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In this investigation, we explored the microrheological characteristics of dilute hydrogels composed exclusively of Poly(vinyl) alcohol (PVA), Phytagel (PHY), and a blend of the two in varying concentrations. Each of these polymers has established applications in the biomedical field, such as drug delivery and lens drops. This study involved varying the sample concentrations from 0.15% to 0.3% (w/w) to assess how the concentration influenced the observed rheological response. Two probe sizes were employed to examine the impact of the size and verify the continuity hypothesis. The use of two polymer blends revealed their immiscibility and tendency to undergo phase separation, as supported by the existing literature. Exploring the microrheological structure is essential for a comprehensive understanding of the molecular scale. Dynamic light scattering (DLS) was chosen due to its wide frequency range and widespread availability. The selected dilute concentration range was hypothesized to fall within the transition from an ergodic to a non-ergodic medium. Properly identifying the sample's nature during an analysis—whether it is ergodic or not—is critical, as highlighted in the literature. The obtained results clearly demonstrate an overlap in the results for the storage (G') and loss moduli (G″) for the different probe particle sizes, confirming the fulfillment of the continuum hypothesis. [ABSTRACT FROM AUTHOR]

Shock wave loading of heterogeneous materials was numerically investigated using three models: a homogeneous alloy model with experimental parameters, an additive approximation model with parameters calculated from the constants and concentrations of the components, and a discrete numerical model constructed based on a random concentration distribution of components over the sample volume. The verification of the computational schemes was done by calculating the shock wave loading of homogeneous materials. Hugoniot curves were plotted and compared with experimental data to show a less than 5% deviation of the numerical results. A series of numerical simulations of spall fracture in homogeneous plates revealed that the free surface velocity profile resulting from spall fracture corresponds to the experimental profile. A relationship was derived to determine the ultimate spall strength for a heterogeneous medium based on the fracture parameters of its homogeneous components. The found homogeneous material parameters were used to simulate the shock wave loading of plates made of nickel titanium and tungsten carbide/cobalt cermet constructed with heterogeneous models. It was shown that the heterogeneous models can be effectively applied to problems of shock wave loading with spall fracture, and the deviation between the calculated free surface velocity of a heterogeneous plate and the experimental data does not exceed 10%. [ABSTRACT FROM AUTHOR]

Abstract During the coal and rock mass fracture process, elastic properties are released and vibration waves are radiated outward. The energy attenuation characteristics of these waves can describe the cumulative damage and elastic energy accumulation of the mass. To investigate coal and rock mass failure characteristics and energy attenuation rules during rockburst, numerical simulation and laboratory testing were utilized to study the energy transfer laws under various parameters. Six variables, including elastic modulus, Poisson’s ratio, bulk density, cohesion, internal friction angle, and void ratio, were selected to simulate the rockburst energy release process under different parameter combinations by adding surface pressure to the model. The coal and rock mass energy attenuation coefficient was obtained by fitting the node energy straight line using the least squares method. The six variables’ influence on vibration wave energy transfer was obtained using analytic hierarchy process program written in MATLAB, and a comprehensive calculation formula was proposed. Using the energy attenuation coefficient, the rock layer energy diffusion distance was calculated and compared with the roof collapse rock layer step distance, resulting in the roof rock layer cutting distance determination. By roof rock strata precutting, rockburst occurrence can be prevented, ensuring safe and efficient coal mine production.

Two innovative and efficient routes were developed to produce glycerol-alkyl ethers employing Williamson reaction conditions in a heterogeneous medium. Thus, the ion exchange resin Amberlyst A26TM −OH form and KOH supported on alumina (KOH/Al2O3) were used as basic solid reagents for alkoxide ion formation. First, glycerol-1,3-iodohydrin and glycerol-1,3-bromohydrin were converted into 1,3-methyl- and 1,3-ethyl glycerol ethers (98–100%) when reacted with MeOH and EtOH, both as solvent and reagent. A second route employed glycerol as an alkoxide ion source and different organic halides such as electrophiles (ethyl iodide, ethyl bromide, allyl bromide, and benzyl bromide) in the presence of Amberlyst A26TM −OH form or KOH/Al2O3. When Amberlyst A26TM −OH resin was used glycerol was converted (100%) to glycerol-1-monoether (73%), -1,3-diether (21%), and -triether (6%) by treating with ethyl bromide or ethyl iodide at 60°C in 1,4-dioxane for 24 h. The use of more reactive halides produced a complex mixture of products. Additionally, the use of ethyl bromide in the presence of KOH/Al2O3, under reflux in 1,4-dioxane for 24 h, led to the consumption of 90% of glycerol with the formation of glycerol-1-ethyl ether (98%) and glycerol-1,3-ethyl ether (2%). The ion exchange resin Amberlyst A26TM −OH could be regenerated and reused in the process.

