Multicomponent Media Research Articles

Simulation of admixture diffusion in a medium with traps under cascade decay of particles

By the continuum-thermodynamic approach it is proposed the mathematical model of mass transfer of admixture in a multicomponent medium with traps under cascade decay of admixture. Whithin scope of the model the admixture concentration on certain step of decay is the source of the mass of the decaying substance, that diffuses and can be sorbed, on the next step. Solutions of the initial-boundary value problems of the cascade type are constructed by the iteration procedure with using Green's functions. The formulae are obtained for finding the mass flows, as well as admixture quantity pass through the layer, at each stage of decay. Software for simulation of the diffusion processes in the body with traps under cascade decay of admixture substances is designed.

Statistical Estimates of Lidar Signals Reflected from the Ocean Bottom

The Monte Carlo method is used to solve the nonstationary equation of laser sensing of an optically dense, complex, multicomponent aqueous medium with allowance for the water–air interface, the contribution of multiple scattering of radiation by the water column, and reflection of the signal from the bottom. As a result, we have obtained dependences of the return signal of a monostatic lidar from the water column and the surface microwaves for various field-of-view angles of the receiver. The results of our calculations show that a lidar detection depth of the bottom up to 50 m is achievable for water optical thicknesses up to 3.5–4. When sensing the bottom up to the limiting depth of 50 m under conditions of very transparent water and Fresnel reflection from its surface, the dynamic range of the signal from the water column reaches 7–9 orders of magnitude.

Fracture of cylindrical ampoules during solid phase synthesis under explosive loading

The paper presents the numerical and experimental study of the behavior of porous reactive mixtures (Al-S and Al-Tf) under explosive loading using a multicomponent medium model. The initial dispersion of the reactive mixture is varied to evaluate its contribution to the fracture of the cylindrical ampoule. The results have shown that the high rate of heat release during the chemical reaction in the bottom part of the ampoule and a sharp increase in pressure lead to the formation of the gas phase, which causes the ampoule fracture. It is found that the higher the initial dispersion of the mixture components is, the more intensive the ampoule failure is.

A phase-field approach embedded in the Theory of Porous Media for the description of dynamic hydraulic fracturing

Hydraulic fracturing is a big issue in the exploitation of oil and gas resources as well as in the production of heat in deep geothermal energy plants. Investigating hydraulic fracturing processes numerically by means of a finite-element analysis, one has to address the porous solid and its pore content within a fully coupled computational approach. For this purpose, the present article combines the well-established Theory of Porous Media with elements of fracture mechanics, especially, with the phase-field approach to fracture, which has proven as a successful tool for the computation of fracturing processes in the field of standard solid mechanics.Although hydraulic fracturing is widely applied in practice, this procedure has not yet been investigated adequately by means of a full theoretical and computational framework on the basis of a multicomponent medium tackling a porous solid skeleton and its pore content with their mutual interaction of deformation and fracture, and fluid-driven processes both in the solid bulk and cracking domains. Addressing these features, the article concentrates on a permeable elastic solid skeleton, where the fracturing process is governed by brittle fracture driven either by a prescribed fluid pressure or by a prescribed fluid influx. Two- and three-dimensional numerical examples computed by use of the coupled solver PANDAS exhibit the possibilities of this approach.

Influence of Initial Parameters on the Performances of the Flow System of Turbines Operating on Low-Boiling Actuating Medium

