 mm has been considered. The volume of the water enveloping the inclusion ranged within 5–20 μL. It has been shown that the ″self-radiation″ of triatomic gases in combustion products (using commercial alcohol as an example) signifi cantly intensifi es (compared to the air heated to the same temperatures) the heating of the inhomogeneous liquid droplet. A comparative analysis of the infl uence of the temperature of the gas medium and of the thickness in the liquid film enveloping the inclusion on the basic characteristic of the process under study, i.e., the time of existence (complete evaporation) of the droplet, has been made. The reliability of the results of theoretical investigations and the legitimacy of the conclusions drawn have been assessed experimentally

**Author:**
O. V. Vysokomornaya, G. V. Kuznetsov, M. V. Piskunov and P. A. Strizhak

**Page:**
799

**DEVELOPMENT OF FLOW AND HEAT TRANSFER DURING FILLING A PIPELINE WITH WATER AT THE PIPE WALL TEMPERATURE BELOW THE FREEZING POINT**

The paper presents the technique of computing flow and heat transfer of water in a pipeline whose initial temperature is lower than the freezing point of water. A feature of the method is the possibility of calculating the process from the moment of pouring water into a pipe on the inner surface of whose wall a layer of ice is being formed. The system of equations describing the process involves nonstationary energy equations for the water flow, ice layer, and for the

pipe wall. It is solved for each section of the pipeline passed by water in a small time interval in the process of fi lling the pipe and further fl ow. The Beginning computer program has been created and implemented in the Visual Basic language for numerical analysis of the process. The calculations made with the aid of this program allow one to estimate the possibility of appearance of an ice plug in the pipeline at the given temperature, water fl ow rate, pipeline

diameter, and conditions of external heat transfer of water fl ow in the pipeline.

**Author:**
É. L. Kitanin Yu. A. Smirnov and M. E. Lebedev

**Keywords:**
freezing of water, filling in a pipeline, computational technique, ice formation

**Page:**
808

**ENERGY EFFICIENCY OF AN INTEGRAL ANTI-ICE SYSTEM BASED ON FLUOROPLASTIC FILMS**

Results of theoretical and experimental investigations of the effi ciency of an integral electrothermal anti-ice system based on fl uoroplastic films are presented. It is shown that the use of this system makes it possible to decrease the energy expended for the de-icing by 30% as compared to the existing electrothermal anti-ice systems and that an integral electrothermal anti-ice system can be used in small and midget aircrafts including unmanned ones.

**Author:**
fl uoroplastic, electrothermal anti-ice system

**Keywords:**
fluoroplastic, electrothermal anti-ice system

**Page:**
815

**TECHNOLOGY OF GASIFICATION OF LIQUEFIED NATURAL GAS**

A fl ow diagram of gasifi cation of a cryogenic liquid, which is based on the utilization of the liquid′s internal energy to obtain a vapor phase, has been presented. The limiting steam fractions of the two-phase flow in a gasifier have been evaluated as applied to the problems of gasification of methane. Consideration has been given to the conditions of phase separation in the field of mass forces. A numerical scheme of solution of a system of gasdynamic equationsfor the two-phase fl ow in a cylindrical coordinate system in a three-dimensional formulation has been implemented. The results of numerical modeling of the conditions of precipitation of particles with a diameter of 2 to 10 μm from a swirling dispersed fl ow have been presented; the role of the particle size in the dynamics of the process of phase separation has been established.

**Author:**
V. G. Tonkonog, I. M. Bayanov, M. I. Tonkonog and B. R. Mubarakshin

**Keywords:**
cryogenic fuels, methane, gasifi cation technology, steam generator, vortex separator, modeling of characteristics, calculation

**Page:**
821

**MODELING THE PROCESS OF PARTICLE FRACTIONATION IN A PNEUMATIC CENTRIFUGAL APPARATUS**

The present investigation pertains to simulation of the aerodynamics of a two-phase nonisothermal twisted turbulent fl ow in the vortex chamber of an air-centrifugal classifi er. The gas phase dynamics was determined with the aid of Reynolds equations whose closure was based on the Wilcox turbulence model. The motion of the solid phase of an ultradisperse powder is simulated by a combination of calculations of the motion trajectories of particular particles in a Lagrangian coordinate system. The infl uence of turbulent diffusion of particles and of other factors on the effi ciency of the segregation of particle fractions by size is shown. The reliability of the results obtained is confi rmed by test studies and by comparing numerical results with well-known experimental data.

