scholarly journals Refined description of momentum transfer in real liquid mixtures

2020 ◽  
Vol 64 (11) ◽  
pp. 154-158
Author(s):  
Arnold Sh. Bicbulatov ◽  
◽  
Asia A. Usmanova ◽  
Keyword(s):  
Chemical Potential ◽  
Particle Density ◽  
Specific Interaction ◽  
Kinetic Equations ◽  
Solid Sphere ◽  
Irreversible Processes ◽  
Transfer Coefficients ◽  
Comparison System ◽  
Viscosity Coefficients ◽  
Dense Media

Viscosity coefficients are required to calculate various heat and mass transfer processes. There is not strict theory that allows calculating viscosity coefficients in real systems. The kinetic theory of dense media for the model of solid sphere, which takes into account only the presence of its own volume of particles, allows us to calculate the transfer coefficients in ideal mixtures. A real mixture of different events the forces of attraction play a significant role in their characteristic behavior at different concentrations of the mixture. The problem of taking into account the real interaction between molecules can be solved using methods of thermodynamics irreversible processes. The formalism of such a solution of kinetic equations is based on a model representation of the behavior of molecules in real systems when indirectly obtaining information about a specific interaction of particles through the value of the chemical potential or activity. This work is a continuation of the development of other published works. To account for the interaction between molecules in real systems, a thermodynamic model of an ideal associated Prigogine solution is used. This model assumed that non-ideal systems can represented as ideal under certain conditions and assumes that attractive forces can act between particles. It is possible to form complexes and their interaction. In accordance with the definition of the chemical potential introduced by Lewis, real systems with particle density n_(i )are replaced by an equivalent ideal mixture with activity a. In this paper, we refine the generalized kinetic equations of dense media used as an ideal comparison system for real solutions. A new expression for the flow term in the kinetic equation is obtained.

scholarly journals Viscosity coefficients in nonideal liquid mixture

2020 ◽  
Vol 64 (11) ◽  
pp. 159-162
Author(s):  
Arnold Sh. Bicbulatov ◽  
◽  
Asia A. Usmanova ◽  
Keyword(s):  
Experimental Data ◽  
Mass Transfer ◽  
Activity Coefficient ◽  
Momentum Transfer ◽  
Kinetic Equations ◽  
Irreversible Processes ◽  
Viscosity Coefficients ◽  
Transfer Processes ◽  
Mass Transfer Processes ◽  
Solid Spheres

To calculate various heat and mass transfer processes, reliable data on the molecular momentum transfer coefficient are required, which should fit seamlessly in to the General algorithm for modeling and calculating various mass transfer processes and devices in the chemical and petrochemical industries in the form of unified programs. This approach is proposed in the description of the momentum transfer mechanism, which is implemented by generalizing the kinetic equations of the model of solid spheres of a system of dense media with the help of methods of the thermodynamics of irreversible processes for associated Prigogine solution model. This allows a more accurate description of the momentum transfer in nonideal solutions. Within the framework of this model, the expression of the collision therm in kinetic equations is refined, which significantly expands the boundaries of the theory’s application. A method for calculation activity coefficient is developed based on experimental data in the liquid-vapor system and the Wilson the equation. This will allow us to improve quantitatively the description of the phenomena of momentum transfer. A comparision was made between the calculated and experimental viscosity coefficients for a highly nonideal aceton-water solution, in which the activity coefficient varies on both components from 1 to 5 units. The average discrepancy between the data at different concentrations is 30%. At the sesame, the discrepancy between the coefficients, calculated according to the theory of solid spheres and experimental data reaches up to 10 times. When specifying the values of the activity coefficients and the interaction parameter between molecules the proposed method will improve the result.