A comparative analysis of supercritical and subcritical steam turbine cycles with low-boiling actuating medium has been done. The effect of initial steam parameters at the turbine inlet on the metering, geometric and power characteristics of the turbine was demonstrated using different actuating media. Steam turbine cycles of this type using the mix (multicomponent) medium or single-component actuating medium that define the amount of capital expenditures and have an impact on the further operation of heat flow diagram have also been compared. Computation studies of the flow system of turbines using different actuating media were carried out taking into consideration the thermodynamic properties and peculiarities of low-boiling actuating media in question. The data of computation studies that were carried out using the software system developed by the IPMash of the National Academy of Sciences of Ukraine showed that the selection of actuating medium should be based on the availability of industrial production that would allow us to reduce the procurement costs for it and the costs for the replenishment of leakages (if available) during the operation. When implementing the low-boiling actuating media-based heat flow diagram it is required to compare the efficiency of thermodynamic cycles, and to estimate the specific quantity of metal and the power efficiency of all the components of power plant. It should also be taken into account that the boundary curve of dryness fraction is of an inclining type and therefore to reduce the costs required for the condensation of actuating medium its parameters should be selected in a way so as to bring the expansion process closer to the boundary curve. It has been established that the overall dimensions of the flow system of turbine with supercritical and subcritical parameters change insignificantly; the flow-rate of actuating medium differs within 10 %, and the electric power changes up to 5 %.

A mathematical model of gas outflow from gas-saturated ice and gas hydrates

This paper considers gas outflow from the agglomerate composed of gas-saturated ice, free gas, and gas hydrates. The agglomerate is considered to be a multicomponent continuous medium.

Derivation of an Effective Model for Metabolic Processes in Living Cells Including Substrate Channeling

A system of reaction-diffusion equations in a multi-component medium with nonlinear flux-conditions and additional reaction-diffusion equations on the interfaces is considered. The model is motivated by metabolic processes in living cells. Especially, we are interested in modeling the central carbon metabolism in plant cells, with particular emphasis on metabolite channeling. The nonlinear reaction terms arising in the equations and boundary conditions are described by structural conditions, which are fulfilled by the kinetics of multi-species enzymatic reactions encountered in cellular metabolism. Starting from a mathematical model at subcellular level, where cellular structures like organelles are resolved, we derive an effective approximations for the cellular processes, by letting the scale parameter given by the ratio between the size of organelles and that of the cell going to zero. To show convergence of the nonlinear terms, we use homogenization concepts developed in Gahn, Neuss-Radu, and Knabner (SIAM J. Appl. Math. 76, 1819–1843 [21]), based on estimates for the shifting operator for Banach-space-valued functions.

Operation effectiveness of wells by enhancing the electric- centrifugal pump

We present the method to improve the operation effectiveness of wells by enhancing the electric-centrifugal pump. Some of the best ways to extend the electric-centrifugal pumps operating lifetime is using today's techniques as well as additional protective equipment as a part of the electric-centrifugal pump. In paper it is shown that high corrosiveness of formation fluid (a multi-component medium composed of oil, produced water, free and dissolved gases) is a major cause of failures of downhole equipment. Coil tubing is the most efficient technology to deal with this problem. The experience of coil tubing operations has proved that high-quality bottom hole cleaning saving the cost of operation due to a decreased failure rate of pumps associated with ejection of mechanical impurity.

Nadra-3D Add-On for Blender Software

Nadra-3D add-on package for Blender software is considered. This add-on allows use of Blender, TetGen, and ParaView software for data pre/post processing for finite element solver Nadra-3D, designed for simulation of spatial processes of filtration, heat transfer, and changes of the stress---strain state of multicomponent media.

Raman spectroscopy as a tool for the collection management of microscope slides

Throughout the history of preparation of biological samples for microscopy the choice of the mounting medium was sometimes dictated merely by availability of the used media. Thus, a plethora of resins and other organic polymers as well as complex mixtures are found to serve as mounting agents in microscope slide collections of museums of natural history, impeding the work for both curators and conservators. Dramatically, in some cases the used mounting media can already be observed to have undergone crystallization and other decomposition processes within few years of mounting demanding immediate action in restoring as well as an imminent precaution in conservation. Therefore, an unambiguous chemical identification of the used agent as well as its current aging stage is of great interest for the biologist community. The technical demands on the analytical approach to obtain this information can be straightforwardly identified. Any used technique has to be non-destructive, yield in molecular information allowing for a chemical identification of the used mounting agents and allow for a spatially well-defined interrogation in a thin sample slice, typically through a transparent cover slip. In this contribution we present a thorough study of the applicability of Raman spectroscopy for the described task. The obtained results clearly demonstrate the successful feasibility of the chosen method for a) a clear distinction between different media, b) the elucidation of the chemical composition of a multicomponent medium and c) an unambiguous identification of real unknown samples by a distinct assignment to a previously recorded spectral library. This library database was built up by recording pure mounting agents and will be provided to the general public. In combination with a Raman spectrometer, it can be an invaluable tool for future curation and conservation endeavors devoted to microscope slide collections at natural history museums.

