[Текст] : статья / I.I. Ryzhkov // Lournal of Applied Mechanics and Technical Physics. - 2011. - Vol. 52, Iss. 4. - p. 560-570DOI 10.1134/S0021894411040080
. -
Аннотация: A model of vibrational convection of a binary mixture with the thermodiffusion effect is considered. The symmetries of model equations are found, depending on the values of physical parameters. A partially invariant solution, which describes separation of the binary mixture in a thermodiffusion column, is constructed and studied. The influence of streamwise vibrations on the flow regime and separation of the mixture is investigated.
Полный текст на сайте правообладателя
Доп.точки доступа:
Stepanova, I.V.; Степанова, Ирина Владимировна; Рыжков, Илья Игоревич
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Group properties and exact solutions of equations for vibrational convection of a binary mixture
Group classification for equations of thermodiffusion in binary mixture
/ I.V. Stepanova // Commun. Nonlinear Sci. Numer. Simul. - 2013. - Vol. 18, Is. 6. - P1341-1346, DOI 10.1016/j.cnsns.2012.10.013. - Cited References: 14. - Author thanks Prof. V.K. Andreev for formulation of the problem and attention to the work. This work is supported by the Integrational Grant No 44 and The Ministry of education and science of Russia, project 14.A18.21.2014.
. - 6. - ISSN 1007-5704
РУБ Mathematics, Applied + Mathematics, Interdisciplinary Applications + Mechanics + Physics, Fluids & Plasmas + Physics, Mathematical
Кл.слова (ненормированные):
Lie symmetry analysis -- Group classification -- Equivalence transformations -- Thermodiffusion -- Binary mixture -- Transport coefficients
Аннотация: Group classification problem is solved for equations of motion of a binary mixture under the buoyancy force and thermodiffusion effect. These equations are parameterized by five arbitrary functions of two arguments. The admissible Lie symmetry algebras of generators are found depending on arbitrary elements. These results are useful for analytical and numerical modeling of the convection in binary mixtures. (C) 2012 Elsevier B. V. All rights reserved.
Доп.точки доступа:
Stepanova, I.V.; Степанова, Ирина Владимировна
Кл.слова (ненормированные):
Lie symmetry analysis -- Group classification -- Equivalence transformations -- Thermodiffusion -- Binary mixture -- Transport coefficients
Аннотация: Group classification problem is solved for equations of motion of a binary mixture under the buoyancy force and thermodiffusion effect. These equations are parameterized by five arbitrary functions of two arguments. The admissible Lie symmetry algebras of generators are found depending on arbitrary elements. These results are useful for analytical and numerical modeling of the convection in binary mixtures. (C) 2012 Elsevier B. V. All rights reserved.
Доп.точки доступа:
Stepanova, I.V.; Степанова, Ирина Владимировна
Scaling of the inner electron diffusion region in collisionless magnetic reconnection
/ A. Divin [et al.] // J. Geophys. Res-Space Phys. - 2012. - Vol. 117. - Ст. A06217, DOI 10.1029/2011JA017464. - Cited References: 43. - The present work is supported partially by the Onderzoekfonds KU Leuven (Research Fund KU Leuven), by the NASA MMS grant NNX08AO84G and by the European Commission's Seventh Framework Programme (FP7/2007-2013) under the grant agreement 263340 (SWIFF project, www. swiff. eu) and 269198 - Geoplasmas (Marie Curie International Research Staff Exchange Scheme). Additional support is provided by RFBR grants 09-05-91000-ANF-a, 12-05-00152-a and 12-05-00918-a, Austrian Science Fund project T193-N16 and by SPSU grants 11.38.47.2011 and 11.38.84.2012. The simulations were conducted on the resources of the Vlaams Supercomputer Centrum (VSC) at the Katholieke Universiteit Leuven. The authors wish to thank the reviewers for their comments that helped to improve the manuscript.
. - ISSN 2169-9380
РУБ Astronomy & Astrophysics
Аннотация: The Sweet-Parker analysis of the inner electron diffusion region of collisionless magnetic reconnection is presented. The study includes charged particles motion near the X-line and an appropriate approximation of the off-diagonal term for the electron pressure tensor. The obtained scaling shows that the width of the inner electron diffusion region is equal to the electron inertial length, and that electrons are accelerated up to the electron Alfven velocity in X-line direction. The estimated effective plasma conductivity is based on the electron gyrofrequency rather than the binary collision frequency, and gives the extreme (minimal) value of the plasma conductivity similar to Bohm diffusion. The scaling properties are verified by means of Particle-in-Cell simulations. An ad hoc parameter needs to be introduced to the scaling relations in order to better match the theory and simulations.
Доп.точки доступа:
Divin, A.; Lapenta, G.; Markidis, S.; Semenov, V.S.; Erkaev, N.V.; Еркаев, Николай Васильевич; Korovinskiy, D.B.; Biernat, H.K.
Аннотация: The Sweet-Parker analysis of the inner electron diffusion region of collisionless magnetic reconnection is presented. The study includes charged particles motion near the X-line and an appropriate approximation of the off-diagonal term for the electron pressure tensor. The obtained scaling shows that the width of the inner electron diffusion region is equal to the electron inertial length, and that electrons are accelerated up to the electron Alfven velocity in X-line direction. The estimated effective plasma conductivity is based on the electron gyrofrequency rather than the binary collision frequency, and gives the extreme (minimal) value of the plasma conductivity similar to Bohm diffusion. The scaling properties are verified by means of Particle-in-Cell simulations. An ad hoc parameter needs to be introduced to the scaling relations in order to better match the theory and simulations.
Доп.точки доступа:
Divin, A.; Lapenta, G.; Markidis, S.; Semenov, V.S.; Erkaev, N.V.; Еркаев, Николай Васильевич; Korovinskiy, D.B.; Biernat, H.K.
