Nonstationary Mass Transfer Research Articles

Complete integrability of the problem of full statistics of nonstationary mass transfer in the simple inclusion process.

The simple inclusion process (SIP) interpolates between two well-known lattice gas models: the independent random walkers and the Kipnis-Marchioro-Presutti model. Here we study large deviations of nonstationary mass transfer in the SIP at long times in one dimension. We suppose that N≫1 particles start from a single lattice site at the origin, and we are interested in the probability P(M,N,T) of observing M of the particles, 0≤M≤N, to the right of the origin at a specified time T≫1. At large times, the corresponding full probability distribution has a large-deviation behavior, -lnP(M,N,T)≃sqrt[T]s(M/N,N/sqrt[T]). We determine the rate function s exactly by uncovering and utilizing complete integrability, by the inverse scattering method, of the underlying equationsof the macroscopic fluctuation theory. We also analyze different asymptotic limits of the rate function s.

Modeling of Non-Stationary Mass Transfer Process in Groundwater

Purpose. Infiltration of contaminated water and accidental spills of chemically hazardous substances into groundwater lead to the formation of large zones of man-made pollution in aquifers. Therefore, it is important to develop protection systems against groundwater pollution. To analyze the effectiveness of such protection systems at the design stage, it is necessary to have scientifically based information on the dynamics of changes in groundwater contamination zones. Such information can be obtained using the method of mathematical modeling. The study aims to create a numerical model for calculating the non-stationary process of geomigration when using chemical protection of groundwater from pollution. Methodology. To describe the dynamics of groundwater flows, two filtration equations are considered, which allow mathematical modeling of the filtration process both for solving planned problems and for solving problems of specialized filtration. A two-dimensional geomigration equation was used to analyze changes in groundwater quality. This equation takes into account the convective transfer of impurities in the filtration flow, dispersion, and the intensity of impurity infiltration into the groundwater flow. This equation is also used to calculate the movement of the neutralizer in groundwater. The numerical integration of the filtration equation was performed using finite difference methods. An implicit splitting scheme was used to numerically integrate the geomigration equation. Findings. A fast-applicable numerical model for calculating groundwater dynamics has been built. The model is also a platform for solving another important task – the calculation of geomigration processes. A numerical model for calculating the unsteady-state geomigration process is proposed, which makes it possible to assess not only the process of formation of contamination zones in the groundwater flow, but also to determine the effectiveness of the method of neutralizing the impurities in the groundwater flow. Originality. Effective numerical models for rapid assessment of changes in groundwater dynamics and quality under the influence of anthropogenic sources have been developed. These models take into account a set of important physical factors that affect the process of geomigration and the process of neutralizing the impurity in the groundwater flow. Practical value. A computer program has been developed that allows determining the effectiveness of the process of neutralizing an aggressive impurity in groundwater by a computational experiment to protect it from anthropogenic pollution.

Nonstationary Mass Transfer of Nutrient Medium for Microorganisms in Mixed Gels

Nonstationary Mass Transfer of Nutrient Medium for Microorganisms in Mixed Gels

Physico-Mechanical Foundations of Theoretical and Engineering Investigation on the Development to Corrosion-Resistant Materials in Buried Structures of Coastal Zones

The paper considers methods of physical and mathematical modeling that can be used to describe the processes of non-stationary mass transfer of free calcium hydroxide in buried concrete and reinforced concrete structures of coastal zones. The authors proposed a mathematical model of mass transfer in an unrestricted two-layer plate in the form of a system of parabolic partial differential equations with boundary conditions of the second kind at the "concrete-liquid" interface and of the fourth kind at the "concrete-soil" interface. In terms of the results of experimental studies of the mechanisms for reducing the quality of concrete due to exposure to sulfate and acidic environments, using the obtained solutions of the mathematical model, it becomes possible to select the optimal composition of concrete with high anticorrosion properties.

