{"title":"Study of pressure wave dynamics in a channel with a spherical bubble cluster","authors":"S.R. Fattakhov","doi":"10.21662/mfs2023.1.004","DOIUrl":"https://doi.org/10.21662/mfs2023.1.004","url":null,"abstract":"The features of wave propagation in a bubbly liquid are associated with the combined interaction of nonlinear, dispersive, and dissipative effects. In a liquid with bubbles, the properties of a practically incompressible liquid, which is a carrier phase, change dramatically with a small volume (and even more so, mass) addition of gas (bubbles), which is a dispersed phase. The peculiarity of bubbly liquids is due to their high static compressibility while maintaining a high density close to that of the liquid, which in turn leads to a low equilibrium speed of sound. In this paper, we study two-dimensional axisymmetric wave perturbations in a channel with water containing a spherical cluster filled with a water-air bubble mixture and located at one of the end boundaries. Based on the results of numerical calculations, the dependence of the maximum pressure amplitude formed in the channel on the geometrical parameters of the cluster is analyzed. It has been established that the presence of a near-end bubble cluster can significantly both increase and decrease the effect of the wave signal incident on the wall, depending on the size of the cluster and its characteristics.","PeriodicalId":309215,"journal":{"name":"Multiphase Systems","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132658902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Acoustic stability of a superheated liquid with vapor–gas bubbles","authors":"A. Safiullin","doi":"10.21662/mfs2023.1.005","DOIUrl":"https://doi.org/10.21662/mfs2023.1.005","url":null,"abstract":"It is known that the physicochemical properties of liquids in a metastable state are mainly determined by the presence of various inclusions in their composition, for example, gas bubbles or solid particles, and it has been established that, under mechanical and thermal equilibrium, the state of a liquid with gas bubbles distributed over the volume due to the action of capillary forces at the interface, always overheated. In this paper, we consider the propagation of weak perturbations in a superheated water-air bubbly medium, when, in addition to water vapor, the bubbles contain an inert gas (for example, air) that does not participate in phase transitions. To describe the problems under consideration, a system of equations is used, which consists of the laws of conservation of mass, the number of bubbles, momentum equations, the Rayleigh–Lamb equation, the equation of heat conduction and diffusion. The solution is sought in the form of a damped traveling wave. Based on the solution of the dispersion equation, maps of the stability zones of the systems under consideration were constructed depending on the magnitude of the liquid overheating on the plane ”volume content — bubble radius“.","PeriodicalId":309215,"journal":{"name":"Multiphase Systems","volume":"271 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131527294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
V. Shagapov, R. Bashmakov, N. O. Fokeeva, A. A. Shammatova
{"title":"Fluid Pressure Dynamics in a Hydraulic Fracture during Transient-Well-Operation Modes","authors":"V. Shagapov, R. Bashmakov, N. O. Fokeeva, A. A. Shammatova","doi":"10.21662/mfs2022.1.009","DOIUrl":"https://doi.org/10.21662/mfs2022.1.009","url":null,"abstract":"At present, hydraulic fracturing is one of the most effective methods for intensifying hydrocarbon production. The paper describes the transient-well-operation modes of the well, establishes a connection between the changing fluid flow in the well and the pressure in the fracture and reservoir. With this purpose, a solution is found to the integro-differential equation that describes the change in pressure in the hydraulic fracture with a known change in pressure in the well or at a given flow rate. Based on the bottomhole pressure change data for a short-term pump operation that maintains a constant flow rate and subsequent pump shutdown (Π-shaped flow rate change), it is convenient to determine the characteristics of a hydraulic fracture using the formulae proposed in the paper. The results of the work can be used in hydrodynamic studies of wells.","PeriodicalId":309215,"journal":{"name":"Multiphase Systems","volume":"127 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114336913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stress-strain state of an underwater offshore oil pipeline taking into account changes in ground conditions and operating parameters","authors":"R. M. Zaripov, R. B. Masalimov","doi":"10.21662/mfs2023.1.003","DOIUrl":"https://doi.org/10.21662/mfs2023.1.003","url":null,"abstract":"The article briefly describes the construction of concreted pipes used in recent years in the construction of offshore gas and oil pipelines. In the formulation of the problem of the stress-strain state of an underwater offshore oil pipeline, the calculated section is conditionally divided into three parts: the middle blurred bare part and the underground parts adjacent to it on the left and right. A brief description of the solution of the problem is given. The results of calculations of the main characteristics of the stress-strain state of the underwater section of the offshore oil pipeline are presented in the form of a diagram of the pipeline deflection and bending stresses, as well as in tables through extreme values of deflection and bending stresses from span and support bending moments for various values of operating parameters and soil conditions in adjacent underground parts. By analyzing the stress- strain state of the calculated section of the offshore oil pipeline, the critical values of the operation parameters and the corresponding critical values of the equivalent longitudinal axial force were determined.","PeriodicalId":309215,"journal":{"name":"Multiphase Systems","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125119000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Collapsing motions of a diatomic gas whose density depends only on time","authors":"I. I. Gumerov, A.A. Katashova, Y. Yulmukhametova","doi":"10.21662/mfs2023.1.002","DOIUrl":"https://doi.org/10.21662/mfs2023.1.002","url":null,"abstract":"One