Flow Past a Spinning Sphere With Surface Blowing and Heat Transfer

2005 ◽  
Vol 127 (1) ◽  
pp. 163-171 ◽  
Author(s):  
H. Niazmand ◽  
M. Renksizbulut
Keyword(s):  
Heat Transfer ◽  
Three Dimensional ◽  
Flow Regimes ◽  
Solid Sphere ◽  
Temporal Variations ◽  
Transfer Coefficients ◽  
Transfer Rates ◽  
Particle Spin ◽  
Flow Past ◽  
Angular Velocities

Computations are performed to determine the transient three-dimensional heat transfer rates and fluid forces acting on a stream-wise spinning sphere for Reynolds numbers in the range 10⩽Re⩽300 and angular velocities Ωx⩽2. In this Re range, classical flow past a solid sphere develops four different flow regimes, and the effects of particle spin are studied in each regime. Furthermore, the combined effects of particle spin and surface blowing are examined. Sphere spin increases drag in all flow regimes, while lift shows a nonmonotonic behavior. Heat transfer rates are not influenced by spin up to a certain Ωx but increase monotonically thereafter. An interesting feature associated with sphere spin is the development of a special wake regime such that the wake simply spins without temporal variations in its shape. For this flow condition, the magnitudes of the lift, drag, and heat transfer coefficients remain constant in time. Correlations are provided for drag and heat transfer.

scholarly journals Dissociation of Quarkonium in Hot and Dense Media in an Anisotropic Plasma in the Nonrelativistic Quark Model

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
M. Abu-Shady ◽  
H. M. Mansour ◽  
A. I. Ahmadov
Keyword(s):  
Binding Energy ◽  
Anisotropic Medium ◽  
Chemical Potential ◽  
Anisotropic Plasma ◽  
Anisotropic Parameter ◽  
Baryonic Chemical Potential ◽  
Nonrelativistic Quark Model ◽  
Dense Media ◽  
Dissociation Temperature ◽  
Nu Method

In this paper, quarkonium dissociation is investigated in an anisotropic plasma in the hot and dense media. For that purpose, the multidimensional Schrödinger equation is solved analytically by Nikiforov-Uvarov (NU) method for the real part of the potential in an anisotropic medium. The binding energy and dissociation temperature are calculated. In comparison with an isotropic medium, the binding energy of quarkonium is enhanced in the presence of an anisotropic medium. The present results show that the dissociation temperature increases with increasing anisotropic parameter for 1S state of the charmonium and bottomonium. We observe that the lower baryonic chemical potential has small effect in both isotropic and anisotropic media. A comparison is presented with other pervious theoretical works.

Design and Development of 850t/h CFB Boiler with Energy Saving Technology

2014 ◽  
Vol 492 ◽  
pp. 13-18 ◽  
Author(s):  
Xian Hong Ren ◽  
Kang Tao Hu ◽  
Jian Chun Zhang ◽  
Ai Cheng Liu ◽  
Hai Rui Yang
Keyword(s):  
Energy Saving ◽  
Design Theory ◽  
Particle Density ◽  
Balance Model ◽  
Transfer Coefficients ◽  
Cfb Boiler ◽  
Operation Conditions ◽  
Ash Formation ◽  
Energy Saving Technology ◽  
The One

Taiyuan Boiler Group Co. Ltd. designed and developed an 850t/h CFB boiler with energy saving technology on the principle of “State Specification Design Theory”. By measuring the ash formation and attrition characteristic of the design coal, with the one dimension mass balance model developed by Tsinghua University, the bed quality of the bed inventory and the pressure drop were modified. Based on the particle density calculated, the heating transfer coefficients were chosen and the arrangements of the heating surfaces were modified. According to the special operation conditions of the user, the practical working conditions for the boiler are determined so as to assure the technical characteristics and structural properties in 850t/h CFB boiler.

scholarly journals Propagation of electromagnetic waves in extremely dense media

2017 ◽  
Vol 32 (15) ◽  
pp. 1750081 ◽  
Author(s):  
Samina Masood ◽  
Iram Saleem
Keyword(s):  
Magnetic Permeability ◽  
Electromagnetic Waves ◽  
Chemical Potential ◽  
Longitudinal Component ◽  
Renormalization Scheme ◽  
Electromagnetic Properties ◽  
Electric Permittivity ◽  
Stellar Objects ◽  
Dense Media ◽  
Exotic Systems