**Author:**
A. V. Shvab and N. S. Evseev

**Keywords:**
twisted turbulent fl ow, heat transfer, centrifugal apparatus, fractionation of particles, Wilcox turbulence model

**Page:**
829

**ESTIMATION OF THE DROP SIZE IN DISPERSED FLOW**

The formulas for calculating the characteristic drop size for the mean Sauter diameter have been compared. The question on various forms of the size distribution of drops has been considered. To substantiate the applicability of the compared formulas for calculating the thermohydrodynamics in the circuits of nuclear power plants, experimental data on the wall temperature in a dispersed fl ow have been used. It has been shown that the Sauter diameter values calculated using the wall temperature in the supercritical region are in good agreement with sparse direct measurements of the drop size in steam–water fl ows. The drop sizes calculated using the tested formulas obtained for two-component gas–liquid fl ows or for single-component fl ows of coolants (various kinds of freons) and liquefied nitrogen turned out to be much lower. It has been shown that it is necessary to recalculate the numerical coeffi cients in the considered formulas in using them for steam–water flows.

**Author:**
N. D. Agafonova and I. L. Paramonova

**Keywords:**
dispersed fl ow, drop size, mean diameter, distribution function

**Page:**
840

**MATHEMATICAL MODEL OF HYDRAULIC FRACTURING OF A BED**

A study has been made of the problem on the process of formation of a zone of higher-than-average permeability with a moving boundary in an initially low-permeability porous medium (problem on hydraulic fracturing of a bed) in a three-dimensional formulation. A characteristic feature of the three-dimensional problem was the taking into account the existence of two zones (zone with a regular permeability and the destruction zone) in the porous medium,

whose contact region was determined using the condition of mass balance on the moving boundary. Special features fundamental to the process of mass transfer in such fi ltration-inhomogeneous porous media have been revealed and analyzed.

**Author:**
G. S. Goncharova and M. G. Khramchenkov

**Keywords:**
permeability, bed, fi ltration inhomogeneity, hydraulic fracturing

**Page:**
848

**MODELING OF THE PROCESS OF FILLING A DOME SEPARATOR WITH THE DECOMPOSITION OF A GAS HYDRATE FORMED DURING THE MOUNTING OF THE INSTALLATION**

Consideration is given to the theoretical foundations of operation of a dome separator designed to collect and subsequently ship gas and oil emissions in the case of fracturing of the well near deep-water reservoirs where thermobaric conditions are favorable for the formation of a gas hydrate. A mathematical model has been constructed that describes the process of fi lling the indicated dome with hydrocarbons and pumping them out it under hydrateformation

conditions. The dynamics of change in the phase temperature in the dome has been described.

**Author:**
I. A. Chiglintsev and A. A. Nasyrov

**Keywords:**
dome separator, hydrocarbons, gas hydrate, gas and oil emissions, fracturing of the well

**Page:**
854

**TRANSFORMATION OF A WATER SLUG IN FREE FALL UNDER THE CONDITIONS OF EXPOSURE TO AN AIR FLOW ORTHOGONAL TO THE DIRECTION OF THE SLUG MOTION**

An experimental study has been made of the infl uence of an orthogonal (side) air fl ow propagating with a velocity to 5 m/s on the phases of transformation of a water slug with an initial volume of 0.05–0.5 liter in free fall from a height of 3 m. Use was made of Phantom V411 and Phantom Miro M310 high-speed video cameras and a Tema Automotive software system with the function of continuous tracking. The laws of retardation of the phases of transformation of the water slug from the instant of formation to that of formation of a droplet cloud under the action of the air flow orthogonal to the direction of the slug motion, and also of the deceleration, removal, and destruction of the droplets and fragments of water separating from the slug surface, have been established.