submodel of gas motion with a linear velocity field is considered in the paper. Namely, a submodel that defines the movements of a polytropic gas with a density that depends only on time. A polytropic gas is a gas for which the internal energy is a function linear in temperature. The submodel under consideration is given by a system of ordinary differential equations of the 22nd order for unknown functions. These functions characterize the movements of gas particles and determine the type of density, pressure and entropy functions. The exact solution is sought for a special case, namely for a diagonal linearity matrix. Two new exact solutions have been found. The type of vector functions of velocity, density and pressure are determined. By the form of the velocity function, the world lines of motion of gas particles are recorded. In the three-dimensional space of coordinates x, y, z, the trajectories of gas particles for various initial data are constructed. A qualitative analysis of the movement was carried out. The Jacobi matrix is constructed. The moments of collapse of gas particles are determined by the value of the Jacobian. Both solutions have collapse: collapse on a straight line and collapse at a point.","PeriodicalId":309215,"journal":{"name":"Multiphase Systems","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121300518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Rakhimov, A. Akhmetov, A. A. Valiev, K. V. Danilko, S. Sametov, D. Khismatullin
{"title":"To the issue of the mechanism of cell migration","authors":"A. Rakhimov, A. Akhmetov, A. A. Valiev, K. V. Danilko, S. Sametov, D. Khismatullin","doi":"10.21662/MFS2019.1.003","DOIUrl":"https://doi.org/10.21662/MFS2019.1.003","url":null,"abstract":"The paper presents the experimental and theoretical aspects of studying the migration of cancer cells through narrow microchannels when interacting with a chemical substance — an attractant. Chemical agents were injected directly from the respective separate reservoir via hydrostatic head. The presence of migration channels of different sizes allowed us to analyze the migration abilities inherent in the cells. Experimental studies on the migration of cancer cell lines were carried out using a microfluidic binary migration cell. It consists of two chambers 50 μm deep, connected by a series of narrow microchannels 10 μm high. The chambers are connected to the tanks from which cancer cells and activating media come. The model features smooth transitions from all tanks to microchannels to prevent accumulation of microbubbles and cells, the presence of a restrictive barrier between a chemoattractant container and a nutrient medium to reduce the effect of capillary forces, sealing the supply channels and cells with cells using a glass plate glued on top. In a series of experiments, the ability of epithelial-like cells of the metastatic prostate cancer DU145 to migrate in the migration microfluidic system developed by us was revealed. The nature of migration depends on the width of the channel and the location of the cells at the time of adding the chemical agent. In wider channels, cells adhere more slowly and are able to perform rolling movements. In narrower channels, the cells are spread over the glass. The mathematical model of concentration-capillary movement, which is a system of equations of the dynamics of an incompressible viscous fluid, written separately for the cell contents and for its environment, is considered as the basis for a theoretical study of cell migration.","PeriodicalId":309215,"journal":{"name":"Multiphase Systems","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130184968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The problem of melting ice in a porous medium saturated with ice and gas","authors":"M. N. Zapivakhina, D. A Umerov","doi":"10.21662/MFS2019.1.008","DOIUrl":"https://doi.org/10.21662/MFS2019.1.008","url":null,"abstract":"The problem of ice formation in a dry, cold, porous medium saturated with ice and gas (air) when pumping warm water is considered in a flat one-dimensional self-similar formulation. The task was considered in volume area. During the injection of warm water from the beginning deep into the reservoir, it spread in a volume region that will divide the reservoir into 3 zones. The first zone was filled with water, the second zone was filled with ice and water, and the third zone was filled with ice and gas. To describe the process of heat and mass transfer, the following hypotheses were used: the temperature of the saturated substance (water, ice or gas) is equal to the temperature of the porous medium; ice and skeleton still; water, ice and skeleton of the reservoir are incompressible; skeletal porosity is constant. On the basis of constructed self-similar solutions, a numerical analysis was performed illustrating the effect of the initial parameters of a dry porous medium saturated with ice and gas, as well as the temperature of the injected water on the temperature and pressure distribution in the porous medium. It has been established that an increase in the temperature of the injected water does not lead to a significant increase in the area of ice decomposition. It is also established that if the pressure of the injected water is increased, this will not lead to a large increase in the area of ice decomposition. However, based on the results obtained, it can be seen that the speed of movement of the melting boundary increases, in particular, as the pressure increases by pe=0.05 MPa, the intermediate region increases by one and a half times. It was found that it is economically more profitable to pump water with a lower temperature, because water with a higher temperature slightly increases the freezing area of the porous soil.","PeriodicalId":309215,"journal":{"name":"Multiphase Systems","volume":"389 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133121829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Investigation of acoustic scattering from a pair soundproof spheres under external influence","authors":"E. Nasibullaeva","doi":"10.21662/mfs2019.1.006","DOIUrl":"https://doi.org/10.21662/mfs2019.1.006","url":null,"abstract":"A mathematical model extension is presented and numerical studies were made for the problem of