This study contains a two-dimensional mathematical model of solute transport in a river with temporally and spatially dependent flow, explicitly focusing on pulse-type input point sources with a fractional approach. This model is analyzed by assuming an initial concentration function as a declining exponential function in both the longitudinal and transverse directions. The governing equation is a time-fractional two-dimensional advection–dispersion equation with a variable form of dispersion coefficients, velocities, decay constant of the first order, production rate coefficient for the solute at the zero-order level, and retardation factor. The solution of the present problem is obtained by the fractional reduced differential transform method (FRDTM). The analysis of the initial retardation factor has been carried out via plots. Also, the influence of initial longitudinal and transverse dispersion coefficients and velocities has been examined by graphical analysis. The impact of fractional parameters on pollution levels is also analyzed numerically and graphically. The study of convergence for the FRDTM technique has been conducted to assess its efficacy and accuracy. [ABSTRACT FROM AUTHOR]

Constructions with vibratory mixing devices designed for processing liquids, suspensions, and gas–liquid dispersions are reviewed analytically. Various design schemes of such devices are discussed, the design features of the working bodies are described, and various design options for vibration drives and equipment operating modes are examined. More than 170 relevant patent documents published within the last 70 years are identified to determine the development trend of the technology. Analysis of the global development trends suggests that inventors are interested in works performed to improve the current types of equipment and to develop new ones. [ABSTRACT FROM AUTHOR]

In this work, we consider a polymer flooding process in heterogeneous media. A system of equations for pressure, water saturation, and polymer concentration describes a mathematical model. For the construction of the fine grid approximation, we use a finite volume method with an explicit time approximation for the transports and implicit time approximation for the flow processes. We employ a loose coupling approach where we first perform an implicit pressure solve using a coarser time step. Subsequently, we execute the transport solution with a minor time step, taking into consideration the constraints imposed by the stability of the explicit approximation. We propose a coupled and splitted multiscale method with an online local correction step to construct a coarse grid approximation of the flow equation. We construct multiscale basis functions on the offline stage for a given heterogeneous field; then, we use it to define the projection/prolongation matrix and construct a coarse grid approximation. For an accurate approximation of the nonlinear pressure equation, we propose an online step with calculations of the local corrections based on the current residual. The splitted multiscale approach is presented to decoupled equations into two parts related to the first basis and all other basis functions. The presented technique provides an accurate solution for the nonlinear velocity field, leading to accurate, explicit calculations of the saturation and concentration equations. Numerical results are presented for two-dimensional model problems with different polymer injection regimes for two heterogeneity fields. [ABSTRACT FROM AUTHOR]

The two-dimensional mathematical modelling has been developed with continuously dumped pollutants in aquifers. The medium of transport has been assumed finite and heterogeneous. The non-uniform and steady groundwater flow through the aquifer has been taken into consideration for the present study. Pollutants are continuously dumped at the source point. At the extreme boundary, flux is assumed zero. Initially. the concentration of pollutants at various places has been assumed exponentially decrease in longitudinal and transversal directions. The impact of the increasing and decreasing nature of non-uniform flow has been presented in two cases of the present research. The two-dimensional governing equations have been analytically solved using Laplace transform variational iteration method (LVIM). The Mathematica package is used for graphical representation. [ABSTRACT FROM AUTHOR]

In this study, a one-dimensional non-linear advection–dispersion equation subject to spatial–temporal dependent advection and dispersion coefficients is solved for a heterogeneous groundwater system. The non-linearity of the governing equation is based on the Freundlich and Langmuir sorption isotherms. The groundwater flow is considered to vary exponentially with time. Also, a generalized theory of the dispersion coefficient is used for extensive study of the model problem. The approximate solutions of the model problem are obtained in a semi-infinite and finite heterogeneous media by employing the Crank–Nicolson scheme. The exact solutions are obtained in both domains by the Laplace transform technique subject to linear sorption isotherm and non-transient flow conditions. Further, various graphical solutions are obtained using MATLAB scripts to examine the contaminant transport behaviour. For quantitative evaluation of the proposed model, a root mean square (RMS) error is computed. Overall, the results show that RMS error of the approximate solutions with respect to the exact solutions is within acceptable limits (less than 5%) for different combinations of discretization parameters. The robustness of the proposed model suggests its better suitability for modelling groundwater transport phenomena under the consideration of a non-linear sorption isotherm.

This paper presents a thermo-mechanical model with phase transition considering changes in the mechanical properties of the medium. The proposed thermo-mechanical model is described by a system of partial differential equations for temperature and displacements. In the model, soil deformations occur due to porosity growth caused by ice and water density differences. A finite-element approximation of this model on a fine grid is presented. The linearization from the previous time step is used to handle the nonlinearity of the problem. For reducing the size of the discrete problem, offline and online multiscale approaches based on the Generalized Multiscale Finite Element Method (GMsFEM) are proposed. A two-dimensional model problem simulating the heaving process of heterogeneous soil with a stiff inclusion was considered for testing the mathematical model and the multiscale approaches. Numerical solutions depict the process of soil heaving caused by changes in porosity due to the phase transition. The movement of the phase transition interface was observed. The change of medium properties, including the elastic modulus, was traced and corresponds to the phase transition interface. The proposed multiscale approaches significantly reduce the size of the discrete problem while maintaining reasonable accuracy. However, the online multiscale approach achieves better accuracy than the offline approach with fewer degrees of freedom. [ABSTRACT FROM AUTHOR]