**Author:**
R. S. Volkov, M. V. Zabelin, G. V. Kuznetsov and P. A. Strizhak

**Keywords:**
water slug, free fall, side air flow

**Page:**
864

**PARAMETRIC LIMITS OF EFFICIENT USE OF A CENTRIFUGAL WATER ATOMIZER IN CONTACT WASTE-GAS HEAT-UTILIZATION UNITS**

The relation for the limiting temperature of water heating in a contact gas–droplet-type apparatus with a centrifugal atomizer has been determined experimentally in relation to the conditions of utilization of heat of power plant wastegases. Investigations were carried out in the range of excess water pressures in front of the atomizer 0.2–0.6 MPa and of the volume fraction of steam in the vapor–gas mixture at the inlet of the apparatus from 0.02 to 0.45. The possibility of using the obtained dependence for calculating the limiting values of the vapor–gas fl ow parameters that limit the range of effi cient operation of the contact apparatus with steam condensation and in the absence of

heated liquid droplet evaporation is shown.

**Author:**
M. K. Bezrodnyi, A. Yu. Rachinskii P. A. Barabash, and N. N. Goliyad

**Keywords:**
contact utilizer, centrifugal atomizer, limiting temperature of water heating, waste-gases, volume fraction of steam

**Page:**
870

**COMPREHENSIVE STUDY OF A SORPTION-BASED STORAGE VESSEL WITH THERMAL CONTROL FOR GASEOUS FUEL**

The authors have presented a calculation model for a gas storage vessel with a microporous adsorbent and a heat pipe with radial fi nning. The model was verifi ed by experimental data derived during the testing of a methane storage vessel in the regime of complete operating cycle. The authors have given the results of parametric investigation which confi rm the important role of the factor of cooling of the adsorbent layer during the charging

of the storage vessel.

**Author:**
L. L. Vasil′ev, L. E. Kanonchik and A. P. Tsitovich

**Keywords:**
storage vessel, methane, adsorbent, thermal control, model, heat and mass transfer, sorption, charging

**Page:**
878

**INVESTIGATION OF THE DRYING OF THIN MATERIALS WITH THE USE OF GENERALIZED COMPLEX VARIABLES**

Methods of processing of experimental data on the drying of thin materials with the use of generalized variables of the drying kinetics are considered. Empirical computational equations for the main parameters of the drying kinetics are presented.

**Author:**
A. I. Ol′shanskii

**Keywords:**
generalized time, rates of heating and removal of moisture, moist body, relative rate of drying, critical moisture content

**Page:**
886

**NONISOTHERMAL FLOW AROUND A CIRCULAR CYLINDER WITH A PERMEABLE LAYER AT MODERATE REYNOLDS NUMBERS**

Results of a numerical investigation of a separation nonisothermal fl ow of an incompressible viscous fl uid around a circular cylinder covered with a permeable porous layer at moderate Reynolds numbers are presented. This flow was defi ned with the use of Navier–Stokes and energy equations, and the fi ltration fl ow in the porous layer was determined by the Forchheimer law. The dependence of the hydrodynamical drag of the indicated cylinder and the

length of the vortex region in the fl ow around it on the Reynolds and Darcy numbers was determined. An analysis of the heat transfer from cylindrical bodies covered with permeable layers of a highly heat-conducting material or a heat-insulating material has been performed.

**Author:**
I. V. Morenko and B. A. Snigerev

**Keywords:**
permeable porous layer, circular cylinder, heat exchange, nonisothermal flow

**Page:**
896

**FLOW OF A NON-NEWTONIAN LIQUID WITH A FREE SURFACE**

A fountain fl ow of a non-Newtonian liquid fi lling a vertical plane channel was investigated. The problem of this flow was solved by the fi nite-difference method on the basis of a system of complete equations of motion with natural boundary conditions on the free surface of the liquid. The stability of calculations was provided by regularization of the rheological Ostwald–de Waele law. It is shown that the indicated fl ow is divided into a zone of two-dimensional fl ow in the neighborhood of the free surface and a zone of one-dimensional fl ow at a distance from this surface. A parametric investigation of the dependence of the kinetic characteristics of the fountain fl ow and the behavior of its free surface on the determining criteria of this fl ow and its rheological parameters has been performed.