Forecast of the Durability of Shore Structures Made of Reinforced Concrete

This paper considers the basic methods of physical-mathematical modeling that are used to describe the processes of non-stationary mass transfer of "free calcium hydroxide" in concrete structures placed in a liquid environment with a defined flow rate. The boundary value problem of "free calcium hydroxide" mass conductivity in dimensionless variables is obtained. To demonstrate the possibilities of the obtained solution, we will carry out a numerical experiment: in which the fluctuation in the field of dimensionless concentrations by the different values of the Fourier number, in accordance with the theory of similarity, will be considered as an indicator of the process time. The study indicated the results of calculating the concentration distributions "free calcium hydroxide" over the dimensionless thickness of the concrete structure at Fourier numbers 0.01; 0.1; 0.2; 0.5 and 1. The study also provides an example of determining the time of reaching the coastal structure surface critical concentration "of free calcium hydroxide" leading to the beginning of high-basic cement concrete. Analysis of the solution also makes it possible to determine the duration of the service life of a reinforced concrete structure, which is determined by the processes occurring at the interface: in concrete - mass conductivity (k), and in the liquid phase - mass transfer (β).

Expert express assessment of the impact of heat and mass transfer processes on the residual life of the WWER-1000 reactor vessel due to cyclic damage

Ukraine remains a country dependent on nuclear energy for both heat supply and satellite supply. In cities close to nuclear power plants, electric heating from the electricity they produce is appropriate. On the other hand, Ukraine is the only country in the world where the worst accident at a nuclear power plant occurred at the Chernobyl NPP Unit 4 on the night of April 26, 1986. Another characteristic feature of Ukraine's nuclear energy is the significant number of power units with exhausted project resources - the so-called "old" power units. Their wear is associated with the influence of heat and mass transfer processes, which lead to periodic thermal deformation of the elements, which causes cyclic damage. An example of expert rapid assessment of the residual life of a specific reactor vessel WWER-1000 is given taking into account the combined action of non-stationary heat and mass transfer and mechanical processes. A detailed express calculation of cyclic (tired) damage to the metal of the WWER-1000 reactor vessel due to the dangerous emergency mode has been performed. The WWER-1000 reactor is the last most widespread and most powerful water-water nuclear reactor of the former USSR, operated on 13 of the 15 operating power units of Ukrainian nuclear power plants (NPPs) - Zaporizhia, Rivne, Khmelnytsky and South Ukraine (SUNPP). The reactor is the most important indispensable element of a nuclear power plant, which determines its safety and resource. Given the design resource and the dates of commissioning of Ukrainian NPP units, the issue of rapid expert assessment of the technical condition of WWER-1000 hulls is quite relevant. Of course, modern engineering has the full range of tools needed to perform such estimates, from powerful computers to advanced computing software. But the known and inevitable costs of modern engineering - complex and time-consuming modeling and calculations. Experience has shown that a certain "reasonable" combination of the use of relatively simplified "light" calculation methods allows us to assess the safety, strength and service life of WWER-1000 reactors very quickly and with the necessary accuracy acceptable for expert opinion. The publication considers as an example the real emergency situation of October 22, 1985 and the WWER-1000 reactor of SUNPP Unit 1. Since this emergency situation led to rapid cooling of this reactor, the calculation of the effect of cyclic damage of reactor steel on the strength and reliability of the reactor vessel is shown. This example and the consideration of the real emergency situation demonstrates the effectiveness and acceptability of the use of estimated expert rapid assessments to accurately determine the reliability and safety of such critical elements of nuclear power plants as nuclear reactor buildings.

