Homogeneous Medium Research Articles

ЭКСПЕРИМЕНТАЛЬНЫЕ ИССЛЕДОВАНИЯ ПРОЦЕССА ПЕРЕМЕШИВАНИЯ ЖИДКОГО НАВОЗА МИКСЕРОМ С КОНИЧЕСКИМ КОЖУХОМ

Mixing in various industries is widely used to obtain homogeneous media in composition, as well as to intensify the processes of mass and heat transfer. So, in livestock, various types of equipment are used to mix liquid manure stored in a manure storage facility. The mixing method and equipment used for its implementation’s choice is due to the aggregate state of the manure mass stored in the manure storage. Most of the currently existing the liquid manure mixing equipment works mainly in stationary regime, at working bodies’ constant angular velocity. At this manure mass volume method of influencing on the manure storage, there are zones in which the mixed media’s flow rate is low, and manure particles do not participate in their movement, and therefore mixing quality is deteriorated. The a mixer with an agitator’s experimental studies results that are encircled by a conical casing, are presented. A mixer is used on farms to mix liquid manure in order to a homogeneous consistency obtaining. This specified unit’s working body is a stirrer, that in depending on its design, can have from two till four blades. However, this stirrer elements’ design already have an upper, its operational capabilities’ limit is well known. In order forming homogeneous manure mass’s unit cost reducing, the flow transported power for stirrer blades possibility increasing was studied. For this task’s performing, a conical casing along the blades’ outer radius was installed. Based on this experimental studies to solve energy saving and stored manure mixing intensification’s problems, the conical mixer’s casing optimal parameters have been determined. The experimental studies’ results of manure mixer with a conical casing’s technical parameters are presented. The dependences of liquid manure mixing process energy intensity on casing nozzle diameter, mixer relative inclination outlet’s angle to the horizontal plane and the number of stirrer’s revolutions are determined.

Modeling and semi-analytical solution for immiscible and miscible fingers formation during enhanced oil recovery

ABSTRACT The fingering phenomenon arises during the secondary and tertiary oil recovery processes when injected fluid (water, gases, nano/biomaterials, or polymer particles) shoots through a porous medium at a relative speed. Oil recovery is influenced by various factors including the fluid type, capillary pressure, permeability, and porous material structure. All these elements play crucial roles in determining the success and efficiency of the oil recovery process. Many scientists have debated the fingering phenomenon from different perspectives. Here, we developed mathematical models with and without considering mass flow rates of oil and water for an inclined oil layer flowing through a homogenous porous medium to generate immiscible fingers. Furthermore, a mathematical model of miscible viscous finger formation with carbonated water injection (flooding) during the enhanced oil recovery process (EOR) has been analyzed in this paper. To solve each of these mathematical models, we used the recently developed approach known as the Method of Directly Defining the inverse Mapping (MDDiM). We found approximate solutions to the nonlinear partial differential equations (PDEs), which describe each modeling of the fingering phenomenon in a homogeneous porous medium by incorporating gravitational effects for several types of flooding and discussed the effects of the saturation rate.

Simplified TTI pure qP-wave equation implemented in the space domain and applied for reverse time migration in TTI media

The assumption that the earth’s subsurface is a homogeneous and isotropic medium enables the imaging of important geologic structures but results in information loss, especially in more complex geologic media. Therefore, considering anisotropy is crucial for seismic imaging, particularly the most common anisotropy in geophysics: the transversely isotropic medium. However, this also means a considerable increase in the computational cost of reverse time migration (RTM). Thus, a new pseudoacoustic wave equation for pure qP-wave in tilted transversely isotropic (TTI) media, which can also be efficiently implemented using the finite-difference (FD) method with the unit vector method (UVM), is proposed, aiming to reduce the computational cost of the RTM. The proposed equation solved with fast Fourier transforms is exact and faster for seismic migration than the base equations found in the literature; however, a greater efficiency is achievable by using FD to compute the second derivatives. In contrast, when solved with the UVM, it is kinematically accurate and significantly faster, although dynamically inaccurate as it is an acoustic approximation. The efficiency and efficacy of this new equation are demonstrated by modeling and migrating synthetic TTI data found in the literature.