**Author:**
E. I. Borzenko and G. R. Shrager

**Keywords:**
non-Newtonian liquid, free surface, fi lling of a channel, numerical simulation

**Page:**
902

**INFLUENCE OF THE VISCOUS DISSIPATION OF A LIQUID FILLING A TUBE ON THE DEFORMATION AND ORIENTATION OF LIQUID ELEMENTS**

The infl uence of the dissipation heating of a liquid fi lling a tube on the deformation, orientation, and distribution of liquid elements was investigated. Mathematical simulation of this process was performed on the basis of the equation of motion of the liquid and its continuity and energy equations with the initial and boundary conditions determined with account of the dependence of the viscosity of the liquid fl ow on its temperature, the presence of a free boundary in it, and the dissipation of its mechanical energy. The problem on the indicated liquid fl ow was solved numerically by the fi nite-difference method. The kinematics of this fl ow and its infl uence on the deformation and orientation of liquid elements was analyzed. The role of the viscous dissipation of the liquid in the formation of the thermomechanical history of the behavior of its elements in the process of fi lling of a tube with it is demonstrated.

**Author:**
E. I. Borzenko, O. Yu. Frolov, and G. R. Shrager

**Keywords:**
circular tube, fountain fl ow, dissipation heating, deformation, molding of polymers, morphology

**Page:**
911

**NONLINEAR DEVELOPMENT OF THE MARANGONI INSTABILITY IN LIQUID FILMS**

A nonlinear mathematical model of the state of the free surface of a nonisothermal liquid fi lm is presented. The basic wave characteristics and the liquid fi lm free surface state have been calculated for moderate Reynolds numbers in the presence of Marangoni instability. A nonlinear parabolic equation for the amplitude of the envelope of wave train and the results of computational experiment on the nonlinear development of Marangoni instability in liquid fi lms

are presented.

**Author:**
L. A. Prokudina

**Keywords:**
liquid fi lm, Marangoni instability, wave train, nonlinear parabolic equation

**Page:**
921

**FLOW AND HEAT TRANSFER ANALYSIS IN A DEFORMABLE CHANNEL**

An analytical solution of the Navier–Stokes equations in a semi-infi nite rectangular channel with porous and uniformly expanding or contracting walls is presented to improve the existing analytical results and to provide a comparison with the exact numerical solutions. The analytical solution is obtained with the use of the homotopy analysis method (HAM) which provides a uniformly valid solution for a wide range of parameters and has a better accuracy. In addition, the heat transfer analysis is presented for the case where the channel walls are kept at a constant temperature. The analytical solution is obtained with the use of three different techniques, and a numerical solution is obtained by the shooting method. A detailed analysis and comparison of the results of all these methods is presented. Heat transfer analysis in a deformable channel has been carried out for the fi rst time.

**Author:**
S. Asghar, Z. Abbas, M. Mushtaq and T. Hayat

**Keywords:**
deformable channel, heat transfer, homotopy analysis method, asymptotic expansion method

**Page:**
929

**COMPUTATIONAL INVESTIGATION OF THE INFLUENCE OF GRAVITATIONAL CONVECTION ON THE GASEOUS MIXTURE PARAMETERS OF THE BARRIER DISCHARGE XECL EXCILAMP**

Calculations have been performed of the influence of gravitational convection on the thermodynamic parameters of the gaseous mixture of the barrier discharge (BD) XeCl excilamp. It has been shown that the presence of convection leads to a three-to-fi vefold decrease in the average temperature of the gaseous mixture in the discharge region. Analysis of the experiments carried out for the BD XeCl excilamp has been performed, and the temperature and convection rate distributions of the gaseous mixture have been determined. It has been shown that the decrease in the
ultraviolet radiation power of the excilamp in the absence of convection is due to the increase in the gaseous mixture temperature to above 400 K, which corresponds to a total discharge power of ~45 W and a heat power of ~2 W.