We obtain effective viscoelasticity coefficients for a heterogeneous medium based on a generalized derivative formalism that reflects internal boundaries in the heterogeneous medium. A solution is sought for the homogenized Green's function of the resulting modified operator taking into account the homogenization and subsequent analysis of the operator. Based on the obtained solution of the many-body problem in a heterogeneous medium, the effective viscoelasticity coefficients integrally take into account the microstructure of the system (physical properties and characteristic phase sizes) in explicit form. [ABSTRACT FROM AUTHOR]

The article is devoted to the study of the possibility of using the principles of circuit design when modeling internal processes occurring in a heterogeneous medium. Modern complex objects in mechanical engineering (elements, processes, components, mixtures, alloys, etc.) can be represented in the form of circuit diagrams, which are understood as a set of elements and relationships between them. Such schemes make it possible to create an unambiguous model of this object. In addition, circuit diagrams allow you to optimize them (and hence objects) in the process of construction: change the number of elements; change the characteristics of the elements. The main advantage of this approach stems from the fact that at present there are special programs, including computer programs, that make it possible to build such models based on the purpose of the functioning of the designed object and the possibilities of its creation. Circuit design in mechanics is the creation of a concept diagram of a future object (method, device, substance), which, when completed (manufactured), will allow the object to achieve its goals. The process of transformation and transfer of an intensive parameter in heterogeneous media is considered, using the example of the propagation of elastic oscillations and thermal processes in them, which is interesting from the point of view of modeling the processes that take place in these media during their flaw detection by the acoustic infrared thermometric method, which is based on the interaction of structural defects with acoustic waves. At the same time, thermal energy is generated at their boundaries, which is an indicator not only of the presence of cracks, but also of their direction and development. When modeling damage such as cracks and fractures in products made of non-metallic heterogeneous materials, special additional elements are introduced that simulate structural integrity violations – relay elements. [ABSTRACT FROM AUTHOR]

The effective coefficients of linear elasticity theory are obtained and analyzed with the aim to analytically describe heterogeneous media. This is done for an arbitrary dimension of the space under consideration and taking into account the generalized derivative formalism. The effective coefficients and their derivatives are explored for the presence of a carrier phase and a structural phase transition (percolation properties) over the entire range of volumetric concentration. Based on the analysis carried out, a comparison is made with the results of existing approaches and with the available data on colloids, suspensions, and granular media. [ABSTRACT FROM AUTHOR]

In this study, a one-dimensional non-linear advection–dispersion equation subject to spatial–temporal dependent advection and dispersion coefficients is solved for a heterogeneous groundwater system. The non-linearity of the governing equation is based on the Freundlich and Langmuir sorption isotherms. The groundwater flow is considered to vary exponentially with time. Also, a generalized theory of the dispersion coefficient is used for extensive study of the model problem. The approximate solutions of the model problem are obtained in a semi-infinite and finite heterogeneous media by employing the Crank–Nicolson scheme. The exact solutions are obtained in both domains by the Laplace transform technique subject to linear sorption isotherm and non-transient flow conditions. Further, various graphical solutions are obtained using MATLAB scripts to examine the contaminant transport behaviour. For quantitative evaluation of the proposed model, a root mean square (RMS) error is computed. Overall, the results show that RMS error of the approximate solutions with respect to the exact solutions is within acceptable limits (less than 5%) for different combinations of discretization parameters. The robustness of the proposed model suggests its better suitability for modelling groundwater transport phenomena under the consideration of a non-linear sorption isotherm. [ABSTRACT FROM AUTHOR]

The radiation divergences of a microsecond laser on ethanol solution of rhodamine 6G and perylene-activated solid-state laser on nanoporous glass–polymere (NPGP) composite are compared, depending on the specific energy of pumping radiation. It is established that the main reasons of large radiation divergence of the NPGP nanocomposite laser are the light scattering of the pumping radiation and laser radiation by the heterogeneous medium of the composite and the thermal self-action. [ABSTRACT FROM AUTHOR]

This study contains a two-dimensional mathematical model of solute transport in a river with temporally and spatially dependent flow, explicitly focusing on pulse-type input point sources with a fractional approach. This model is analyzed by assuming an initial concentration function as a declining exponential function in both the longitudinal and transverse directions. The governing equation is a time-fractional two-dimensional advection–dispersion equation with a variable form of dispersion coefficients, velocities, decay constant of the first order, production rate coefficient for the solute at the zero-order level, and retardation factor. The solution of the present problem is obtained by the fractional reduced differential transform method (FRDTM). The analysis of the initial retardation factor has been carried out via plots. Also, the influence of initial longitudinal and transverse dispersion coefficients and velocities has been examined by graphical analysis. The impact of fractional parameters on pollution levels is also analyzed numerically and graphically. The study of convergence for the FRDTM technique has been conducted to assess its efficacy and accuracy.