Linear filtration waves in a layered heterogeneous formation

Solutions to the problem of a filtration-wave pressure field in a layered inhomogeneous medium with a pressure pulse specified on the left boundary are obtained. The problem statement contains a two-dimensional wave equation in the central layer, a wave equation that takes into account the predominance of vertical motion in the environment, symmetry conditions in the center of the formation, equality of pressures and flows at the interfaces, the absence of disturbances of the filtration wave field at the initial moment of time and at an infinite distance from the source of disturbance. The article found an exact solution to the problem obtained using the Laplace–Carson and the Fourier transform of sine, an asymptotic solution and an exact solution for the special case of a homogeneous medium. It is shown that when the formal parameter tends to zero, the exact solution coincides with the main asymptotic approximation. The tendency of the thickness of the central layer to infinity reduces the solution for a layered inhomogeneous medium to an expression describing the pressure fields in a homogeneous medium. Spatiotemporal dependencies describing the dynamics of the pressure pulse in layered inhomogeneous and homogeneous media were constructed, and the general properties and features of linear filtration waves in layered inhomogeneous and homogeneous layers were studied.

Investigation of the temperature field in gas condensate reservoirs taking into account thermodynamic effects

Based on modeling of non-isothermal filtration of a multiphase fluid, taking into account thermohydrodynamic effects and heat of condensation, the formation of a temperature field in a homogeneous porous medium at different pressures at the onset of condensation is studied. A numerical model of one-dimensional two-phase filtration taking into account the phase transition is obtained. Testing of the numerical solution was carried out on the basis of a well-known analytical solution for non-isothermal two-phase filtration in a reservoir taking into account mass transfer. The change in gas flow rate during condensate precipitation and the change in temperature over time on the well wall are considered. It is shown that, depending on the pressure of the onset of condensation (the radius of the onset of condensation in the formation), a different rate of formation of the temperature field in the formation is observed after the well is put into operation: the temperature anomaly can be positive, negative or inverse. The results of numerical experiments can be used when planning field studies in gas condensate wells.

Physics-Informed Neural Networks with Periodic Activation Functions for Solute Transport in Heterogeneous Porous Media

Simulating solute transport in heterogeneous porous media poses computational challenges due to the high-resolution meshing required for traditional solvers. To overcome these challenges, this study explores a mesh-free method based on deep learning to accelerate solute transport simulation. We employ Physics-informed Neural Networks (PiNN) with a periodic activation function to solve solute transport problems in both homogeneous and heterogeneous porous media governed by the advection-dispersion equation. Unlike traditional neural networks that rely on large training datasets, PiNNs use strong-form mathematical models to constrain the network in the training phase and simultaneously solve for multiple dependent or independent field variables, such as pressure and solute concentration fields. To demonstrate the effectiveness of using PiNNs with a periodic activation function to resolve solute transport in porous media, we construct PiNNs using two activation functions, sin and tanh, for seven case studies, including 1D and 2D scenarios. The accuracy of the PiNNs’ predictions is then evaluated using absolute point error and mean square error metrics and compared to the ground truth solutions obtained analytically or numerically. Our results demonstrate that the PiNN with sin activation function, compared to tanh activation function, is up to two orders of magnitude more accurate and up to two times faster to train, especially in heterogeneous porous media. Moreover, PiNN’s simultaneous predictions of pressure and concentration fields can reduce computational expenses in terms of inference time by three orders of magnitude compared to FEM simulations for two-dimensional cases.