**Author:**
A. A. Pikulev, S. L. Turutin and É. A. Sosnin

**Keywords:**
XeCl excilamp, gravitational convection, Navier–Stokes equations

**Page:**
942

**OPTIMAL IMPELLER CLEARANCE FOR A DUAL STIRRED UNBAFFLED TANK WITH A CONCAVE BLADE IMPELLER**

An experimental investigation of unbaffl ed stirred tanks is carried out with the use of a dual concave blade impeller to evaluate the mass transfer coeffi cient, power number, and vortex depth. The effect of the impeller clearance on mass transfer is analyzed to estimate the optimal impeller clearance for lower and upper impellers. It is found that the lower impeller positioned at 0.25 of the tank diameter with the clearance between the lower and upper impellers equal to 0.38 of the tank diameter gives the maximum mass transfer coeffi cient. A comparison with the results for dual Rushton and Rushton-concave impellers at the optimal clearance shows that the concave-concave impellers are most effi cient. The scale-up criteria for optimal, geometrically similar systems of unbaffl ed stirred tanks with a dual concave impeller are proposed.

**Author:**
T. T. Devi and B. Kumar

**Keywords:**
concave blade, clearance, mass transfer, power number, Rushton impeller, unbaffl ed tank, vortex

**Page:**
950

**COMPARISON BETWEEN THE KUTATELADZE–KHABAKHPASHEVA AND OSTWALD–DE WAELE RHEOLOGICAL MODELS IN DESCRIBING GENERALIZED NEWTONIAN LIQUIDS WITH THE USE OF EXPERIMENTAL MEASUREMENTS**

The results of viscosimetric measurements of generalized Newtonian liquids (glycerin, 3% solution of Na–CMC, 70% water solution of starch, TNK Magnum SAE 5W40 motor oil) in the temperature range from 274 to 323 K and shear rates of up to 320 1/s are presented. The method of determining the rheological constants of the Kutateladze–Khabakhpasheva model and of the Ostwald–de Waele model of liquid viscosity power law for generalized Newtonian liquids is presented. The rheological constants of both models are obtained for the indicated liquids.

**Author:**
B. R. Abaidullin, E. K. Vachagina, and A. I. Kadyirov

**Keywords:**
generalized Newtonian liquid, rheological constants, liquid viscosity power law, viscosimetric measurements

**Page:**
957

**STOCHASTIC MODEL OF HEAT CONDUCTION WITH STOCHASTIC BOUNDARY CONDITIONS**

One-dimensional stochastic models of heat conduction with different types of boundary conditions have been developed. Boundary-value problems for mean temperature and temperature field dispersion in the region of heat conduction have been formulated. A generalization of the indicated one-dimensional boundary-value problems to the case of a large number of measurements in invariant form is given.

**Author:**
V. V. Shevelev

**Keywords:**
heat conduction, stochasticity, boundary conditions

**Page:**
965

**ANALYTICAL INVESTIGATION OF HEAT TRANSFER IN AN ANISOTROPIC BAND WITH HEAT FLUXES ASSIGNED AT THE BOUNDARIES**

An analytical solution of a nonstationary problem of the theory of heat conduction in an anisotropic band under heat transfer conditions at the boundaries has been obtained for the fi rst time by applying the Fourier transformation with respect to the longitudinal variable and the Laplace transformation for time. The problem is formulated and solved in regions with anisotropy of general form when the principal axes of the heat conduction tensor are set at an angle

that orients these axes relative to the Cartesian coordinate system.

**Author:**
V. F. Formalev and S. A. Kolesnik

**Keywords:**
heat conduction, anisotropy, thermal conductivity tensor, direct and inverse integral transformations, analytical solution, heat transfer, nonstationary temperature fields

**Page:**
975

**BOUNDARY CHARACTERISTICS FOR THE GENERALIZED HEAT-CONDUCTION EQUATION AND THEIR EQUIVALENT REPRESENTATIONS**

On the basis of the consideration of the boundary-value problem for the generalized equation of heat conduction in bounded nonuniform spaces with Dirichlet, Neumann, and Robin boundary conditions, corresponding sequences of boundary characteristics have been obtained. For each of these sequences, defi nite integro-differential representations (relations) have been constructed. It has been shown that approximate analytical solutions can

be obtained for bounded nonuniform regions with variable transfer coeffi cients in the Cartesian, cylindrical, and spherical coordinate systems. On the basis of systems of algebraic equations, approximate analytical solutions have been constructed with approximately equal accuracies independently of the calculation scheme used (with the introduction of the temperature-disturbance front or without it, i.e., by multiple integration of the heat-conduction

equation over the whole computational region). These solutions have a negligibly small error and, therefore, can be considered as conditionally exact.