Formation of Zones with Maximum Supersonic Cavitation Intensity in Single-Component and Multicomponent Media

Experimental studies have been made on the formation of highly active cavitation zones in fluid media at high pressures (up to 6.5 MPa) and temperatures (up to 150°C) with the use of a high-power ultrasonic installation. It has been shown that attempts to increase the cavitation intensity in single-component and multicomponent media by increasing the power of the ultrasonic installation to above a certain limit lead to a strong degradation of the cavitation processes. This is due to the appearance of hydrodynamical flows generated by longitudinal vibrations of the installation radiator waveguide. Eliminating or weakening such flows makes it possible to increase markedly the efficiency of cavitation treatment by increasing the medium pressure (in the range of 0.5–1.5 MPa) and choosing the optimum ratio between the temperature of the medium and the power of the ultrasonic installation (specific acoustic power of the radiator). We recommend to use for the cavitation intensity index the acoustic activity of the cavitation zone (acoustic noise amplitude in the frequency range of 200 kHz–10 MHz), as well as its physical activity determined by the destruction rate of thin-layer indicators.

Equations for the evolution of a growing or evaporating free microdroplet under nonstationary conditions of diffusion and heat transfer in a multicomponent vapor–gas medium

A set of equations has been derived for the nonstationary composition, size, and temperature of a growing or evaporating multicomponent microdroplet of a nonideal solution under arbitrary initial conditions. Equations for local nonstationary diffusion molecular and heat fluxes in a mixture of a multicomponent vapor with a noncondensable carrier gas have been obtained within the framework of nonequilibrium thermodynamics with allowance for hydrodynamic flow of the medium. The derived closed set of equations takes into account the nonstationarity of the diffusion and heat transfer, effect of thermodiffusion and other cross effects in the multicomponent vapor–gas medium, the Stefan flow, and droplet boundary motion, as well as the nonideality of the solution in the droplet. The general approach has been illustrated by the consideration of the multicomponent medium at low concentrations of vapors taking into account its thermal expansion due to the Stefan flow in the case of a nonstationary diffusion regime of the nonisothermal condensation growth of a one-component droplet.

A simple way to model the pressure dependency of rock velocity

Modeling the pressure dependency of rock velocity is important for interpreting and comparing the seismic and earthquake data from different depths. This study develops a multicomponent differential effective medium model for the elastic properties of porous rocks with two types of pores in the grain background without mixing order. The developed model is applied to modeling the pressure dependent elastic velocity of porous rocks by incorporating the variation of stiff and compliant porosity as a function of pressure. The pressure dependent stiff and compliant porosity were inverted from the measured total porosity under pressure using a dual porosity model, and the unknown constant stiff and compliant pore aspect ratios were inverted by best fitting the modeled velocity to the measured data. Application of the approach to a low porosity granite and a medium porosity sandstone sample showed that the pressure dependency of rock velocity can be satisfactorily modeled by the developed model using the pressure dependent stiff and compliant porosity and carefully estimated stiff and compliant pore aspect ratio values.

Continuum radiative heat transfer modeling in multi-component anisotropic media in the limit of geometrical optics

Continuum-scale equations of radiative transfer and corresponding boundary conditions are derived for a multi-component anisotropic medium consisting of components in the range of geometrical optics. The derivations are obtained by employing the volumeaveraging theory. This study generalizes the previous derivations obtained for multi-component isotropic media.