Computer homogenization of porous piezoceramics of different ferrohardness with random porous structure and inhomogeneous polarization field

The article is concerned with the homogenization problems, in which the effective moduli of porous piezoceramic composites are determined taking into account the inhomogeneity of the polarization field. The homogenization problems are solved by the finite element method in the framework of the theory of effective moduli and the Hill energy principle using the ANSYS package. To this end, in static problems of electroelasticity, the displacements and electric potential, which are linear in spatial variables, are specified on the boundary of a representative volume to provide constant stress and electric induction fields for a homogeneous reference medium. After solving a set of boundary value problems under different boundary conditions and determining the volume-averaged stress components and the electric induction vector, a complete set of effective moduli for the piezoelectric composite is calculated. A representative volume of the piezocomposite is created in the form of a regular finite element mesh consisting of cubic elements. Pores in the representative volume are assumed to be filled with a piezoelectric material with extremely small moduli. Finite elements with pore properties are selected according to a simple random algorithm. The inhomogeneous polarization field is found by solving an electrostatic problem, in which the polarization process in the representative volume is modeled based on a simplified linear formulation. The local coordinate systems for individual finite elements of the composite matrix are specified by the directions of the polarization vectors. In the following, when solving the problems of electroelasticity, these local coordinate systems associated with the elements of the piezoelectric matrix allow recalculating the material properties according to the formulas of transformation of the tensor components as the coordinate systems rotate. In addition, consideration is given to different models describing the change in the moduli of the material from an unpolarized state to a polarized one as a function of the polarization vector. Computational experiments were carried out for three types of piezoceramics: soft ferroelectric piezoceramics PZT-5H, piezoceramics PZT-4 of medium ferrohardness, and piezoceramics PZT-8 with higher degree of ferrohardness. The dependences of the effective moduli on porosity are compared for different laws of polarization inhomogeneity and different kinds of piezoceramic material of the composite matrix.

Microscale Simulation of Carbon Support Structure Degradation in Polymer Electrolyte Fuel Cell

Understanding the mechanism of Polymer electrolyte fuel cell (PEFC) degradation plays an important role in improving fuel cell performance and durability. For the PEFC system, the structure of catalyst layers (CLs) is the critical component that determines cell performance. The PEFC degradation due to the reduction of carbon on the CLs has been investigated in previous studies [1]. In our past studies, we focused on the actual heterogeneous porous structure of catalyst layer. From these results, it was found that mass transport performance of oxygen and proton in heterogeneous porous catalyst layer, which consists of carbon support, ionomer and void space, is much lower than that of theoretical prediction in homogeneous porous media [2-5]. In addition, it depends on the structure of carbon black, the coating structure of ionomer and the local distribution of these materials. Thus, it is important to understand and to predict the carbon support structure change by degradation because this structural degradation strongly affect the mass transport performance. In this work, the effect of CLs porous carbon support degradation on cell performance is investigated by microscale simulation.The CLs structures, consisting of porous carbon, ionomer, and Pt, are created by our previous study multi-block method [2,6]. In our simulation, we focus on studying the effect of CLs' beginning-of-life (BOL) and end-of-life (EOL) structure in the degradation process. The CLs creation procedure is illustrated in Fig. 1. Firstly, CLs structure are created by packing CB and covered ionomer and Pt. The amount of ionomer and Pt are assumed as constant during the degradation process. Therefore, the amount of carbon is reduced in EOL structure. In this study, various CLs structures with decreasing of carbon volume are constructed. Furthermore, the mechanical stress distribution under compression condition was simulated in each structure to understand the effect of framework of carbon on local porosity in catalyst layer. The effect of carbon corrosion in CLs is investigated by calculating the cell performance of PEFC of each CLs structure by ORR mass transport and electrochemical reaction calculation with our previous method [6].The cell performance is significantly decreased by reducing carbon. The degradation mechanism of PFEC is explained by degradation of not only effective surface area but also the porous structure change which affect oxygen diffusion performance. Moreover, compared with BOL structure the apparant thickness of covered ionomer layer is higher in EOL structures because of carbon corrosion and constancy of ionomer. Hence, the higher oxygen diffusion resistance in secondary pore and ionomer layer occur in CLs degradation structures. The effect of this dynamic structure change on cell output performance will be reported in this presentation.Acknowledgements:This research was supported by the New Energy and Industrial Technology Development Organization (NEDO), Japan, grant number P20003-20001327-0.