The Joint Motion of Two Binary Mixtures in a Flat Layer
[Текст] : статья / V. K. Andreev // Journal of Siberian Federal University. Mathematics & Physics = Журнал Сибирского федерального университета. Математика и физика. - 2008. - Т. 1, № 4. - С. 349-370
Аннотация: The invariant solution of the equations of thermodiffusional motion is investigated. This solution describes the motion of two immiscible incompressible binary mixtures with a common flat interface under the action of pressure gradient and thermocapillary forces. The stationary flow of such system is found. If the pressure gradient in one of the mixtures tends to zero sufficiently fast, then the motion of mixtures is slowed down by the viscous friction. On the other hand, if there exists a finite limit of pressure gradient when time tends to infinity, then the solution tends to the stationary state.
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Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Андреев, Виктор Константинович
Аннотация: The invariant solution of the equations of thermodiffusional motion is investigated. This solution describes the motion of two immiscible incompressible binary mixtures with a common flat interface under the action of pressure gradient and thermocapillary forces. The stationary flow of such system is found. If the pressure gradient in one of the mixtures tends to zero sufficiently fast, then the motion of mixtures is slowed down by the viscous friction. On the other hand, if there exists a finite limit of pressure gradient when time tends to infinity, then the solution tends to the stationary state.
Полный текст на сайте журнала
Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Андреев, Виктор Константинович
Symmetry Analysis of Equations for Convection
[Текст] : статья / I.I. Ryzhkov // Journal of Siberian Federal University. Mathematics & Physics = Журнал Сибирского федерального университета. Математика и физика. - 2008. - Т. 1, № 4. - С. 410-431
Кл.слова (ненормированные):
Lie symmetry group -- equivalence transformation -- binary mixture -- convection -- Soret and Dufour
Аннотация: The differential equations describing convection in binary mixture with Soret and Dufour effects are considered. The symmetry classification of these equations with respect to the constant parameters is made. It is shown that a generator producing equivalence transformations of constants is defined accurately up to a factor arbitrarily depending on these constants. The equivalence group admitted by the governing equations is calculated. Using this group, a transformation connecting the systems with and without Soret and Dufour terms is derived. In pure Soret case, it reduces to a linear change of temperature and concentration. The presence of Dufour effect requires an additional change of thermal diffusivity and diffusion coefficient. A scheme for reducing an initial and boundary value problem for Soret–Dufour equations to a problem for the system without these effects is proposed.
Полный текст на сайте журнала
Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Рыжков, Илья Игоревич
Кл.слова (ненормированные):
Lie symmetry group -- equivalence transformation -- binary mixture -- convection -- Soret and Dufour
Аннотация: The differential equations describing convection in binary mixture with Soret and Dufour effects are considered. The symmetry classification of these equations with respect to the constant parameters is made. It is shown that a generator producing equivalence transformations of constants is defined accurately up to a factor arbitrarily depending on these constants. The equivalence group admitted by the governing equations is calculated. Using this group, a transformation connecting the systems with and without Soret and Dufour terms is derived. In pure Soret case, it reduces to a linear change of temperature and concentration. The presence of Dufour effect requires an additional change of thermal diffusivity and diffusion coefficient. A scheme for reducing an initial and boundary value problem for Soret–Dufour equations to a problem for the system without these effects is proposed.
Полный текст на сайте журнала
Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Рыжков, Илья Игоревич
Properties of Solution of a Boundary Value Problem Describing Simultaneous Flow of Two Binary Mixtures
[Text] : статья / V.K. Andreev // Proceeding of the Steklov Institute of Mathematics. - 2008. - Suppl. 1. - p. 1-4
Доп.точки доступа:
Андреев, Виктор Константинович
Доп.точки доступа:
Андреев, Виктор Константинович
The IVIDIL experiment onboard the ISS: Thermodiffusion in the presence of controlled vibrations
[Text] : статья / V. Shevtsova [et al.] // Comptes Rendus Mécanique. - 2011. - Vol. 339, Iss. 5. - p. 310–317DOI 10.1016/j.crme.2011.03.007
. -
Кл.слова (ненормированные):
Diffusion -- Thermodiffusion -- Soret effect -- Vibrations -- Microgravity -- Experiment -- Interferometry
Аннотация: The IVIDIL (Influence of VIbrations on DIffusion in Liquids) experiment was aimed at utilizing the International Space Station for investigating the effects of vibrations on liquid diffusion and thermodiffusion. The SODI-IVIDIL project of ESA is gathering together European, Canadian and Russian researchers with complementary skills to prepare and carry out the experiment, to process the raw data and perform numerical modeling of the phenomena. The experiment IVIDIL started on the October 5, 2009. In total 55 experimental runs were successfully completed by 20 January, 2010. A general description of the ISS facility related to the diffusion experiments and accessible for European researchers is briefly presented and some details about IVIDIL instrument are given. The scientific interest of this short article is focused on one of the objectives of the experiment: performing precise measurements of diffusion and thermodiffusion coefficients for binary mixtures in the absence of gravity. We demonstrate possibility of the experimental environment and report on the first results related to measurements of mass transport coefficients in the mixture with the negative Soret effect: 10% isopropanol (IPA)–90% water.
Полный текст на сайте правообладателя
Доп.точки доступа:
Shevtsova, V.; Mialdun, A.; Melnikov, D.; Ryzhkov, I.I.; Рыжков, Илья Игоревич; Gaponenko, Y.; Гапоненко, Юрий Анатольевич; Saghir, Z.; Lyubimova, T.; Legros, J.C.