The paper studies wave propagation in 1 D bimodular media. Four cases are investigated: two cases with an external step load applied to a prestressed bimodular rod and two cases with a sign-alternating pulse applied to an unloaded bimodular rod. Shock wave formation and energy dissipation are observed in two cases. Analytical solutions showing the distortion of a wave profile due to shock wave formation for all cases are derived. A method of suppressing an arbitrary tensile pulse in a bimodular rod by creating a compressive pulse is proposed. Validation by numerical modeling using a Godunov-type explicit difference scheme is performed. [ABSTRACT FROM AUTHOR]

The effective transfer coefficients of a heterogeneous medium are obtained based on the formalism of a generalized derivative, which reflects the internal boundaries of a heterogeneous medium. The formula for the generalized derivative is a consequence of applying the variational apparatus to the energy functional for a heterogeneous medium, taking into account the indicator function characterizing the phase at a point. The solution is sought for the homogenized Green's function based on the modified operator obtained, and the homogenization is carried out. Based on an analysis of an integro-differential equation with discontinuities and the introduced hypotheses, the solution has the form of a Yukawa potential that characterizes the transition layer caused by charge screening from the physical point of view. This potential is aimed at expressing the solution of the many-body problem in a heterogeneous medium and reflecting the collective influence of the phases on the field propagating through the system. As a result of the solution found, the effective transport coefficients integrally take into account the microstructure of the system (physical properties of phases and characteristic scales) in an explicit form. [ABSTRACT FROM AUTHOR]

In this work, we consider a polymer flooding process in heterogeneous media. A system of equations for pressure, water saturation, and polymer concentration describes a mathematical model. For the construction of the fine grid approximation, we use a finite volume method with an explicit time approximation for the transports and implicit time approximation for the flow processes. We employ a loose coupling approach where we first perform an implicit pressure solve using a coarser time step. Subsequently, we execute the transport solution with a minor time step, taking into consideration the constraints imposed by the stability of the explicit approximation. We propose a coupled and splitted multiscale method with an online local correction step to construct a coarse grid approximation of the flow equation. We construct multiscale basis functions on the offline stage for a given heterogeneous field; then, we use it to define the projection/prolongation matrix and construct a coarse grid approximation. For an accurate approximation of the nonlinear pressure equation, we propose an online step with calculations of the local corrections based on the current residual. The splitted multiscale approach is presented to decoupled equations into two parts related to the first basis and all other basis functions. The presented technique provides an accurate solution for the nonlinear velocity field, leading to accurate, explicit calculations of the saturation and concentration equations. Numerical results are presented for two-dimensional model problems with different polymer injection regimes for two heterogeneity fields.

In this article, a fitted finite element method is proposed and analyzed for non-Fourier bio heat transfer model in multi-layered media. Specifically, we employ the Maxwell–Cattaneo equation on the physical media which has a discontinuous coefficients. Convergence properties of the semidiscrete and fully discrete schemes are investigated in the L 2 norm. Optimal a priori error estimates for both the schemes are proved. Numerical experiment is conducted to confirm the theoretical findings. [ABSTRACT FROM AUTHOR]

The effect of dynamic spall damage on the response of layered medium subjected to one-dimensional impact involving an impactor and a multi-layered target is investigated. The study examines the damage caused by elastic waves below the Hugoniot Elastic Limit (HEL) during impact events. Analytical expressions of stress and particle velocity derived from mass and momentum conservation principles are utilized to solve the wave interactions within the impactor-target system, considering reflections, transmissions, and wave interactions between layers. These analytical expressions, integrated into a computational framework, facilitate the monitoring of material responses following each wave interaction, thereby analysing the impact response of the layered medium. Wave interactions, resulting in tensile stresses, that can cause damage to the target have been identified. A strain-based damage initiation and evolution law is incorporated into the developed computer program to predict damage in each layer of a medium. Damage alters the medium's impact behaviour by decreasing stress magnitude and inducing temporal delays in the response due to attenuated wave propagation speed. The occurrences of tensile stress are explored, analysing spatial and temporal variations of multiple damage incidents within the layered medium. The tension at the interface between two layers can induce damage in one or both adjacent layers, leading to debonding between layers. The effect of damage on the impact response of the medium is analysed by comparing the results for the damaged and undamaged target scenarios. The impact behaviour of a single-layer and a multi-layer target obtained from the present model, in terms of stress and particle velocity, is verified through Finite Element simulations of the identical impact problems, where the damage evolution criterion is incorporated using a VUMAT subroutine. The outcomes derived from this study align closely with Finite Element (FE) results. [Display omitted] • Investigation of spall damage in a layered medium under one-dimensional impacts. • Analytical expressions of stress and velocity for all possible wave interactions. • Spatial and temporal variations of multiple damage incidents in a layered medium. • Stress reduction and temporal delay in medium's impact response due to damage. • Accurate prediction of stress and velocity profiles in the heterogeneous medium. [ABSTRACT FROM AUTHOR]