A theoretical modelling of strengthening mechanism in graphene-metal nanolayered composites

Graphene-metal nanolayered composites (GMNCs) are a new generation of nano-structural composites characterized by a very high density of graphene reinforced interfaces (GRI) between metal nanolayers. Compared to traditional graphene flake reinforced composites, GMNCs have much higher strength, toughness and ductility due to the excellent ability of GRI on constraining dislocation motion and crack propagation. Despite numerous experimental and numerical studies on the mechanical behavior of GMNCs, the underlying strengthening mechanism is still not fully understood due to the absence of appropriate theoretical model. This paper proposes a continuum mechanics based theoretical model to explain the strengthening mechanism in GMNCs. In this model, the metal matrix and the GRI are simulated as homogenous elastic medium of infinite extend and inextensible thin membrane of zero thickness, respectively. Using the theoretical model, two boundary value problems namely (i) A circular prismatic dislocation loop approaching to the GRI and (ii) A mixed mode I/II penny-shaped crack near the GRI are formulated to reveal the two key strengthening mechanism: dislocation blocking and crack shielding, respectively. The two problems are solved analytically by the Generalized Kelvin's Solution (GKS) based method for 3D elasticity and Fredholm integral integration technique. Exact closed form solution for the Peach-Koehler (P-K) force on the dislocation loop is obtained. An efficient numerical scheme is developed to solve the Fredholm integral integration for the crack problem with very high accuracy. It is shown that our theoretical model can well capture and explain the strengthening mechanism observed in experiments. Moreover, the dominant role of Poisson's ratio on the strengthening efficiency is also revealed by our model. This finding implies the exciting possibility that the strength of GMNCs can be tailored by controlling the Poisson's ratio of the metal matrix. The present theoretical modeling can provide valuable insights into the mechanics-based design of GMNCs.

Controlling the counterintuitive optical repulsive thrust of nano dimers with counter propagating type waves and background medium.

This work focuses on the utilization of counter-propagating plane waves for optical manipulation, which provides a unique approach to control the behavior of Rayleigh and Dipolar nanoparticles immersed in a homogeneous or heterogeneous medium. Our study presents an interesting finding of a repulsive force between plasmonic-chiral heterodimers where the particles move away from each other in both near and far field regions. Interestingly, this repulsive thrust supports the wave like nature of light for the case of homogeneous background but particle type nature of light for heterogenous background. At first, we have investigated the theory underlying the optical trapping of the chiral particle and the impact of this phenomenon on the overall repulsive behavior of the heterodimers placed in air (homogeneous) background. After that, our proposed set-up has further been investigated putting in air-water interface (heterogenous background) and by varying light angle only a little bit. Our observation for this interface case is suggesting the transfer of Minkowski momentum of photon to each optically pulled Rayleigh or dipolar particle of the dimer set, which ultimately causes a broad-band giant repulsive thrust of the dimers. However, in absence of the other particle in the cluster, a single half-immersed particle does not experience the pulling force for the broad-band spectrum. The 'common' reason of the observed repulsive thrust of the dimers for both the aforementioned cases has been attributed to "modified" longitudinal Optical Binding Force (OBF). Technically, this work may open a new way to control the repulsion and attraction between the nanoparticles both in near and far field regions by utilizing the background and the counter-propagating waves. We also believe that this work manifests a possible simple set-up, which will support to observe a background dependent wave 'or' particle nature of light experimentally.

SIMULATION OF THE PROPAGATION OF A PLANE ELECTROMAGNETIC WAVE IN AN INHOMOGENEOUS NONABSORBING MEDIUM

Analytical solutions of the Ishimaru's parabolic equation for the coherence function of the electromagnetic field, which describe the temporal properties of the pulse at the output of a heterogeneous non-dissipative medium, are considered. A generalization of the approach used in the Ishimaru model to describe the time evolution of a monochromatic electromagnetic pulse enveloping in homogeneous non-dissipative media is obtained for the case of non-homogeneous non-dissipative media. Thus, an attempt was made to take into account the influence of the heterogeneity of the medium on the shape of the resulting pulse. When solving the given problem, the difficulties associated with the calculation of the continuous integral arising in the space of diffusion trajectories were overcome. This made it possible to obtain an explicit expression for the Green's function of the task and to build a computational algorithm based on which a number of numerous experiments were conducted. The analysis of the work was carried out based on the apparatus of quadratic integral functionals based on the solutions of differential stochastic equations. In the paper, the invariant temporal properties of the envelope of monochromatic electromagnetic pulses recorded after passing through a flat layer of a scattering heterogeneous medium, i.e., properties that remain unchanged when the parameters of the medium vary, in particular, the distribution of the concentration of scattering centers. The dynamics of the formation of time plumes of the scattered wave, in which the tail part is located in the peripheral time area, were analyzed. When propagating at the speed of transformation of the wave front, it reflects the appearance of the layers of the scattering region and its longitudinal shape. It is noted that the development of the proposed approximation approach to the processes affecting the time delay of electromagnetic pulses can be the accounting for the attenuation of radiation during its propagation in an inhomogeneous absorbing medium.