Кл.слова (ненормированные):
Diffusion -- Thermodiffusion -- Soret effect -- Vibrations -- Microgravity -- Experiment -- Interferometry
Аннотация: The IVIDIL (Influence of VIbrations on DIffusion in Liquids) experiment was aimed at utilizing the International Space Station for investigating the effects of vibrations on liquid diffusion and thermodiffusion. The SODI-IVIDIL project of ESA is gathering together European, Canadian and Russian researchers with complementary skills to prepare and carry out the experiment, to process the raw data and perform numerical modeling of the phenomena. The experiment IVIDIL started on the October 5, 2009. In total 55 experimental runs were successfully completed by 20 January, 2010. A general description of the ISS facility related to the diffusion experiments and accessible for European researchers is briefly presented and some details about IVIDIL instrument are given. The scientific interest of this short article is focused on one of the objectives of the experiment: performing precise measurements of diffusion and thermodiffusion coefficients for binary mixtures in the absence of gravity. We demonstrate possibility of the experimental environment and report on the first results related to measurements of mass transport coefficients in the mixture with the negative Soret effect: 10% isopropanol (IPA)–90% water.
Полный текст на сайте правообладателя
Доп.точки доступа:
Shevtsova, V.; Mialdun, A.; Melnikov, D.; Ryzhkov, I.I.; Рыжков, Илья Игоревич; Gaponenko, Y.; Гапоненко, Юрий Анатольевич; Saghir, Z.; Lyubimova, T.; Legros, J.C.
On a convective flow of a binary mixture in a vertical layer
[Text] : статья / V. K. Andreev, I. V. Stepanova // Journal of Applied and Industrial Mathematics. - 2011. - Vol. 5, Iss. 4. - p. 491-499DOI 10.1134/S199047891104003X
. -
Аннотация: Under study is an invariant solution of the equations of thermal diffusive convection which describes a stationary process of a binary mixture flow in a vertical layer under the action of the pressure gradient and the buoyancy force that depends nonlinearly on temperature and concentration. Some general properties of this solution are established and an existence theorem is proved. Analysis of the numerical solution of the problem is carried out in the cases of a power-law and exponential dependence of the buoyancy force on its argument.
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Доп.точки доступа:
Stepanova, I.V.; Степанова, Ирина Владимировна; Андреев, Виктор Константинович
Аннотация: Under study is an invariant solution of the equations of thermal diffusive convection which describes a stationary process of a binary mixture flow in a vertical layer under the action of the pressure gradient and the buoyancy force that depends nonlinearly on temperature and concentration. Some general properties of this solution are established and an existence theorem is proved. Analysis of the numerical solution of the problem is carried out in the cases of a power-law and exponential dependence of the buoyancy force on its argument.
Полный текст на сайте правообладателя
Доп.точки доступа:
Stepanova, I.V.; Степанова, Ирина Владимировна; Андреев, Виктор Константинович
Symmetries of equations for vibrational convection in binary mixture
[Text] : статья / I. V. Stepanova, I. I. Ryzhkov // Proceedings of 5-th Int. Workshop in Group analysis of differential equations and integrable system. - 2011. - p. 200-206
. - ISBN 978-9963-700-07-3
Аннотация: Dust kinetic Alfven waves (DKAW) instability with Kappa-distributed ions streaming effects have been examined rigorously in a uniform dusty magnetoplasma. A dispersion relation of low-frequency DKAW instability on the dust acoustic velocity branch is obtained in a low-beta Lorentzian plasma. It is found that nonthermality is more effective for dust kinetic Alfven waves in the perpendicular component having finite larmor radius effects. Lorentzian type charging currents are obtained with the aid of Vlasov theory. Effect of different dust parameters on the growth rates of instability are considered. Damping/instability due to dust charge fluctuation is found to be insensitive to the form of the distribution function for DKAW. Possible applications to dusty space plasmas are pointed out.
Сборник трудов на сайте издательства
Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Ryzhkov, I.I.; Рыжков, Илья Игоревич; Степанова, Ирина Владимировна; International Workshop in Group analysis of differential equations and integrable system(5 ; June 6–10, 2010 ; Protaras)
Аннотация: Dust kinetic Alfven waves (DKAW) instability with Kappa-distributed ions streaming effects have been examined rigorously in a uniform dusty magnetoplasma. A dispersion relation of low-frequency DKAW instability on the dust acoustic velocity branch is obtained in a low-beta Lorentzian plasma. It is found that nonthermality is more effective for dust kinetic Alfven waves in the perpendicular component having finite larmor radius effects. Lorentzian type charging currents are obtained with the aid of Vlasov theory. Effect of different dust parameters on the growth rates of instability are considered. Damping/instability due to dust charge fluctuation is found to be insensitive to the form of the distribution function for DKAW. Possible applications to dusty space plasmas are pointed out.
Сборник трудов на сайте издательства
Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Ryzhkov, I.I.; Рыжков, Илья Игоревич; Степанова, Ирина Владимировна; International Workshop in Group analysis of differential equations and integrable system(5 ; June 6–10, 2010 ; Protaras)
Analysis of financial time series with binary N-grams frequency dictionaries
[] / M. G. Sadovsky, I. Borovikov // J. Sib. Fed. Univ. Math. Phys. - 2014. - Vol. 7, Is. 1. - P112-123
. - ISSN 1997-1397
Аннотация: The paper presents a novel approach to statistical analysis of financial time series. The approach is based on n-grams frequency dictionaries derived from the quantized market data. Such dictionaries are studied by evaluating their information capacity using relative entropy. A specific quantization of (originally continuous) financial data is considered: so called binary quantization. Possible applications of the proposed technique include market event study with the n-grams of higher information value. The finite length of the input data presents certain computational and theoretical challenges discussed in the paper. also, some other versions of a quantization are discussed. © Siberian Federal University. All rights reserved.