We study the propagation of electromagnetic (EM) waves in extremely dense exotic systems with very unique properties. These EM waves develop a longitudinal component due to interactions with the medium. Renormalization scheme of QED is used to understand the propagation of EM waves in both longitudinal and transverse directions. The propagation of EM waves in a quantum statistically treatable medium affects the properties of the medium itself. The electric permittivity and the magnetic permeability of the medium are modified and influence the related behavior of the medium. All the electromagnetic properties of a medium become a function of temperature and chemical potential of the medium. We study in detail the modifications of electric permittivity and magnetic permeability and other related properties of a medium in the superdense stellar objects.

scholarly journals Thermodynamics of Low-Dimensional Trapped Fermi Gases

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Francisco J. Sevilla
Keyword(s):  
Isothermal Compressibility ◽  
Chemical Potential ◽  
Particle Density ◽  
Fermi Gas ◽  
Fermi Gases ◽  
Nonmonotonic Dependence ◽  
Characteristic Temperatures ◽  
Low Dimensionality ◽  
Thermodynamic Regime ◽  
Low Dimensional

The effects of low dimensionality on the thermodynamics of a Fermi gas trapped by isotropic power-law potentials are analyzed. Particular attention is given to different characteristic temperatures that emerge, at low dimensionality, in the thermodynamic functions of state and in the thermodynamic susceptibilities (isothermal compressibility and specific heat). An energy-entropy argument that physically favors the relevance of one of these characteristic temperatures, namely, the nonvanishing temperature at which the chemical potential reaches the Fermi energy value, is presented. Such an argument allows interpreting the nonmonotonic dependence of the chemical potential on temperature, as an indicator of the appearance of a thermodynamic regime, where the equilibrium states of a trapped Fermi gas are characterized by larger fluctuations in energy and particle density as is revealed in the corresponding thermodynamics susceptibilities.

Void Formation in the Growing Scale Induced by the Divergence of the Diffusive Ionic Flux in High Temperature Oxidation of Metals

2009 ◽  
Vol 289-292 ◽  
pp. 1-13 ◽  
Author(s):  
Toshio Maruyama ◽  
Mitsutoshi Ueda ◽  
Kenichi Kawamura
Keyword(s):  
High Temperature ◽  
High Temperature Oxidation ◽  
Chemical Potential ◽  
Quantitative Estimation ◽  
Kinetic Equations ◽  
Void Formation ◽  
Ionic Flux ◽  
Temperature Oxidation ◽  
Ionic Fluxes ◽  
Formation Behavior

Voids are frequently generated and dispersed in oxide scales formed in high temperature oxidation of metals. The divergence of ionic flux may play an important role in the void formation in a growing scale. Kinetic equations were derived for describing chemical potential distribution, ionic fluxes and their divergence in the scale. The divergence was found to be the measure of void formation. Defect chemistry in scales is directly related to the sign of divergence and gives an indication of the void formation behavior. The quantitative estimation on the void formation was successfully applied to a growing magnetite scale in high temperature oxidation of iron at 823 K.

scholarly journals Transverse Momentum Distributions of Hadrons Produced in Pb-Pb Collisions at LHC EnergysNN=2.76TeV

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Saeed Uddin ◽  
Inam-ul Bashir ◽  
Riyaz Ahmed Bhat
Keyword(s):  
Experimental Data ◽  
Transverse Momentum ◽  
Chemical Potential ◽  
Particle Density ◽  
Strong Increase ◽  
Collective Flow ◽  
Alice Experiment ◽  
Particle Species ◽  
Transverse Momentum Spectra ◽  
Freeze Out

The transverse momentum spectra of several types of hadrons,p,p̅,K+,K-,Ks0,Λ,Ω,Ω̅,Ξ-, andΞ̅produced in most central Pb-Pb collisions at LHC energysNN=2.76 TeV have been studied at midrapidity (|y|<0.5) using an earlier proposed unified statistical thermal freeze-out model. The calculated results are found to be in good agreement with the experimental data measured by the ALICE experiment at LHC. The model calculation fits provide the thermal freeze-out conditions in terms of the temperature and collective flow effect parameters for different particle species. Interestingly the model parameter fits to the experimental data reveal stronger collective flow in the system and lesser freeze-out temperatures of the different particle species as compared to Au-Au collisions at RHIC. The strong increase of the collective flow appears to be a consequence of the increasing particle density at LHC. The model used incorporates a longitudinal as well as transverse hydrodynamic flow. The chemical potential has been assumed to be nearly equal to zero for the bulk of the matter owing to high degree of nuclear transparency effect at such collision energies. The contributions from heavier decay resonances are also taken into account.