• The method can be used to quantify transient water flux in deep and shallow media. • It is efficient for a wide range of flow velocities and abrupt flux changes. • The flux estimation can be done using temperatures from any observation segment. • We improve the way to give an initial temperature profile in transient conditions. Heat has become an increasingly utilized hydrological tracer for quantifying groundwater flow due to its universal distribution and environmental friendliness. Estimating time-varying groundwater flux is of great significance for understanding the transient behavior of the groundwater system. Most heat tracing models for acquiring transient water flux were specially designed for the near-surface medium that rely on periodic temperature signals, but few can be applicable to deep groundwater flux estimates. Models estimating flux in deep aquifers usually assume constant flow velocity over time, which cannot delineate the temporal patterns of groundwater flow. Here, we propose a numerical approach for automatically quantifying transient vertical groundwater flux from temperature time series at multiple depths. The approach can be applied to deep as well as near-surface homogeneous and heterogeneous media with flexible boundary conditions. The accuracy of the approach is demonstrated through three synthetic experiments and one real case test using data from a field site. Our approach shows fine temporal resolution for rapidly changing flow under various conditions and accurate estimates for a wide range of flow velocities. We conduct analyses to investigate the influence of different strategies to give an initial temperature profile on flux estimates. The results highlight the necessity of accurately giving an initial temperature profile under transient conditions. This study improves the heat tracing approach for estimating time-varying water fluxes, especially in a deep well, which would be beneficial to monitoring and managing groundwater flows with the development of high-resolution temperature observation technology. [ABSTRACT FROM AUTHOR]

This paper presents a thermo-mechanical model with phase transition considering changes in the mechanical properties of the medium. The proposed thermo-mechanical model is described by a system of partial differential equations for temperature and displacements. In the model, soil deformations occur due to porosity growth caused by ice and water density differences. A finite-element approximation of this model on a fine grid is presented. The linearization from the previous time step is used to handle the nonlinearity of the problem. For reducing the size of the discrete problem, offline and online multiscale approaches based on the Generalized Multiscale Finite Element Method (GMsFEM) are proposed. A two-dimensional model problem simulating the heaving process of heterogeneous soil with a stiff inclusion was considered for testing the mathematical model and the multiscale approaches. Numerical solutions depict the process of soil heaving caused by changes in porosity due to the phase transition. The movement of the phase transition interface was observed. The change of medium properties, including the elastic modulus, was traced and corresponds to the phase transition interface. The proposed multiscale approaches significantly reduce the size of the discrete problem while maintaining reasonable accuracy. However, the online multiscale approach achieves better accuracy than the offline approach with fewer degrees of freedom.

The development of the cryolithozone requires building and numerically implementing mathematical models of multiphysics thermoelastic processes involving with first-order phase transitions and occurring in the foundations of engineering structures and buildings. Numerical implementation of such models is associated with computational difficulties due to various types of heterogeneities in applied problems and the nonlinearity of governing equations, which require very fine grids, increasing computational costs. We develop a numerical method for solving a thermoelasticity problem with phase transitions based on the generalized multiscale finite-element method (GMsFEM). The main idea of the GMsFEM is to construct multiscale basis functions that take the medium heterogeneities into account. The approximation on a fine grid is carried out using the finite-element method with standard linear basis functions. To verify the accuracy of the proposed multiscale method, we solve two- and three-dimensional problems in heterogeneous media. Numerical results show that the multiscale method can provide a good approximation to the solution of the thermoelasticity problem with a phase transition on a fine grid with a significant reduction in the dimensionality of the discrete problem. [ABSTRACT FROM AUTHOR]

Biochar has received continuous attention in recent years due to its high specific surface area, rich micropores, and many types of functional groups. In this study, the migration behavior of modified micro-nano biochar (MMNBC) in heterogeneous media under the influence of ionic strength and flow rate was studied by column experiments. The results showed that the mobility of MMNBC could be increased by increasing the flow rate and decreasing IS. The retention of MMNBC in quartz sand coated with clay minerals was higher than that of pure quartz sand, and the difference existed due to the surface properties. The main reason is that the clay mineral coating adds cations on the surface of quartz sand, which generates electrostatic interaction with MMNBC, which promote the adsorption of MMNBC on the medium. This study provides a theoretical basis for effectively controlling the groundwater environment problems caused by the migration of biochar.

The relevance of solving the technological problem of guaranteed inactivation of microflora by heating in liquid media and the preservation of their useful components, in particular, in wine materials, is substantiated. Traditional heat treatment with heating up to 70...75 °C leads to a deterioration in the properties of the medium due to the thermal decomposition of its useful components. Newer is the technology of heating by the energy of the microwave field in the working chamber. But its significant drawback is the formation of standing waves in the metal chamber, causing local zones of overheating in places of maxima and underheating in places of wave minima. The consequence of this is the deterioration of the chemical composition of products and unsatisfactory inactivation of microflora. The elimination of these disadvantages of microwave processing of media is proposed to be carried out in a non-resonant chamber developed by the authors. Selective heating in the new chamber is produced by the energy of a uniform microwave field. At the same time, there are no local overheating and underheating of products. The technical implementation of a non-resonant type chamber involves the concentration of field energy in the volume of production, the conversion of the ballast field energy into thermal energy and its utilization. The work includes theoretical substantiation and experimental confirmation of the advantages of the new technology compared to the traditional one. Selective heating of products in a non-resonant working chamber entails the possibility of reducing the temperature required for guaranteed inactivation of microflora by 25...30 °C. This helps to preserve the components of the product due to the absence of overheating and reduce energy costs. In addition, it provides: exclusion of harmful radiation from the working chamber; prevention of self-overheating of the generator and exclusion of the dependence of the energy efficiency of the chamber on the level of its loading with products. [ABSTRACT FROM AUTHOR]