Calibration of absorbing boundary layers for geoacoustic wave modeling in pseudo-spectral time-domain methods

Abstract. This paper develops a calibration methodology of the artificial absorbing techniques typically used by Fourier pseudo-spectral time-domain (PSTD) methods for geoacoustic wave simulations. Specifically, we consider the damped wave equation (DWE) that results from adding a dissipation term to the original wave equation, the sponge boundary layer (SBL) that applies an exponentially decaying factor directly to the wavefields, and finally, a classical split formulation of the perfectly matched layer (PML). These three techniques belong to the same family of absorbing boundary layers (ABLs), where outgoing waves and edge reflections are progressively damped across a grid zone of NABL consecutive layers. The ABLs used are compatible with a pure Fourier formulation of PSTD. We first characterize the three ABLs with respect to multiple sets of NABL and their respective absorption parameters for homogeneous media. Next, we validate our findings in heterogeneous media of increasing complexity, starting with a layered medium and finishing with the SEG/EAGE 3D salt model. Finally, we algorithmically compare the three PSTD–ABL methods in terms of memory demands and computational cost. An interesting result is that PML, despite outperforming the absorption of the other two ABLs for a given NABL value, requires approximately double the computational time. The parameter configurations reported in this paper can be readily used for PSTD simulations in other test cases, and the ABL calibration methodology can be applied to other wave propagation schemes.

ANALYTICAL AND NUMERICAL SOLUTIONS OF THE PARABOLIC EQUATION ISHIMARU FOR THE ELECTROMAGNETIC FIELD, DESCRIBING THE TEMPORARY PROPERTIES OF THE OUTPUT VIDEO-PULSE HETEROGENEOUS NON-DISSIPATIVE MEDIUM

The parabolic Ishimaru equation for the electromagnetic field coherence function, which describes the temporal properties of pulse at the output of inhomogeneous non-dissipative medium, is considered. The generalization of the approach used in the Ishimaru model to describe the temporal evolution of the envelope of the monochromatic electromagnetic video-pulse in homogeneous non-dissipative media is generalized to the case of non-homogeneous nondissipative media. An attempt was made to take into account the influence of the inhomogeneity of the medium on the shape of the resulting pulse. An explicit expression for the Green's function of the problem is obtained and number of numerical experiments are carried out. The paper studies the invariant longitudinal (temporal) properties of the envelope of monochromatic electromagnetic pulses recorded after passing through flat layer of the scattering inhomogeneous medium, i.e. properties that remain unchanged when the environment parameters vary. Examples of numerical experiments are given.

Pore-scale natural convection in cavities filled with randomly distributed heat-conducting particles

Three-dimensional numerical simulations were carried out to analyze natural convection in a differentially heated cubic cavity filled with spherical particles. Three models were considered: a fluid-only case for reference, a homogeneous porous media approximation, and a heterogeneous model that considered the actual structure of the solid particles. DEM (discrete element method) simulations were used to generate a realistic particle distribution for the construction of volumetric meshes for the heterogeneous model. The impact of thermal conduction through the solid particles was evaluated by varying the solid to fluid ratio ( K * ) within the range 0.02 − 50 for Rayleigh numbers between 103 and 105. Additionally, different number and diameter of the particles inside the cavity were evaluated. The results of the homogeneous approximation indicate a continuous decrease in the Nusselt number (Nu) as K * increases, associated with a higher effective thermal conductivity and the pressure drop. However, the more realistic heterogeneous model predicted the opposite trend. For K * <1, solid particles acted as thermal insulators, impeding fluid flow, while for K * > 1 conduction heat transfer between the isothermal walls and the particles was highly efficient and the particles surface area acted like extensions of the isothermal walls, facilitating heat transfer to the fluid phase, especially at lower Rayleigh values.