Scopus,
РИНЦ
Держатели документа:
Institute of computational modelling SB RAS, Akademgorodok, Krasnoyarsk, 660036, Russian Federation
Nekkar.Net Labs, Ltd, CA, United States
Доп.точки доступа:
Sadovsky, M.G.; Садовский, Михаил Георгиевич; Borovikov, I.
Аннотация: The paper presents a novel approach to statistical analysis of financial time series. The approach is based on n-grams frequency dictionaries derived from the quantized market data. Such dictionaries are studied by evaluating their information capacity using relative entropy. A specific quantization of (originally continuous) financial data is considered: so called binary quantization. Possible applications of the proposed technique include market event study with the n-grams of higher information value. The finite length of the input data presents certain computational and theoretical challenges discussed in the paper. also, some other versions of a quantization are discussed. © Siberian Federal University. All rights reserved.
Scopus,
РИНЦ
Держатели документа:
Institute of computational modelling SB RAS, Akademgorodok, Krasnoyarsk, 660036, Russian Federation
Nekkar.Net Labs, Ltd, CA, United States
Доп.точки доступа:
Sadovsky, M.G.; Садовский, Михаил Георгиевич; Borovikov, I.
Ostroumov-Birikh solution of convection equations with nonlinear buoyancy force
[Text] / V. K. Andreev, I. V. Stepanova // Appl. Math. Comput. - 2014. - Vol. 228. - P. 59-67, DOI 10.1016/j.amc.2013.11.002. - Cited References: 21. - The work is supported by RFBR Grant (project 11-01-00283) and Integrational grant of SB of RAS (project 44).
. - ISSN 0096-3003. - ISSN 1873-5649
РУБ Mathematics, Applied
Аннотация: The thermodiffusion convection equations with nonlinear buoyancy force are studied. Some particular solutions for describing of thermoconcentration flows are found. Two boundary value problems are solved for thermal convection case. The comparison with the linear Oberbeck-Boussinesq model is given. (C) 2013 Elsevier Inc. All rights reserved.
WOS,
Scopus
Держатели документа:
[Andreev, Viktor K.
Stepanova, Irina V.] Inst Computat Modelling SB RAS, Krasnoyarsk 660036, Russia
ИВМ СО РАН
Доп.точки доступа:
Andreev, V.K.; Андреев, Виктор Константинович; Stepanova, I.V.; Степанова, Ирина Владимировна; RFBR [11-01-00283]; Integrational grant of SB of RAS [44]
Рубрики:
THERMOCAPILLARY LIQUID LAYERS
2-LAYER FLOW
INSTABILITIES
Кл.слова (ненормированные):
Exact solutions -- Convection -- Binary mixture -- Thermodiffusion -- One-layer and two-layer flows
THERMOCAPILLARY LIQUID LAYERS
2-LAYER FLOW
INSTABILITIES
Кл.слова (ненормированные):
Exact solutions -- Convection -- Binary mixture -- Thermodiffusion -- One-layer and two-layer flows
Аннотация: The thermodiffusion convection equations with nonlinear buoyancy force are studied. Some particular solutions for describing of thermoconcentration flows are found. Two boundary value problems are solved for thermal convection case. The comparison with the linear Oberbeck-Boussinesq model is given. (C) 2013 Elsevier Inc. All rights reserved.
WOS,
Scopus
Держатели документа:
[Andreev, Viktor K.
Stepanova, Irina V.] Inst Computat Modelling SB RAS, Krasnoyarsk 660036, Russia
ИВМ СО РАН
Доп.точки доступа:
Andreev, V.K.; Андреев, Виктор Константинович; Stepanova, I.V.; Степанова, Ирина Владимировна; RFBR [11-01-00283]; Integrational grant of SB of RAS [44]
Experimental and numerical analysis of mass transfer in a binary mixture with Soret effect in the presence of weak convection
[Text] / Y. . Gaponenko, A. . Mialdun, V. . Shevtsova // Eur. Phys. J. E. - 2014. - Vol. 37, Is. 10. - Ст. 90, DOI 10.1140/epje/i2014-14090-5. - Cited References: 18. - This work is supported by the PRODEX programme of the Belgian Federal Science Policy Office and ESA.
. - ISSN 1292-8941. - ISSN 1292-895X
РУБ Chemistry, Physical + Materials Science, Multidisciplinary + Physics, Applied + Polymer Science
Аннотация: One of the targets of the experiment IVIDIL (Influence Vibrations on Diffusion in Liquids) conducted on-board ISS was to study the response of binary mixtures to vibrational forcing when the density gradient results from thermal and compositional variations. Compositional variations were created by the Soret effect and can strengthen or weaken the overall density gradient and, consequently, the response to vibrational forcing. We present the results of two experimental runs conducted on-board ISS in the frame of the experiment IVIDIL for low and strong vibrational forcing. The experimental observations revealed that a significant mean flow is set within 2 minutes after imposing vibrations and later in time it varies weakly and slowly due to the Soret effect. A mathematical model has been developed to compute the thermal and concentration fields in the experiment IVIDIL and verify the accuracy of picture processing based on the classical approach used in non-convective systems with the Soret effect. The effect of temperature and concentrations perturbations by joint action of vibrational convection and Soret effect on long time scale are carefully examined. The model demonstrates that image processing used for non-convective systems is suitable for the systems with vibration-affected thermodiffusion experiment.
WOS
Держатели документа:
[Gaponenko, Y.
Mialdun, A.