Dairy wastewater utilization: separation of whey proteins in membrane and chromatographic processes

Dairies are obligated to utilize whey after cheese production. From an environmental protection point of view, the high content of lactose and proteins in post-production wastes, like whey, is harmful for the environment. From another point of view, whey is a source of very valuable, active proteins, particularly lactoferrin and serum albumin. Their modulatory potential is exhibited in their pure form and improves after partial, controlled hydrolysis. Unfortunately, the fractionation of this multicomponent medium is not an easy task. The paper describes an integrated process of fractionation of whey proteins. After the first step of treatment based on membrane techniques, the concentrated, most valuable whey proteins were subjected to a few steps of chromatographic separation. The separation properties of the ultrafiltration membranes were unexpected. The typical cut-off boundary was shifted in the direction of components having a lower molecular weight. After laboratory-scale testing, a concept for an industrial-scale process for the isolation of the most valuable whey proteins with purities of nearly 100% was elaborated.

Surface defects formation on strained thin films growing via chemical reaction: a model

We investigated in a general way evolution of the elastic flat surface of the crystal during its growth from multicomponent media. The morphological instability caused by mechanical stress has been demonstrated and conditions under which a multicomponent thin film retains its shape have been found. As an example, we have analyzed growth of GaN on different substrates and discussed the impact of III/V ratio on the stability of the GaN epitaxial film growing by HVPE.

Polarization interactions in multi-component defocusing media

We study dark–bright soliton interactions in multi-component media such as nonlinear optical media in the defocusing regime and repulsive Bose–Einstein condensates. This is achieved using the recently developed formalism of the inverse scattering transform for the defocusing multi-component nonlinear Schrödinger equation with non-zero boundary conditions. We show that, generically, these interactions result in a non-trivial polarization shift for the bright components. We compute such polarization shift analytically and compare it to that in focusing two-component nonlinear Schrödinger systems.

Function evaluation of the molecular scattering angle in multicomponent gaseous medium

The molecular interaction potential (2(n+3),6) for the multicomponent gaseous medium is proposed. To compute the values of a function of scattering angle, an asymptotic analysis is performed that permits the explicit expressions for this function to be obtained. The trajectories of molecules described on a set of real and complex numbers are first considered.

Destruction of cylindrical ampoules containing solid phase reaction mixtures under explosive loading

Peculiarities of solid-phase synthesis are experimentally and numerically investigated in the aluminum-sulfur and aluminum-teflon mixtures placed in cylindrical ampoules under explosive loading. In the experiments, the parameters of explosive loading are chosen close to those that are commonly used for explosive compaction of inert porous fillers in cylindrical ampoules. The experimental results show that cylindrical ampoules are damaged when a mixture capable of ultrafast exothermic reactions is used as filler under explosive loading. To find the reasons of ampoule damage, the numerical computations are carried out by the finite element method based on the model of a multicomponent medium. The synthesis reaction in the mixture is described using the phenomenological model of irreversible chemical reactions based on zero-order kinetics. Simulation of porous mixture compaction is carried out using the kinetic model of the active type, which determines the growth or collapse of pores continually changing the material properties and causing stress relaxation. The sharp increase in pressure is found in the bottom part of the ampoule after reflection of the shock wave from the bottom lid of the ampoule in the form of a compression wave, which is accompanied by increasing the rate of chemical reactions. The high rate of heat release during chemical reactions in the bottom part of the ampoule leads to the formation of gas phase, which leads to further increase in pressure and fracture of the ampoule.

Morphological stability criterion for a spherical crystallization front in a multicomponent system with chemical reactions

The morphological stability of a spherical crystal growing from a multicomponent medium due to the chemical reaction has been investigated. The approach used in this study is applicable to the case where the chemical compound forming the crystal does not exist in a gaseous (dissolved) form (for example, GaN). The investigation has been performed according to the classical scheme by the expansion of an infinitesimal deviation of the crystallization front from the initial shape into a series with the subsequent calculation of the time dependence of the coefficients of the expansion. It has been found that there is a similarity of the stability criteria for single-component and multicomponent crystals. In a multicomponent system, the single-component supersaturation analog determining the stability of a particle is the affinity of the chemical reaction. It has been shown that the morphological stability can also depend on the formation of other phases on the surface of the initial crystal, which is excluded in a single-component medium.