Phase variation of Laguerre-Gaussian vortex beams in a homogeneous atmospheric medium under finite amplitude acoustic wave perturbation

In this article, we have derived the acoustic pressure and medium refractive index expressions in a homogeneous atmospheric medium perturbed by a planar finite amplitude acoustic wave. In a planar finite amplitude acoustic wave perturbation, we developed a Laguerre–Gaussian vortex beam transmission model in a homogeneous atmospheric medium. We investigated the effects of different acoustic source parameters on the phase of the Laguerre–Gaussian vortex beam transmission, considering the atmospheric medium’s viscous effect. The results show that acoustic waves of finite amplitude distort the refractive index distribution of a homogeneous atmospheric medium. At a given distance, the amplitude of the refractive index gradually increases with increasing acoustic wave transmission distance. At the same time, the phase of the Laguerre–Gaussian vortex beam is rotated by the perturbation of the finite-amplitude acoustic wave, and the phase always returns to its initial position. Unlike linear acoustic waves, changes in the homogeneous atmospheric refractive index distribution and the homogeneous phase of the Laguerre–Gaussian vortex light no longer satisfy the periodic variation when perturbed by finite-amplitude acoustic waves. Under the same conditions, the effect of finite-amplitude acoustic waves on the phase of the Laguerre–Gaussian vortex light is stronger than that of linear acoustic waves. Finally, the effects of different acoustic pressure and frequency of the source on the phase of the Laguerre–Gaussian vortex beam transmission are calculated. The results show that different acoustic parameters at the source can be used to achieve phase modulation at different distances and intensities.

Оценка эффективности метода гиперплоскостей в задаче частичной идентификации неизвестного вещества

The problem of partial identification of a homogeneous medium of unknown chemical composition is investigated. The medium is subjected to repeated transillumination by X-ray fluxes collimated in energy and direction. According to the results of measuring the flux density of radiation entering and leaving the medium, it is necessary to establish the difference in the chemical composition of the medium from some in advance given substances. It is assumed that the measurements of radiation fluxes contain errors for which their maximum relative values are known. As a mathematical basis for the study the method of hyperplanes proposed earlier by the author is taken. The results of numerical calculations performed for problems of various dimensions and for a number of groups of specific chemical elements. Numerical estimates have been obtained for several groups of organic substances, under which any two substances will be successfully distinguished from each other by the results one single measurement experiment on transillumination. Using the hyperplane method in the identification problem for groups of organic substances showed enough high efficiency. As a result of computer calculations, it is shown that that any of the 1287 considered pairs of organic substances is well distinguishable if the total relative measurement error of the probing radiation flux does not exceed 9.726 \%. The analysis of the dependence of the mass attenuation coefficients of radiation from the atomic number for all chemical elements of the periodic system has been carried out and conclusions about the behavior of the identification accuracy with an increase in the dimension of the problem were done. A justification is given that the hyperplane method will be effective in solving the problem of identification for other groups of chemical elements and identification accuracy does not get worse as the dimension of the problem increases.

Spatial-temporal high-order rotated-staggered-grid finite-difference scheme of elastic wave equations for TTI medium