Shevtsova, V.] Univ Libre Bruxelles, MRC, EP CP 165 62, B-1050 Brussels, Belgium
[Gaponenko, Y.] Inst Computat Modelling SB RAS, Krasnoyarsk 660036, Russia
ИВМ СО РАН
Доп.точки доступа:
Gaponenko, Y.; Гапоненко, Юрий Анатольевич; Mialdun, A.; Shevtsova, V.; PRODEX programme of the Belgian Federal Science Policy Office; ESA
Аннотация: One of the targets of the experiment IVIDIL (Influence Vibrations on Diffusion in Liquids) conducted on-board ISS was to study the response of binary mixtures to vibrational forcing when the density gradient results from thermal and compositional variations. Compositional variations were created by the Soret effect and can strengthen or weaken the overall density gradient and, consequently, the response to vibrational forcing. We present the results of two experimental runs conducted on-board ISS in the frame of the experiment IVIDIL for low and strong vibrational forcing. The experimental observations revealed that a significant mean flow is set within 2 minutes after imposing vibrations and later in time it varies weakly and slowly due to the Soret effect. A mathematical model has been developed to compute the thermal and concentration fields in the experiment IVIDIL and verify the accuracy of picture processing based on the classical approach used in non-convective systems with the Soret effect. The effect of temperature and concentrations perturbations by joint action of vibrational convection and Soret effect on long time scale are carefully examined. The model demonstrates that image processing used for non-convective systems is suitable for the systems with vibration-affected thermodiffusion experiment.
WOS
Держатели документа:
[Gaponenko, Y.
Mialdun, A.
Shevtsova, V.] Univ Libre Bruxelles, MRC, EP CP 165 62, B-1050 Brussels, Belgium
[Gaponenko, Y.] Inst Computat Modelling SB RAS, Krasnoyarsk 660036, Russia
ИВМ СО РАН
Доп.точки доступа:
Gaponenko, Y.; Гапоненко, Юрий Анатольевич; Mialdun, A.; Shevtsova, V.; PRODEX programme of the Belgian Federal Science Policy Office; ESA
The invariant solution of thermal diffusion equations for a non-linear buoyancy force
[Text] : статья / I. V. Stepanova // PMM JOURNAL OF APPLIED MATHEMATICS AND MECHANICS. - 2013. - Vol. 77, Iss. 3. - p. 330-337DOI 10.1016/j.jappmathmech.2013.09.009
. -
Аннотация: A model of the thermal-diffusion convection of a binary mixture when there is a non-linear dependence of the buoyancy force on the temperature and concentration is considered. An invariant solution, which describes the steady flow of the mixture in a plane vertical layer, is constructed and investigated. The effect of non-linearity of the buoyancy force on the type of flow is examined.
Полный текст на сайте правообладателя
Доп.точки доступа:
Степанова, Ирина Владимировна
Аннотация: A model of the thermal-diffusion convection of a binary mixture when there is a non-linear dependence of the buoyancy force on the temperature and concentration is considered. An invariant solution, which describes the steady flow of the mixture in a plane vertical layer, is constructed and investigated. The effect of non-linearity of the buoyancy force on the type of flow is examined.
Полный текст на сайте правообладателя
Доп.точки доступа:
Степанова, Ирина Владимировна
Long-wave instability of a plane multicomponent mixture layer with the Soret effect
[Text] : статья / I.I. Ryzhkov // Fluid Dynamics. - 2013. - Vol. 48, Iss. 4. - p. 477-490DOI 10.1134/S0015462813040078
. -
Аннотация: Long-wave instability that arises in a plane multicomponent mixture layer with the Soret effect is investigated. The layer is heated from above or below in the gravity field. The solution of the linearized equations of motion is sought in the form of a series in powers of the wave number assumed to be small. For the mixture with an arbitrary number of components the critical parameters of instability are determined. For binary and ternary mixtures the stability maps are plotted. The regions where the long- and short wave perturbations are the most dangerous are distinguished in the space of physical parameters. The analytical results are compared with the numerical solution of the linearized equations over a wide wave number range. As an example, instability in a ternary hydrocarbon mixture is considered.
Полный текст на сайте правообладателя
Доп.точки доступа:
Рыжков, Илья Игоревич
Аннотация: Long-wave instability that arises in a plane multicomponent mixture layer with the Soret effect is investigated. The layer is heated from above or below in the gravity field. The solution of the linearized equations of motion is sought in the form of a series in powers of the wave number assumed to be small. For the mixture with an arbitrary number of components the critical parameters of instability are determined. For binary and ternary mixtures the stability maps are plotted. The regions where the long- and short wave perturbations are the most dangerous are distinguished in the space of physical parameters. The analytical results are compared with the numerical solution of the linearized equations over a wide wave number range. As an example, instability in a ternary hydrocarbon mixture is considered.
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Доп.точки доступа:
Рыжков, Илья Игоревич
On thermal diffusion separation in binary mixtures with variable transport coefficients
/ I. I. Ryzhkov, I. V. Stepanova // Int. J. Heat Mass Transf. - 2015. - Vol. 86. - P268-276, DOI 10.1016/j.ijheatmasstransfer.2015.02.069
. - ISSN 0017-9310
Кл.слова (ненормированные):
Analytical solutions -- Binary mixture -- Diffusion -- Thermal diffusion -- Variable transport properties -- Differential equations -- Diffusion -- Heat transfer -- Mass transfer -- Mixtures -- Ordinary differential equations -- Plates (structural components) -- Suspensions (fluids) -- Thermal conductivity -- Thermal diffusion -- Transport properties -- Colloidal suspensions -- Concentration profiles -- Constant temperature -- Diffusion separation -- Heat and mass transfer -- One-dimensional equation -- Stationary heat transfer -- Transport coefficient -- Binary mixtures
Аннотация: The stationary heat transfer and Soret separation of a binary mixture between parallel plates with different constant temperatures is studied allowing for variable transport properties. The mixture is described by non-linear one-dimensional equations of heat and mass transfer, where the density, thermal conductivity, and Soret coefficient depend on temperature and concentration. A general procedure for integrating these equations is proposed. The problem is reduced to the ordinary differential equation of first order, which describes the trajectory of the system in the concentrationerature plane, and implicit dependence of temperature on space coordinate. It is shown that the solution for concentration is unique if the density and thermal conductivity do not depend on concentration. Analytical solutions of the problem are derived in a number of cases, while the most general case is treated numerically. The non-linear temperature and concentration profiles in different binary mixtures (aqueous solutions, colloidal suspensions, polymer blend) are constructed and analyzed. A procedure for extracting the dependence of Soret coefficient on temperature and concentration from the experimentally measured thermal and compositional profiles is suggested. © 2015 Elsevier Ltd.All rights reserved.