Heat and mass transfer in laminated glued timber bar

The main prerequisites for the development of wooden housing construction in Russia are given, which determined the goal of this study - to develop a mathematical model of heat and mass transfer (moisture transfer) in glued timber for rational design of enclosing structures. Lamellas can be classified as a capillary ‒ porous body. leaning on theory of academician A.V. Lykov, the formulation of the problem of heat and mass transfer in a multilayer glued laminated timber is presented a system of equations describing non-stationary heat, mass and pressure transfer under real possible operating conditions of enclosing structures is considered. An analytical method is proposed for calculating both individual lamellas and the entire multilayer glued beam. The proposed technique allows the method of solving the inverse problem to directly calculate the resistance value of the entire bar from the unsteady temperature field. The system of equations describing the process is nonlinear and analytically insoluble. To solve the problem, a combined method for solving boundary value problems of heat transfer was used, which is based on a combination of elements of analytical and numerical solutions. A feature of the problem under consideration is that the middle lamella has heat-conducting inclusions in the form of a bough. Method is that the entire heat transfer process is divided into a number of small time intervals. Within each interval, we assume that the temperature is constant at the interface between layers and a constant heat flux through the contacting surfaces, i.e. perfect thermal contact.

Non-stationary mass transfer of oil-water mixture in reservoirs with a system of horizontal wells

The paper presents a physical and mathematical model of quasi-three-dimensional non-stationary filtration of a water-oil mixture in a system of horizontal wells and the corresponding numerical calculation method. Based on them, a computer program was created, designed to solve a number of scientific and production problems. The developed model and program are aimed at theoretical and numerical study of the processes of mass transfer of the oil-water mixture in the field of analysis, maintenance and development of natural formations with high-viscosity oil deposits. The results of numerical experiments for calculating the two-phase flow of an incompressible fluid in a reservoir are given as an example of a real field, located in the north of Western Siberia. The paper proposes an approach to discretization of the computational domain, based on the construction of a dynamic computational grid in a natural semi-fixed coordinate system. For the first time, the problem of calculating two-phase mass transfer using a semi-fixed natural grid and an analytical expression for the flow rates of phases in current streams of a found shape has been solved. Based on the proposed model, calculation and parametric studies of various modes of field development with a system of parallel horizontal wells were performed.

Nonstationary Mass Transfer and Controlling the Process During the Laminar Motion of a Liquid in Packed-Column Apparatuses

Approximate solutions have been obtained for the equations of nonstationary mass transfer in packed-column apparatuses, and a method has been proposed to calculate them under the conditions of laminar motion of a liquid phase and displacement of a gas. On the basis of the nonstationary-mass-transfer equations, a problem of control of packed-column apparatuses has been solved. The solutions of the equations have been obtained in the form of an expansion of functions in a trigonometric series; formulas to determine the values of terms in the series have been presented. Initial conditions for the equations of nonstationary mass transfer are equations of a stationary process. Exact and approximate solutions for the stationary-mass-transfer equations have been obtained based on which an algorithm has been proposed for designing packed-column apparatuses. A calculation of the process of absorption of an acetone vapor from air by water has been carried out. Plots of the control and of the concentration change in controlling and with different perturbations have been presented.

Численное исследование нестационарного тепломассообмена в криогенном резервуаре долговременного хранения с подвижной границей раздела фаз

Численное исследование нестационарного тепломассообмена в криогенном резервуаре долговременного хранения с подвижной границей раздела фаз