**Author:**
V. A. Kot

**Keywords:**
heat-conduction equation, multiple integration, temperature-disturbance front, boundary characteristics, approximate integral method

**Page:**
985

**METHOD OF MINIMAX OPTIMIZATION IN THE COEFFICIENT INVERSE HEAT-CONDUCTION PROBLEM**

Consideration has been given to the inverse problem on identifi cation of a temperature-dependent thermal-conductivity coeffi cient. The problem was formulated in an extremum statement as a problem of search for a quantity considered as the optimum control of an object with distributed parameters, which is described by a nonlinear homogeneous spatially one-dimensional Fourier partial equation with boundary conditions of the second kind. As the optimality criterion, the authors used the error (minimized on the time interval of observation) of uniform approximation of the temperature computed on the object′s model at an assigned point of the segment of variation in the spatial variable to its directly measured value. Pre-parametrization of the sought control action, which a priori records its description accurate to assigning parameters of representation in the class of polynomial temperature functions, ensured the reduction of the problem under study to a problem of parametric optimization. To solve the formulated problem, the authors used an analytical minimax-optimization method taking account of the alternance properties of the sought optimum solutions based on which the algorithm of computation of the optimum values of the sought parameters is reduced to a system (closed for these unknowns) of equations fixing minimax deviations of the calculated values of temperature from those observed on the time interval of identifi cation. The obtained results confi rm the effi ciency of the proposed method for solution of a certain range of applied problems. The authors have studied the infl uence of the coordinate of a point of temperature measurement on the exactness of solution of the inverse problem.

**Author:**
A. N. Diligenskaya and É. Ya. Rapoport

**Keywords:**
coefficient inverse heat-conduction problem, parametric optimization, minimax-optimization method

**Page:**
1008

**REFINEMENT OF THE UPPER AND LOWER BOUNDS OF EFFECTIVE HEAT CONDUCTIVITY COEFFICIENTS OF RIB-REINFORCED COMPOSITE MEDIA**

We propose two refi ned structural models of the thermal behavior of a rib-reinforced composite medium at general anisotropy of the materials of compound components. For the criterion of equivalence of the rib-reinforced composite to the fi ctitious homogeneous anisotropic material, equality of the specifi c heat dissipation in them was used, which permits determining the upper and lower bounds of the effective heat conductivity coeffi cients of the composite material. The design values of the effective heat conductivity coeffi cients of a honeycomb structure with cavities fi lled and not fi lled with foam plastic have been determined. It has been shown that the refi nement of certain thermal characteristics of 12%, and the refi ned "fork" of values of these quantities, does not exceed 2.5%. Indirect comparison has been made between the calculated and experimental values of the effective heat conductivity coeffi cients of such compounds, which has shown that the results obtained in the work are qualitatively reliable

**Author:**
A. P. Yankovskii

**Keywords:**
heat conductivity, composites, rib reinforcement, structural theories, general anisotropy, dissipative equivalence, effective characteristics, light fi ller, ribbed structures

**Page:**
1014

**DETONATION-SYNTHESIS NANODIAMONDS IN COMPOSITIONS OF ULTRAHIGH-MOLECULAR-WEIGHT POLYETHYLENE**

A study has been made of the infl uence of an ultradisperse carbonaceous product, i.e., detonation-synthesis nanodiamonds, on the structure and properties of nanocomposites based on ultrahigh-molecular-weight polyethylene using electron microscopy and acoustic, electrophysical, thermomechanical, and x-ray phase analysis methods It has been shown that a diamond blend is a structurally active fi ller of ultrahigh-molecular-weight polyethylene, which changes the crystalline and supermolecular structure of the polymer during its melt crystallization under the conditions of uniaxial plastic deformation. The developed polymer nanocomposites based on ultrahigh-molecular-weight polyethylene, which contain 0.5–0.25 wt.% of the diamond blend, possess higher than average indices of hardness, modulus of elasticity, and electrical conductivity manifested to a larger extent in the frequency range 1–10 kHz, a low friction factor (0.15–0.18), and high resistance to wear under dry-friction conditions (the wear rate is 10^{–4}–10^{–5} mg/m).