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Держатели документа:
Institute of Computational Modelling SB RASAkademgorodok,Krasnoyarsk, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Stepanova, I.V.; Степанова, Ирина Владимировна; Рыжков, Илья Игоревич
Кл.слова (ненормированные):
Analytical solutions -- Binary mixture -- Diffusion -- Thermal diffusion -- Variable transport properties -- Differential equations -- Diffusion -- Heat transfer -- Mass transfer -- Mixtures -- Ordinary differential equations -- Plates (structural components) -- Suspensions (fluids) -- Thermal conductivity -- Thermal diffusion -- Transport properties -- Colloidal suspensions -- Concentration profiles -- Constant temperature -- Diffusion separation -- Heat and mass transfer -- One-dimensional equation -- Stationary heat transfer -- Transport coefficient -- Binary mixtures
Аннотация: The stationary heat transfer and Soret separation of a binary mixture between parallel plates with different constant temperatures is studied allowing for variable transport properties. The mixture is described by non-linear one-dimensional equations of heat and mass transfer, where the density, thermal conductivity, and Soret coefficient depend on temperature and concentration. A general procedure for integrating these equations is proposed. The problem is reduced to the ordinary differential equation of first order, which describes the trajectory of the system in the concentrationerature plane, and implicit dependence of temperature on space coordinate. It is shown that the solution for concentration is unique if the density and thermal conductivity do not depend on concentration. Analytical solutions of the problem are derived in a number of cases, while the most general case is treated numerically. The non-linear temperature and concentration profiles in different binary mixtures (aqueous solutions, colloidal suspensions, polymer blend) are constructed and analyzed. A procedure for extracting the dependence of Soret coefficient on temperature and concentration from the experimentally measured thermal and compositional profiles is suggested. © 2015 Elsevier Ltd.All rights reserved.
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WOS
Держатели документа:
Institute of Computational Modelling SB RASAkademgorodok,Krasnoyarsk, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Stepanova, I.V.; Степанова, Ирина Владимировна; Рыжков, Илья Игоревич
Onset of convection in a two-phase binary mixture with the Soret effect in weightlessness
/ I. I. Ryzhkov, S. P. Tsarev // Phys. Fluids. - 2015. - Vol. 27, Is. 7. - Ст. 072103, DOI 10.1063/1.4926891
. - ISSN 1070-6631
Кл.слова (ненормированные):
Binary mixtures -- Temperature -- Weightlessness -- Concentration gradients -- Conservation of mass -- Critical temperature difference -- Interfacial concentrations -- Latent heat release -- Mechanical equilibrium -- Onset of convection -- Temperature differences -- Mixtures
Аннотация: The linear stability of mechanical equilibrium in a two-layer system formed by different phases of the same binary mixture is investigated. The temperature difference is applied to the layers by heating and cooling the opposite rigid boundaries. In the state of mechanical equilibrium, the applied temperature gradient induces concentration gradients due to the Soret effect. The conservation of mass for the mixture components leads to the dependence of layer thicknesses on the applied temperature difference. In weightlessness, the main mechanisms of instability in the considered system are related to phase change and Marangoni effect. The calculations are performed for cyclohexane-methanol binary mixture, which has a liquid-liquid miscibility gap. The analytical solution of amplitude equations for monotonic perturbations is found and expression for the critical temperature difference is derived. It is shown that the phase change instability is long-wave and favoured when the difference between interfacial concentrations in the basic state decreases. When the Marangoni effect is taken into account, additional monotonic and oscillatory modes appear. They result from the interplay between thermocapillarity and phase change with latent heat release/absorption. The most unstable monotonic and oscillatory modes are identified depending on the heating regime and relative thickness of the layers. © 2015 AIP Publishing LLC.
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Держатели документа:
Institute of Computational Modelling SB RAS, Akademgorodok, Krasnoyarsk, Russian Federation
Institute of Space and Information Technologies, Siberian Federal University, 79 Svobodny pr., Krasnoyarsk, Russian Federation
Доп.точки доступа:
Tsarev, S.P.; Рыжков, Илья Игоревич
Кл.слова (ненормированные):
Binary mixtures -- Temperature -- Weightlessness -- Concentration gradients -- Conservation of mass -- Critical temperature difference -- Interfacial concentrations -- Latent heat release -- Mechanical equilibrium -- Onset of convection -- Temperature differences -- Mixtures
Аннотация: The linear stability of mechanical equilibrium in a two-layer system formed by different phases of the same binary mixture is investigated. The temperature difference is applied to the layers by heating and cooling the opposite rigid boundaries. In the state of mechanical equilibrium, the applied temperature gradient induces concentration gradients due to the Soret effect. The conservation of mass for the mixture components leads to the dependence of layer thicknesses on the applied temperature difference. In weightlessness, the main mechanisms of instability in the considered system are related to phase change and Marangoni effect. The calculations are performed for cyclohexane-methanol binary mixture, which has a liquid-liquid miscibility gap. The analytical solution of amplitude equations for monotonic perturbations is found and expression for the critical temperature difference is derived. It is shown that the phase change instability is long-wave and favoured when the difference between interfacial concentrations in the basic state decreases. When the Marangoni effect is taken into account, additional monotonic and oscillatory modes appear. They result from the interplay between thermocapillarity and phase change with latent heat release/absorption. The most unstable monotonic and oscillatory modes are identified depending on the heating regime and relative thickness of the layers. © 2015 AIP Publishing LLC.