acoustic scattering from two soundproof spheres (the case of hard spheres) with an arbitrary acoustic impedance under the action a spherical wave from a monopole radiation source arbitrarily located in space. The case of two spheres is of practical interest, since, on the one hand, the scattered fields from the spheres interact with each other, and on the other hand, the interaction is simple enough for it to be studied in detail. When solving the Helmholtz equations, a numerical technique based on the fast multipole method is used, which allows to achieve high accuracy of the results obtained with minimal computer time. The testing of the algorithm was carried out on the basis of the known data (from the literature) of the response on the surface of one of the spheres in the case when the axis connecting the monopole radiation source and the center of the first sphere is perpendicular to the axis connecting the centers of the two spheres. The pressure distribution around the spheres is investigated for different values of the distance between the centers of the spheres and the arbitrary location of the monopole radiation source in space. It is shown that with certain parameters of the system, the presence of a second sphere can lead to the appearance of an increase or decrease zone of pressure. The obtained results will further allow generalizations of the mathematical model to the cases of acoustic scattering from a pair of sound-permeable spheres (cases of gas bubbles or liquid droplets) and many spheres (both coaxially and arbitrarily arranged in space), and can also be used for test calculations during verification numerical solution of these generalized problems.","PeriodicalId":309215,"journal":{"name":"Multiphase Systems","volume":"420 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122947397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Analytical studies of suspension acoustics","authors":"M. Galimzyanov, V. Shagapov","doi":"10.21662/mfs2019.1.004","DOIUrl":"https://doi.org/10.21662/mfs2019.1.004","url":null,"abstract":"The one-dimensional unsteady flow of the suspension is considered taking into account the standard assumptions for this problems: the mixture is monodisperse, there is no crushing and sticking of particles, viscosity and thermal conductivity are essential only in the process of interfacial interaction. The mixture supposed perfect. The particles are taken absolutely solid and spherical, and the liquid is linearly compressible. The frictional force acting on a single spherical particle is taken into account. The solution to the original system is sought in the form of a traveling wave. On the basis of one-dimensional unsteady equations of fluid flow with solid particles dispersion relations are written out and formulas for phase velocities are derived. Formulas for the attenuation coefficient of the perturbation frequency are got. It has been established that at low frequencies, depending on the magnitude of <i>ρ̃<sup>0</sup><sub>p0</sub>=ρ<sup>0</sup><sub>p0</sub>/ρ<sup>0</sup><sub>ℓ0</sub></i> the equilibrium speed can be higher or lower than the speed of sound in the carrier phase. If the dispersed phase is heavier than the carrier phase (<i>ρ̃<sup>0</sup><sub>p0</sub>>1</i>), then the equilibrium velocity exceeds the speed of sound. This is due to the fact that at low frequencies, when velocity equilibrium is realized, the compressibility of the mixture occurs only owing to the carrier phase, and the mixture becomes heavier (inertial) because of the content of the dispersed phase at (<i>ρ̃<sup>0</sup><sub>p0</sub>>1</i>). When (<i>ρ̃<sup>0</sup><sub>p0</sub><1</i>), the mixture in contrast is lighter than the carrier phase, and the equilibrium velocity becomes higher than the speed of sound. At high frequencies the sound velocity does not depend on <i>ρ̃<sup>0</sup><sub>p0</sub></i> and is equal to the sound velocity for the carrier phase.","PeriodicalId":309215,"journal":{"name":"Multiphase Systems","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131198159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Convection of thermoviscouse fluid in a cell heated from the side","authors":"V. Kuleshov, K. V. Moiseev","doi":"10.21662/MFS2019.1.010","DOIUrl":"https://doi.org/10.21662/MFS2019.1.010","url":null,"abstract":"The work is devoted to the peculiarities of free-convective flow of liquids with viscosity temperature anomaly (the presence of extremes on the viscosity curve). Examples of such liquids are polymer solutions, metal melts, well-purified liquid sulfur, and other fluids. The mechanism of the anomalous viscosity behavior of such liquids (in the case of polymers) can be explained by polymerization and depolymerization reactions. At a certain temperature interval, the molecules of a substance interlock, forming long chains and, as a result, increasing the viscosity, then when the upper limit polymerization temperature is reached, the reaction begins that is reverse to the polymerization, which proceeds according to the chain mechanism and results in the sequential cleavage of molecules from the chain and leads to a decrease in viscosity . The features of behavior of such environments are currently not well understood and require increased attention to experimental and theoretical studies, especially now, mainly due to the intensive development of computer technologies and numerical modeling. Based on computational experiments on the process of free convection of a liquid with a Gaussian dependence of viscosity on temperature, the possibility of the existence of isolated regimes of convection of a liquid in a square cell heated from the side is shown. It was assumed that the viscosity function has one extremum and is unambiguously described by two parameters: the ratio of the highest to the lowest viscosity at a given temperature range and the degree of fullness of a given temperature range. As a mathematical model, a system of equations was used in the Oberbeck–Boussinesq approximation. For the numerical solution of the system of equations, the control volume method with the SIMPLE procedure is modified and implemented.","PeriodicalId":309215,"journal":{"name":"Multiphase Systems","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132407629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}