Thermodynamics and foundations of mass-action kinetics

2005 ◽  
Vol 30 (1-2) ◽  
pp. 3-113 ◽  
Author(s):  
Miloslav Pekař
Keyword(s):  
Chemical Kinetics ◽  
Reaction Rate ◽  
Chemical Potential ◽  
Kinetic Equations ◽  
Reaction Rates ◽  
Equilibrium States ◽  
Mass Action ◽  
Rate Equations ◽  
Mass Action Kinetics ◽  
Non Equilibrium

A critical overview is given of phenomenological thermodynamic approaches to reaction rate equations of the type based on the law of mass-action. The review covers treatments based on classical equilibrium and irreversible (linear) thermodynamics, extended irreversible, rational and continuum thermodynamics. Special attention is devoted to affinity, the applications of activities in chemical kinetics and the importance of chemical potential. The review shows that chemical kinetics survives as the touchstone of these various thermody-namic theories. The traditional mass-action law is neither demonstrated nor proved and very often is only introduced post hoc into the framework of a particular thermodynamic theory, except for the case of rational thermodynamics. Most published “thermodynamic'’ kinetic equations are too complicated to find application in practical kinetics and have merely theoretical value. Solely rational thermodynamics can provide, in the specific case of a fluid reacting mixture, tractable rate equations which directly propose a possible reaction mechanism consistent with mass conservation and thermodynamics. It further shows that affinity alone cannot determine the reaction rate and should be supplemented by a quantity provisionally called constitutive affinity. Future research should focus on reaction rates in non-isotropic or non-homogeneous mixtures, the applicability of traditional (equilibrium) expressions relating chemical potential to activity in non-equilibrium states, and on using activities and activity coefficients determined under equilibrium in non-equilibrium states.

Phase field approaches of bone remodeling based on TIP

2016 ◽  
Vol 41 (1) ◽  
Author(s):  
Jean-François Ganghoffer ◽  
Rachid Rahouadj ◽  
Julien Boisse ◽  
Samuel Forest
Keyword(s):  
Bone Remodeling ◽  
Phase Field ◽  
Bone Matrix ◽  
Kinetic Equations ◽  
Diffuse Interface ◽  
Irreversible Processes ◽  
Internal Variables ◽  
Second Phase ◽  
Modeling Framework ◽  
Sequence Of Events

AbstractThe process of bone remodeling includes a cycle of repair, renewal, and optimization. This adaptation process, in response to variations in external loads and chemical driving factors, involves three main types of bone cells: osteoclasts, which remove the old pre-existing bone; osteoblasts, which form the new bone in a second phase; osteocytes, which are sensing cells embedded into the bone matrix, trigger the aforementioned sequence of events. The remodeling process involves mineralization of the bone in the diffuse interface separating the marrow, which contains all specialized cells, from the newly formed bone. The main objective advocated in this contribution is the setting up of a modeling and simulation framework relying on the phase field method to capture the evolution of the diffuse interface between the new bone and the marrow at the scale of individual trabeculae. The phase field describes the degree of mineralization of this diffuse interface; it varies continuously between the lower value (no mineral) and unity (fully mineralized phase, e.g. new bone), allowing the consideration of a diffuse moving interface. The modeling framework is the theory of continuous media, for which field equations for the mechanical, chemical, and interfacial phenomena are written, based on the thermodynamics of irreversible processes. Additional models for the cellular activity are formulated to describe the coupling of the cell activity responsible for bone production/resorption to the kinetics of the internal variables. Kinetic equations for the internal variables are obtained from a pseudo-potential of dissipation. The combination of the balance equations for the microforce associated to the phase field and the kinetic equations lead to the Ginzburg–Landau equation satisfied by the phase field with a source term accounting for the dissipative microforce. Simulations illustrating the proposed framework are performed in a one-dimensional situation showing the evolution of the diffuse interface separating new bone from marrow.

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