**Author:**
V. I. Dubkova,a A. P. Korzhenevskii, N. P. Krut′ko, V. G. Komarevich, and L. V. Kul′bistkaya

**Keywords:**
polymer, ultrahigh-molecular-weight polyethylene, nanodiamonds, nanocomposites, diamond blend, x-ray degree of crystallinity, resistance to wear, morphology

**Page:**
1024

**FULLERITES AND "GROWTH STRUCTURES" OF NANOOBJECTS**

Structures of fullerites formed from fullerene-containing soots have been examined by electron-microscopy methods. The principle of identifi cation of fullerene-containing materials has been proposed. The authors assume that one of the found morphostructures can be the initial step of formation of nanoindividuals of varying composition.

**Author:**
T. A. Shabanova, N. G. Prikhod′ko, M. Auelkhankyzy, and Z. A. Mansurov

**Keywords:**
fullerene, fullerite, morphostructure, calculation of electron diffraction patterns

**Page:**
1034

**EQUATION OF DIFFUSION OF A COMPOSITE MIXTURE INTO A COMPOSITE MEDIUM**

The equation of diffusion of a composite mixture into a composite medium has been obtained for the fi rst time. The assumption used is that the macropoint of the medium, i.e., an elementary macrovolume, in which the statistical parameters of distribution of inhomogeneities coincide with the corresponding values assigned for the medium as a whole, is small compared to the geometric dimensions of the volume considered. The ″Reuss–Voigt fork″ has been obtained for determining the limits of the change in the diffusion coeffi cient. Thereafter the fork is narrowed to the ″Kravchuk–Tarasyuk fork.″ Effective diffusion coeffi cients are obtained as an arithmetic mean value of the Kravchuk–Tarasyuk fork. The found averaged physical parameters can be used in solving specifi c physical problems

for inhomogeneous media.

**Author:**
A. S. Kravchuk, A. I. Kravchuk, and T. S. Popova

**Keywords:**
lamellar, structurally inhomogeneous composite material, macropoint of composite material, discrete random quantity, averaging, effective characteristics of a medium, Voigt hypothesis, Reuss hypothesis, Hill′s approximation, Kravchuk–Tarasyuk fork

**Page:**
1041

**HOW THE TERM "SHOCK WAVES" CAME INTO BEING**

The present paper considers the history of works on shock waves beginning from S. D. Poisson′s publication in 1808. It expounds on the establishment of the Polytechnic School in Paris and its fellows and teachers — Gaspard Monge, Lazare Carnot, Joseph Louis Gay-Lussac, Simeon Denis Poisson, Henri Navier, Augustin Louis Cauchy, Joseph Liouville, Ademar de Saint-Venant, Henri Regnault, Pierre Dulong, Emile Jouguet, Pierre Duhem, and others. It also describes the participation in the development of the shock wave theory of young scientists from the universities of Cambridge, among which were George Airy, James Challis, Samuel Earnshaw, George Stokes, Lord Rayleigh, Lord Kelvin, and James Maxwell, as well as of scientists from the Göttingen University, Germany — Bernhard Riemann and Ernst Heinrich Weber. The pioneer works on shock waves of the Scottish engineer William Renkin, the French artillerist Pierre-Henri Hugoniot, German scientists August Toepler and Ernst Mach, and a Hungarian scientist Gyözö Zemplén are also considered.

**Author:**
N. A. Fomin

**Keywords:**
shock wave, explosion, combustion, shock adiabat, sound waves, supersonic flows

**Page:**
1047