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WOS
Держатели документа:
Institute of Computational Modelling SB RAS, Akademgorodok, Krasnoyarsk, Russian Federation
Institute of Space and Information Technologies, Siberian Federal University, 79 Svobodny pr., Krasnoyarsk, Russian Federation
Доп.точки доступа:
Tsarev, S.P.; Рыжков, Илья Игоревич
Investigation of Fickian diffusion in the ternary mixtures of water-ethanol-triethylene glycol and its binary pairs
/ J. C. Legros [et al.] // Phys. Chem. Chem. Phys. - 2015. - Vol. 17, Is. 41. - P27713-27725, DOI 10.1039/c5cp04745e
. - ISSN 1463-9076
Аннотация: We present a comprehensive experimental study of isothermal Fickian diffusion in the ternary and binary liquid mixtures of water, ethanol, and triethylene glycol over the entire ternary composition space. 21 ternary mixtures inside the composition triangle have been investigated by means of the Taylor dispersion technique and 30 binary mixtures by Taylor dispersion and/or optical beam deflection in a Soret cell. The scalar binary diffusion coefficient has been determined along all three binary boundaries of the composition space and compared with estimations based on the Stokes-Einstein relation using stick or slip boundary conditions. The four elements of the ternary diffusion matrix and the diffusion eigenvalues were determined over a large portion of the composition triangle. The pseudo-binary diffusion coefficients obtained in Taylor dispersion experiments with either one of the two independent concentrations kept constant are comparable to the two diffusion eigenvalues. One of the two off-diagonal elements of the diffusion matrix is of the same order as the diagonal ones and, hence, not negligible, whereas the other one is approximately one order of magnitude smaller. Where available, our results compare well with literature data. The investigated compositions also comprise the five compositions that are scheduled for microgravity experiments in the ESA DCMIX3 project. This journal is © the Owner Societies 2015.
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Держатели документа:
Microgravity Research Center, Universite Libre de Bruxelles (ULB), CP-165/62 Av. F.D. Roosevelt 50, B-1050 Brussels, Belgium
Institute of Computational Modelling SB RAS, Krasnoyarsk, Russian Federation
Physikalisches Institut, Universitat Bayreuth, Bayreuth, Germany
National Research Tomsk Polytechnic University, Russian Federation
Доп.точки доступа:
Legros, J. C.; Gaponenko, Y.; Гапоненко, Юрий Анатольевич; Mialdun, A.; Triller, T.; Hammon, A.; Bauer, C.; Kohler, W.; Shevtsova, V.
Аннотация: We present a comprehensive experimental study of isothermal Fickian diffusion in the ternary and binary liquid mixtures of water, ethanol, and triethylene glycol over the entire ternary composition space. 21 ternary mixtures inside the composition triangle have been investigated by means of the Taylor dispersion technique and 30 binary mixtures by Taylor dispersion and/or optical beam deflection in a Soret cell. The scalar binary diffusion coefficient has been determined along all three binary boundaries of the composition space and compared with estimations based on the Stokes-Einstein relation using stick or slip boundary conditions. The four elements of the ternary diffusion matrix and the diffusion eigenvalues were determined over a large portion of the composition triangle. The pseudo-binary diffusion coefficients obtained in Taylor dispersion experiments with either one of the two independent concentrations kept constant are comparable to the two diffusion eigenvalues. One of the two off-diagonal elements of the diffusion matrix is of the same order as the diagonal ones and, hence, not negligible, whereas the other one is approximately one order of magnitude smaller. Where available, our results compare well with literature data. The investigated compositions also comprise the five compositions that are scheduled for microgravity experiments in the ESA DCMIX3 project. This journal is © the Owner Societies 2015.
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Держатели документа:
Microgravity Research Center, Universite Libre de Bruxelles (ULB), CP-165/62 Av. F.D. Roosevelt 50, B-1050 Brussels, Belgium
Institute of Computational Modelling SB RAS, Krasnoyarsk, Russian Federation
Physikalisches Institut, Universitat Bayreuth, Bayreuth, Germany
National Research Tomsk Polytechnic University, Russian Federation
Доп.точки доступа:
Legros, J. C.; Gaponenko, Y.; Гапоненко, Юрий Анатольевич; Mialdun, A.; Triller, T.; Hammon, A.; Bauer, C.; Kohler, W.; Shevtsova, V.
Об условиях существования однонаправленных течений бинарных смесей
[Текст] : статья / В. К. Андреев // Некоторые актуальные проблемы современной математики и математического образования. Герценовские чтения - 2015 : материалы 68-ой научной конференции. - 2015. - Т. LXVIII. - С. 12-18
. - ISBN 978-5-8064-2095-5
Перевод заглавия: On the existence conditions of a binary mixtures unidirectional flows
Кл.слова (ненормированные):
state equation -- unidirectional flows -- binary mixture -- exact solution -- уравнение состояния -- однонаправленное течение -- бинарная смесь -- точное решение
Аннотация: Рассматриваются уравнения однонаправленных стационарных течений бинарных смесей. Условия существования таких течений накладывают ограничения на уравнения состояния смеси и представления решений. В случае модели Обербека - Буссинеска анализ условий совместности проведён полностью. Построены новые точные решения, показывающие их существенное отличие от классических.