In the finite-difference (FD) solution of the elastic wave equation for TTI medium, the traditional FD scheme can improve the computational accuracy of the spatial derivatives. However, the difference discretization on the temporal partial derivatives still uses the FD scheme of second-order accuracy, which cannot guarantee the computational accuracy of the temporal partial derivatives and often causes the temporal dispersion problem. The temporal high-order FD scheme can improve the computational accuracy of the temporal partial derivatives. Nevertheless, due to the complexity of the elastic wave equation in TTI medium, using the conventional staggered-grid technique to solve the elastic wave equation, some spatial derivatives need to be approximated by spatial interpolation, which will become new error and reduce the accuracy of the solution of the equations. Therefore, the currently commonly used temporal high-order FD method for the elastic wave equation in isotropic medium cannot be directly applied to the simulation of anisotropic medium. To solve the above problems, we propose a new temporal high-order rotated-staggered-grid FD stencil and derive a new temporal high-order FD scheme under this new stencil for the TTI medium elastic wave equation. Then we estimated the FD coefficients of the new stencil using Taylor series expansions (TE) and optimized the FD coefficients based on least squares (LS). Numerical experiments of the homogeneous TTI medium model and the modified BP model demonstrate that the TE + LS-based temporal high-order rotated-staggered-grid FD scheme can well solve the temporal dispersion in the numerical simulation of TTI medium.

Optical Parameters of Aluminum Alloy Samples Irradiated by High Current Relativistic Electron Beams

The aluminum alloys D16, D16AT are widely used as construction materials in the aircraft industry. Questions connected with the enhancement of the properties of the construction elements made of the alloys through surface modification are of great interest now. The objects of the study in our paper are the samples of the aluminum alloy D16AT subjected to irradiation by high-current relativistic electron beams. Leaving aside the material science aspects, in this work we focused on modeling the optical properties of the samples. The problem is relevant because optical methods for surface analysis have become widespread due to their versatility and efficiency. Through the treatment of the preliminary measured ellipsometry data, we obtain the optical constants of the samples and their dispersion in the visible region of wavelength. The method used consists of an approximation of the reflection coefficient calculated from the ellipsometry data by finding the values of the parameters in the model. The last is performed by the least squares method. The reflection coefficient is assumed to correspond to the semibounded uniaxial medium with the optical axis perpendicular to the interface between the medium and the homogeneous and dielectric ambient medium. The dielectric function of the semibounded medium is approximated by the Drude-Lorentz model. The possibility of birefringence of the samples caused by the irradiation with electron beams is discussed.

RESEARCH OF TECHNOLOGICAL EQUIPMENT FOR THE PRODUCTION OF BULK FOOD MIXTURES

The development of technologies and modern equipment for the agricultural sector, as well as growing competition in the field of growing major agricultural products, lead agricultural producers to try to optimize their own production. The process of mixing can be thought of as the volumetric movement of particles of two or more components to obtain a homogeneous medium (in terms of composition, physical, mechanical, and other properties). To mix bulk materials, external forces must be applied to allow the particles of the components to be mixed to move relative to each other. The heterogeneity of the mixture depends on a number of reasons, in particular: the supply of the initial components to the vibrating mixer; insufficient mixing of the bulk mixture causes a deviation in the distribution of component particles, etc. An analysis of existing mixer designs has shown that most technological processes use rotary drum mixers and mixers with rotating working bodies - paddle, screw, frame. To study the process of mixing bulk food mixtures, a laboratory and experimental setup was developed, consisting of a vibration-centrifugal mixer, a loading hopper, and a control panel. The developed machine (mixer) is based on the task of intensifying the process of mixing materials by reducing the adhesive forces between material particles through the use of the gravitational effect. Vibrational impact on the mixing of materials and the mixer's working bodies significantly increases the process productivity, reduce energy consumption and improves the quality of the mixture. The developed design can be widely used in various industries in the production of spices, bakery mixes, feed, protein and vitamin supplements.

Study of imbibition phenomenon in homogeneous porous medium model for oil recovery with temporal-fractional approach

In this article, the phenomenon of countercurrent imbibition in a specific displacement method occurs within a dipping homogeneous porous medium. This phenomenon plays a vital role in the process of oil recovery, which motivates our analysis. To overcome the difficulties associated with the nonlinear partial differential equation governing the countercurrent imbibition phenomenon, we have been using two distinct methods: the natural transform decomposition method and the variational iteration transform method with their convergence analysis for solutions. These techniques give different perspectives and enable us to obtain approximate solutions. Notably, both the proposed methods demonstrate the potential for substantial production of oil during the secondary oil recovery process in the petroleum industry. The obtained results by the proposed methods show the efficiency in optimizing the oil recovery rate.