LOCAL PARAMETERS OF THE SURFACE ROUGHNESS OF ELECTROCHEMICALLY DEALLOYED Ag-Pd ALLOYS

Local characteristics of surface roughness of the polycrystalline Ag-Pd solid solutions (4 and 8 at. % Pd) which underwent potentiostatic electrochemical dealloying in an acidic nitrate aqueous solution were determined by scanning electron and atomic force microscopy. A qualitative analysis of the SEM and AFM micrographs demonstrated substantial morphological roughening of the surface of Ag-Pd alloys. This results from the formation of hollows and cracks caused by selective leaching of electronegative silver and recrystallization of electropositive palladium into its highly-developed phase. A quantitative analysis of the AFM-data allowed us to determine the numerical values of the main local roughness characteristics of anodically modified alloys. The negative value of the coefficient of surface asymmetry indicates the formation of deep cavities during the dealloying process. The recorded mean roughness generally depends on the AFM-scanning zone, but it stabilizes if the scan zone exceeds several tens of micrometers. The roughness of dealloyed Ag-Pd systems is of micro- and nano-size and increases with anodic potential and electric charge of the electrochemical modification of both studied Ag4Pd and Ag8Pd alloys. This effect can be accounted for by a significant rise in the anodic dissolution rate of silver from the alloys in the overcritical region of polarization, resulting in the formation of deeper surface defects. An increase in the average height of surface irregularities with modification time conforms to the square root law, confirming the non-stationary mass transfer kinetics of the selective dissolution process. Variation of the anodic potential and electric charge makes it possible to find the optimal conditions for the electrochemical synthesis of electrode Ag-Pd materials with given values of arithmetic mean and root-mean-square roughness. The assumption that harmonic sinusoidal function represents the Ag-Pd surface microprofile proved the linear dependence of the roughness factor on dealloying time.

Modeling of Conductive Drying Polygraphic Materials of Capillary-Porous Colloidal Structure

An approach to studying the processes of thermal treatment (heating, drying) of some types of polygraphic materials is proposed, which is based on the theory of nonstationary heat and mass transfer. The approach has been approbated for the process of conductive (contact) drying of a board sheet. The results of numerical investigations are applicable in practice in studying the processes of heat and moisture transfer in capillary-porous colloidal structures, as a result of which optimization of the technological regimes of drying-out and provision of the required qualitative characteristics of the products is possible for both polygraphic and other industrial areas.

Wave approach for modeling pressure swing adsorption

A new approach to modeling of the pressure swing adsorption (PSA) based on a wave method for calculating non-stationary periodic mass transfer processes is proposed. The analysis of solutions for plants designed to produce oxygen from air is given. The conditions necessary for highly efficient operation of PSA plants are formulated. The results of calculations for various brands of zeolites are followed, allowing optimizing a choice of zeolite for the set working conditions.

КОНЦЕПТУАЛЬНІ ОСНОВИ АНАЛІЗУ ТЕПЛО- І МАСОПЕРЕНОСУ У ШАРУВАТИХ КАПІЛЯРНО-ПОРИСТИХ ТІЛАХ

The phenomena of contact heat and mass transfer between materials of different physical and chemical structures are quite widespread in the technological processes of various industries, which leads to the need for further studies of their kinetics, for example, when drying capillary-porous bodies. It has been established that many researchers studied non-stationary problems of heat and mass exchange of a piecewise-homogeneous unbounded two-layered plate with the surrounding medium, but some details of these processes have not yet been established. The authors of the paper give an analytical solution of the non-stationary problem of heat and mass conductivity of a piecewise homogeneous unbounded double-layered plate, which, with one surface, takes part in convective heat and mass transfer with the surrounding medium with constant potentials of heat and mass transfer, while the other surface is heat and moisture-insulated . This model adequately describes the processes of heat and mass exchange in a canvas, exhibited in the museum's premises, to which the flow of visitors moves. The first layer simulates the paints that are applied of the picture, and the second one – directly the basis of the painting (the art painting itself). As a result of the solution of the problem by mathematical physics, the influence of individual heat and mass transfer criteria on heat and mass transfer in this plate is established. The results obtained by the authors can be used to specify and improve the existing engineering methods for calculating the parameters of nonstationary heat and mass transfer in layered capillary-porous bodies, as well as to develop more advanced algorithms for controlling the artificial microclimate of museum premises on the basis of modern information technologies and fuzzy logic controllers / controllers, as in the stages of designing (constructing) artificial intelligence systems for the management of the climate of museum premises, and in their real modes their operation.