Biochar has received continuous attention in recent years due to its high specific surface area, rich micropores, and many types of functional groups. In this study, the migration behavior of modified micro-nano biochar (MMNBC) in heterogeneous media under the influence of ionic strength and flow rate was studied by column experiments. The results showed that the mobility of MMNBC could be increased by increasing the flow rate and decreasing IS. The retention of MMNBC in quartz sand coated with clay minerals was higher than that of pure quartz sand, and the difference existed due to the surface properties. The main reason is that the clay mineral coating adds cations on the surface of quartz sand, which generates electrostatic interaction with MMNBC, which promote the adsorption of MMNBC on the medium. This study provides a theoretical basis for effectively controlling the groundwater environment problems caused by the migration of biochar. [ABSTRACT FROM AUTHOR]

Abstract Due to the complexity of heterogeneous medium models, the corresponding research methods still have great limitations, and hence, there is a dearth of research findings. To study the problem of dynamic stress concentration in heterogeneous media, the scattering of SH waves by circular holes in a full-space periodic heterogeneous continuum medium is investigated based on the propagation characteristics of elastic waves in complex heterogeneous media. The wave equation of SH waves propagating in heterogeneous media with the elastic shear modulus and density varying in the form of trigonometric functions is solved by using the complex function method, the wave function expansion method, and the auxiliary function method. On this basis, the wave field and stress field are derived, and the expression of the dynamic stress concentration factor (DSCF) on the boundary of a circular hole is given. The effects of the reference wavenumber and the variation period of the heterogeneous medium on the distribution of the DSCF on the boundary of a circular hole are analyzed through numerical examples. The results show that when the circular hole defect is within one heterogeneous period of the medium, shortening of the heterogeneous period of the medium reduces the peak of the DSCF due to high-frequency waves on the boundary of the circular hole. [ABSTRACT FROM AUTHOR]

A heterogeneous material obtained by means of cold gas dynamic spraying with subsequent laser processing is studied. The reasons for reduction of the particle size of boron carbide B4C under the action of a laser beam and the chemical composition of the material containing the "lost" material of B4C particles are examined. A mathematical model, which takes into account the dissolution of B4C particles and the presence of a chemical reaction, is developed. The elastic properties of the deposited heterogeneous material are analyzed with the use of continuum approaches that describe heterogeneous media and are based on averaging of the original stochastic equations. [ABSTRACT FROM AUTHOR]

We provide some analytical account of the influence of the internal boundaries of a heterogeneous medium on the propagation of an elastic stress field through it. The generalized derivative serves as the mathematical concept displaying the microstructure of a heterogeneous system. Using the generalized derivative we modify the operator in the initial model of linear elasticity. The Green's function (built on the operator) displays the microstructural features of the system. We use the method of conditional moments to obtain the effective coefficients of elasticity which are included in the averaged equations and describing the elastic properties of a heterogeneous medium. This approach leads to the integrals containing the modified averaged Green's function and the correlation function of the structure geometry. Using these terms, we integrally take into account the microstructure of the system in the final effective elasticity coefficients. [ABSTRACT FROM AUTHOR]

Storage of liquefied gas in an underground cavity created in hard rocks is a promising new technology that can significantly reduce the dimensions of a storage facility. The intense heat transfer between the cryogenic fluid and the surrounding rocks leads to the formation of an ice ring in water-saturated rocks, which acts as a natural protective barrier. In this paper, we provide a general theoretical analysis of the existence and evolution of the freezing ring. The analysis is based on solving the problem of heat transport in heterogeneous domain with two thermal waves initiated inside the domain and propagating into two opposite directions. The analytical solution was obtained by the modified Karman–Pohlhausen integral method. We have developed the extension of this method to a heterogeneous medium, in which the effect of the temperature semi-stabilization occurs. It has been shown that the propagation of the freezing front is non-monotonic and changes direction, so that the lifetime of the ice ring is finite. General analytical formulae have been obtained that describe all process parameters depending on the thickness of the insulating layer, in particular: the maximum thickness of the ice ring, its lifetime, conditions of existence, the critical thickness of the insulation above which the ice ring does not arise, as well as the global evolution of the temperature field. These results enable to select an optimal thickness of the insulation. • The essence of the paper: the propagation of two opposite thermal waves caused by a cryogenic fluid stored in rocks. • Fully analytical solution of the heat transfer problem has been obtained. • An ice ring can be formed, protective or destructive, which behaves non-monotonically in time and has a finite lifetime. • An optimal and critical insulation thickness can be calculated. • A modification of the Karman–Pohlhausen integral method has been developed, which takes into account the effect of semi-stabilization. [ABSTRACT FROM AUTHOR]