The unidirectional steady flows of a binary mixtures equations are considered. The study is focused on the conditions for the buoyancy force function admits above flows. For the Oberbeck -Boussinesq model the problem is complete solved. Some new exact solutions are found. Comparison with the classical well-known solutions are given.
РИНЦ
Держатели документа:
Институт вычислительного моделирования СО РАН
Доп.точки доступа:
Andreev V.K.; Некоторые актуальные проблемы современной математики и математического образования (2015 ; 13.04 - 17.04 ; Санкт-Петербург)
Перевод заглавия: On the existence conditions of a binary mixtures unidirectional flows
| УДК |
Кл.слова (ненормированные):
state equation -- unidirectional flows -- binary mixture -- exact solution -- уравнение состояния -- однонаправленное течение -- бинарная смесь -- точное решение
Аннотация: Рассматриваются уравнения однонаправленных стационарных течений бинарных смесей. Условия существования таких течений накладывают ограничения на уравнения состояния смеси и представления решений. В случае модели Обербека - Буссинеска анализ условий совместности проведён полностью. Построены новые точные решения, показывающие их существенное отличие от классических.
The unidirectional steady flows of a binary mixtures equations are considered. The study is focused on the conditions for the buoyancy force function admits above flows. For the Oberbeck -Boussinesq model the problem is complete solved. Some new exact solutions are found. Comparison with the classical well-known solutions are given.
РИНЦ
Держатели документа:
Институт вычислительного моделирования СО РАН
Доп.точки доступа:
Andreev V.K.; Некоторые актуальные проблемы современной математики и математического образования (2015 ; 13.04 - 17.04 ; Санкт-Петербург)
On one two-dimensional stationary flow of a binary mixture and viscous fluid in a plane layer
/ M. V. Efimova // J. Sib. Fed. Univ. Math. Phys. - 2016. - Vol. 9, Is. 1. - P30-36, DOI 10.17516/1997-1397-2016-9-1-30-36
. - ISSN 1997-1397
Кл.слова (ненормированные):
Binary mixture -- Convective motion -- Oberbeck-Boussinesq equations -- Steady flow
Аннотация: Nonlinear model of convection in Oberbeck-Boussinesq approximation describing the flat joint motion of a binary mixture and viscous fluid with a common interface is investigated. It is important that the longitudinal temperature gradient and the concentration is quadratic dependence on the coordinate x. Stationary solution of the system is built. © Siberian Federal University. All rights reserved.
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Смотреть статью
Держатели документа:
Institute of Computational modelling SB RAS, Akademgorodok, 50/44, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Efimova, M. V.
Кл.слова (ненормированные):
Binary mixture -- Convective motion -- Oberbeck-Boussinesq equations -- Steady flow
Аннотация: Nonlinear model of convection in Oberbeck-Boussinesq approximation describing the flat joint motion of a binary mixture and viscous fluid with a common interface is investigated. It is important that the longitudinal temperature gradient and the concentration is quadratic dependence on the coordinate x. Stationary solution of the system is built. © Siberian Federal University. All rights reserved.
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WOS,
Смотреть статью
Держатели документа:
Institute of Computational modelling SB RAS, Akademgorodok, 50/44, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Efimova, M. V.
Unidirectional flows of binary mixtures within the framework of the Oberbeck-Boussinesq model
[Text] / V. K. Andreev, I. V. Stepanova // Fluid Dyn. - 2016. - Vol. 51, Is. 2. - P136-147, DOI 10.1134/S0015462816020022. - Cited References:17. - The work was supported financially by the Russian Foundation for Basic Research (project No. 14-01-00067).
. - ISSN 0015-4628. - ISSN 1573-8507
РУБ Mechanics + Physics, Fluids & Plasmas
Кл.слова (ненормированные):
Oberbeck-Boussinesq model -- thermodiffusion -- unidirectional flow -- binary -- mixture
Аннотация: Existence conditions are investigated for the unidirectional flows of binary mixtures describable by the equations of motion in the Oberbeck-Boussinesq approximation with account for the thermodiffusion effect. Possible solutions are classified, known and novel classes of exact solutions being distinguished. For the solutions obtained different formulations of boundary-value problems are proposed. Flows between two rigid walls with given heat distribution laws are described.
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Держатели документа:
Russian Acad Sci, Siberian Branch, Inst Computat Modelling, Akademgorodok 50,Str 44, Krasnoyarsk 660036, Russia.
Siberian Fed Univ, Inst Math & Fundamental Informat, Pr Svobodnyi 79, Krasnoyarsk 660041, Russia.
Доп.точки доступа:
Andreev, V. K.; Stepanova, I. V.; Russian Foundation for Basic Research [14-01-00067]
Кл.слова (ненормированные):
Oberbeck-Boussinesq model -- thermodiffusion -- unidirectional flow -- binary -- mixture
Аннотация: Existence conditions are investigated for the unidirectional flows of binary mixtures describable by the equations of motion in the Oberbeck-Boussinesq approximation with account for the thermodiffusion effect. Possible solutions are classified, known and novel classes of exact solutions being distinguished. For the solutions obtained different formulations of boundary-value problems are proposed. Flows between two rigid walls with given heat distribution laws are described.
WOS,
Смотреть статью
Держатели документа:
Russian Acad Sci, Siberian Branch, Inst Computat Modelling, Akademgorodok 50,Str 44, Krasnoyarsk 660036, Russia.
Siberian Fed Univ, Inst Math & Fundamental Informat, Pr Svobodnyi 79, Krasnoyarsk 660041, Russia.
Доп.точки доступа:
Andreev, V. K.; Stepanova, I. V.; Russian Foundation for Basic Research [14-01-00067]