Flows and Heat Exchange in a Geothermal Bed in the Process of Extraction of a Vapor–Water Mixture from It

With the use of the finite-difference method, a nonstationary nonlinear problem on the heat and mass transfer in a geothermal bed in the process of extraction of a vapor–water mixture from it was solved numerically with regard for the heat exchange between the bed and the surrounding rocks. The results obtained were analyzed and compared with the results of earlier investigations. It was established that the heat exchange between the bed and its roof and bottom influences the heat and mass transfer in the neighborhood of a producing well in it. It is shown that this heat exchange increases somewhat the pressure (temperature) of the phase transition of the heat-transfer medium and changes its saturation with water. At the stage of stationary heat and mass transfer in the bed, this change leads to a decrease in the water saturation of the heat-transfer medium, i.e., to an additional evaporation of water from it. However, at the stage of substantially nonstationary heat and mass transfer in the bed, the pattern is more complex: within certain time intervals, the heat exchange in separate regions of the bed decreases the content of vapor in the heat-transfer medium (increases its saturation with water). Moreover, in both the cases of absence and presence of heat exchange between the bed and the surrounding rocks, the distributions of the water saturation of the heat-transfer medium in the bed executes damped oscillations and, in so doing, approaches the stationary state.

Evaluation of Radiation Consequences of Releases in Accidents with Spills of Liquid Radioactive Materials in Areas with Forced Ventilation

This report focuses on assessment of radiation consequences of releases in accidents with spills of liquid radioactive materials in areas with forced ventilation. During the study, characteristic dependences between parameters of liquid radioactive materials and air exchange in areas with forced ventilation and associated radiation consequences were determined. The proposed approach is based on the theory of non-stationary heat and mass transfer in surface evaporation of liquid heated below the boiling temperature. The physical model includes: liquid radioactive material, steam-aerosol radioactive mixture, air of forced ventilation, airborne filters, and floor of the emergency area. The key aspects of the model are evaporation of liquid material, its removal with exhaust ventilation and partial trapping on airborne filters. It is considered that the steam-aerosol radioactive mixture is released to the environment after filters. The advantage of this model is the possibility to determine integral release of radionuclides to the environment and activity concentration of air in the emergency area at any moment after beginning of the accident, effective dose received by an adult during 14 days for a wide range of input thermodynamic and geometrical parameters, different operating modes of the ventilation system and different productivities of the filtering system. Results from assessment of radiation consequences for the selected accident are presented and the associated effect of filtering systems is analyzed.

Nonstationary Mass Transfer Near the Surface of a Cylindrical Body

The problem of nonstationary diffusion of the target component to a phase that is external relative to the surface of a cylindrical body has been formulated and solved analytically. From the found solution the dependences have been obtained for calculating the instantaneous mass transfer coefficient and the phase-contact-time mean mass transfer coefficient, on the basis of which the process of extraction of technological pollutants from fibrous materials has been analyzed.

Нестационарная модель тепломассопереноса при сублимации минеральных пленок в потоке эндогенного флюида

Нестационарная модель тепломассопереноса при сублимации минеральных пленок в потоке эндогенного флюида

Nonstationary mass transfer in a drying chamber–adsorber system under conditions of nonequilibrium adsorption of steam

Simulation of filtration and nonequilibrium adsorption of steam in an adsorber and a comparison of calculated and experimental data were carried out.

Effect of Quincke Rotation and Taylor Circulation on Mass Transfer from a Fluid Drop in a Constant Electric Field

We consider non-stationary convective mass transfer in a binary system comprising a stationary dielectric two-dimensional fluid drop embedded into an immiscible dielectric liquid under the influence of a constant uniform electric field. The partial differential equation of diffusion is solved by means of a similarity transformation, and the solution is obtained in a closed analytical form. Dependence of Sherwood number vs. the strength of the applied electric field is analyzed. It is shown that an electric field can be used for enhancement of the rate of mass transfer in terrestrial and reduced gravity environments.