• Spectral radiative properties of semi-transparent media charaterized up to 1350 K. • Monte Carlo Ray Tracing accurately compute the spectral radiative properties. • Complex indices of both semi-transparent microphases of a material are identified. • Spectral absorption indices are identified at the microscale up to 1350 K. • A new methodology is proposed for efficient investigation of radiative properties. Complex refractive indices of micrometric aluminosilicate fibers and of silica aerogel, components of a biphasic and semi-transparent material, were identified in the mid-infrared range from 295 to 1350 K. The identification was carried out by successive applications of a methodology combining infrared spectroscopy (FTIR), X-ray microtomography and Monte Carlo Ray Tracing. This identification technique proves to be an interesting tool for material design since it is now possible to forecast the radiative properties of heterogeneous and semi-transparent materials composed of identical microphases but involving different proportions and spatial distributions. With this approach, it is no longer necessary to identify effective indices or perform systematic FTIR spectroscopy measurements to get a first overview of the radiative properties of a new spatial layout of the microphases. [ABSTRACT FROM AUTHOR]

For practical applications, the description of processes occurring during the flow of two-phase gas-liquid mixtures requires a simple physical and mathematical model that describes the behavior of a two-phase medium in the entire range of phase concentrations changes and in a wide range of pressure changes. Problems of this kind arise in various branches of industry and technology. In the space industry, one often has to deal with the movement of various gases in rocket nozzles, consider the combustion, condensation of various vapors on the nozzle walls and their further impact on the velocity sublayer at the nozzle wall. The large acoustic effect arising from the engines affects the gas-liquid mixture in the nozzles of rocket engines. In the metal industry, metal cooling occurs with the help of nozzles in which the emulsion mixture is supplied under high overpressure. But this is only a short list of applied issues in which one has to deal with a problem of this type. The paper presents the results and directions of study of the problems of two-phase dispersed gas-droplet flows in the nozzles. The main methods of investigation of two- phase heterogeneous flows are described. The main characteristics of heterogeneous two-phase flows in the nozzles, which were confirmed by experimental results, are presented. The calculation of the air-droplet flow in the Laval nozzle is given. The technique, which is based on integral energy equations for two-phase dispersed flows, is described. The main problems and questions concerning the further description and studying of two-component flows are stated.

Сonsistent physics and mathematics model of electromagnetic waves propagation in heterogeneous medium using the generalized wave equation and the Dirichlet theorem is built. The data of numerical simulation of the electromagnetic interference interaction with a fibrous material having a double porosity. The results of numerical simulation show that the presence of micro- and macropores (medium with double porosity) of the fabric ensures maximum masking effect.

The propagation of a short compression pulse in heterogeneous targets containing ceramic inclusions of different sizes is studied numerically. The case of a heterogeneous material with inclusions of macroscopic size is considered. It is shown that during propagation in all targets, the initial shape of the shock pulse evolves to a shape corresponding to an elastic stress-strain state in which its amplitude and length do not depend on the distance traveled. It is found that for heterogeneous materials with large inclusions, the rate of decrease in pulse amplitude is greater than for heterogeneous materials with small inclusions. [ABSTRACT FROM AUTHOR]

In the present study, an analytical solution is obtained for two-dimensional advection–dispersion equation with variable coefficients in a semi-infinite heterogeneous porous medium. Dispersion coefficient and groundwater velocity are assumed to vary temporally as well as spatially while the retardation factor varies spatially only. The first-order decay and zero-order production terms are also considered into account. The variations in parameters along both longitudinal and transverse directions are of exponentially decreasing nature. Initially the geological formation is considered not solute free. The nature of pollutant is considered of conservative and is assumed to be originating from time-dependent varying point source. New time and space variables are introduced to convert the variable coefficients of the advection–dispersion equation into constant coefficients. Analytical solution of the proposed model is obtained by employing Laplace integral transformation technique (LITT). The proposed analytical solution is illustrated graphically to study the effects of various parameters on the solute transport for temporally exponentially decreasing and sinusoidal nature velocities. [ABSTRACT FROM AUTHOR]

The paper explores issues of both optimization and rational design of heterogeneous traffic servicing integrated systems. The primary goal of the paper is to develop a toolkit for selection of structure variants and parameters of distributed systems with a heterogeneous medium as part of a subsystem of managing the modelling and upgrading of the systems in question. The research subject is a system consisting of air and cable multiple-access systems. The multiobjective problem of structure variants has been solved for systems that differ in access protocols, communication media and transmission velocity within these media, as well as in quality of transmission channels and quantity of customers. Preferred Pareto set of system construction variants has been derived. The selection problem has been solved within the double-objective space for each type of traffic with consequent merging of obtained results. The structure of a model information system, which was used as one of the application objects for obtained results and for the comparison of characteristics, went through a number of stages of comprehensive upgrade that resulted in merging of all types of customers in united subsystems of integral traffic, realization of unified functioning of these subsystems with a connectivity to a common access system and with an output into a united transportation system, which, consequently, led to formation of a joint data stream. [ABSTRACT FROM AUTHOR]

Fractional derivatives, owing to their nonlocal behavior, are well suited for modeling the fate of contaminants in a heterogeneous medium. This study develops the mathematical formulation and the solution of a one-dimensional (1D) fractional flux advection-dispersion equation (FFADE) for an increasing or decreasing nonlinear source of contamination in the permeable region. In the proposed model, the first-order space derivative is replaced with the fractional derivative of order (α−1) (1<α<2) in a Riemann-Liouville sense. The model assumes a spatiotemporally varying dispersion and seepage velocity, constant dispersion and uniform seepage velocity, linear dispersion and linear seepage velocity, and quadratic dispersion and linear seepage velocity, exhibiting various levels of medium heterogeneity. Initially, the medium is considered to be polluted with solute concentration c0 and spatially varying specific concentration ci. The approximate solution to the model is obtained by the modified Adomian decomposition method. It is remarked that change in the medium's heterogeneity alters the peak of solute concentration, and the presence or absence of advection in the solute transport process significantly affects the concentration distribution. The obtained results are validated with field data available in the literature. The obtained solutions may be used to predict solute concentration in the permeable region from penetrating contaminant sources situated at any place along a vertical plane perpendicular to the direction of, for example, groundwater flow. [ABSTRACT FROM AUTHOR]

To explore the grouting reinforcement mechanism of heterogeneous rock and soil in a fault fracture zone, based on the F2 fault grouting project of Yonglian Tunnel, the filling area composed of loose and soft media in the fault is defined as the advantageous grouting diffusion region, which is divided into loose and weak diffusion regions according to the slurry diffusion form. A self-developed grouting reinforcement test system is used to carry out grouting reinforcement tests on the heterogeneous rock and soil. The existence of the advantageous diffusion region can effectively improve the reinforced body strength. The slurry in the reinforced body containing the loose medium mainly expands outwards in the form of first infiltration and then compaction, and the slurry vein mainly remains in the advantageous diffusion region. The slurry in the reinforced body containing the soft medium mainly diffuses in the form of compaction splitting, which can form thicker splitting of the grouting veins. When the reinforced body is destroyed, the body containing the loose medium is mostly conically fractured, indicating complete lithology and homogeneous material. Moreover, the reinforced body containing the soft medium always forms a penetrating crack along the slurry vein or near the grouting vein. Focusing on the heterogeneous stratum consisting of fault breccia and soft plastic fault gouge, controllable slurry dynamic adjustment, same-hole multi-sequence sub-gradient grouting, and localized grouting control are proposed. The grouting control method is applied to the case of Yonglian Tunnel, and a superior grouting reinforcement effect is achieved. [ABSTRACT FROM AUTHOR]

In this study, imbibition process is investigated in heterogeneous hydrocarbon reservoir using the non-classical (effective viscous finger) model equations proposed by Luo et al. (SPE Res. Eval. Engineering, 20(4), 1–16 2017). Counter-current spontaneous imbibition is analyzed in different heterogeneous porous media. The heterogeneity is mainly due to the spatial variation of the porosity and absolute permeability. The proposed mathematical model is solved considering the Implicit Pressure Explicit Saturation Scheme (IMPES) via finite difference method (FDM). Effect of the viscosity ratio, growth rate exponent of the fingering function, and the maximum fingering cross section on the normalized water saturation are analyzed. The present model is verified in the limiting case of classical model equations in homogeneous medium. It is noted that rate and extent of the counter-current imbibition are significantly controlled by the distribution of heterogeneous parameters like porosity and absolute permeability of the reservoir. [ABSTRACT FROM AUTHOR]

The paper concerns numerical study of non-Fourier bio heat transfer model in multi-layered media. Specifically, we employ the Maxwell–Cattaneo equation on the physical media with discontinuous coefficients. A fitted finite element method is proposed and analyzed for a hyperbolic heat conduction model with discontinuous coefficients. Typical semidiscrete and fully discrete schemes are presented for a fitted finite element discretization with straight interface triangles. The fully discrete space–time finite element discretizations are based on second order in time Newmark scheme. Optimal a priori error estimates for both semidiscrete and fully discrete schemes are proved in L ∞ (L 2) norm. Numerical experiments are reported for several test cases to confirm our theoretical convergence rate. Finite element algorithm presented here can be used to solve a wide variety of hyperbolic heat conduction models for non-homogeneous inner structures. [ABSTRACT FROM AUTHOR]

In this paper, 3-D heterogeneous medium, containing small inhomogeneous zones, subjected to a short-pulse laser has been examined by solving the transient radiative transfer equation. Both curved-line advection method and STEP schemes of the FTn finite volume method have been applied. The curved-line advection method predictions proved that a decrease of the false scattering and ray effects are obtained. In fact, there was a good agreement between the curved-line advection method and the Monte Carlo method. However, the STEP results are slightly mismatching the predictions of the aforementioned reference method. Then, the effects of the absorption coefficient, the size, the number and the position of inhomogeneous zone on the transmittance and reflectance signals have been analyzed. The predictions showed that the increase of the size of the inhomogeneity reduces the intensity of radiation. For both homogenous and heterogonous medium, the change of the detector position varies both the broadening of the signal pulse-width and the time with peak reflectance and/or transmittance. That is can be explained by the effects of the distance and the medium property between the laser-incident source and the detector position. Thus, these both parameters are the main factors for determining the peak position and the pulse broadening. Finally, the effects of the absorption coefficient in the inhomogeneity zone on the absolute values of logarithmic slope has been discussed. The results proved that the absolute values of logarithmic slope may be a perfect indicator for detecting any abnormal absorbing zones in the medium. [ABSTRACT FROM AUTHOR]