scholarly journals The equation of state of a cell fluid model in the supercritical region

2018 ◽  
Vol 21 (4) ◽  
pp. 43502 ◽  
Author(s):  
Kozlovskii ◽  
Pylyuk ◽  
Dobush
Keyword(s):  
Equation Of State ◽  
Fluid Model ◽  
Supercritical Region ◽  
A Cell

scholarly journals Equation of State of a Cell Fluid Model with Allowance for Gaussian Fluctuations of the Order Parameter

2020 ◽  
Vol 65 (12) ◽  
pp. 1080
Author(s):  
I.V. Pylyuk ◽  
O.A. Dobush
Keyword(s):  
Equation Of State ◽  
Order Parameter ◽  
Chemical Potential ◽  
Fluid Model ◽  
Repulsive Interaction ◽  
Collective Variables ◽  
Relative Temperature ◽  
A Cell ◽  
Supercritical Temperature

The paper is devoted to the development of a microscopic description of the critical behavior of a cell fluid model with allowance for the contributions from collective variables with nonzero values of the wave vector. The mathematical description is performed in the supercritical temperature range (T > Tc) in the case of a modified Morse potential with additional repulsive interaction. The method, developed here for constructing the equation of state of the system by using the Gaussian distribution of the order parameter fluctuations, is valid beyond an immediate vicinity of the critical point for wide ranges of the density and temperature. The pressure of the system as a function of the chemical potential and density is plotted for various fixed values of the relative temperature, both with and without considering the above-mentioned contributions. Compared with the results of the zero-mode approximation, the insignificant role of these contributions is indicated for temperatures T > Tc. At T < Tc, they are more significant.

scholarly journals The I-Love-Q Relations for Superfluid Neutron Stars

Universe ◽  
2021 ◽  
Vol 7 (4) ◽  
pp. 111
Author(s):  
Cheung-Hei Yeung ◽  
Lap-Ming Lin ◽  
Nils Andersson ◽  
Greg Comer
Keyword(s):  
Fluid Dynamics ◽  
Equation Of State ◽  
Neutron Stars ◽  
Quadrupole Moment ◽  
Fluid Model ◽  
Normal Component ◽  
Approximate Equation ◽  
Mean Field Model ◽  
Polytropic Model ◽  
Two Fluid

The I-Love-Q relations are approximate equation-of-state independent relations that connect the moment of inertia, the spin-induced quadrupole moment, and the tidal deformability of neutron stars. In this paper, we study the I-Love-Q relations for superfluid neutron stars for a general relativistic two-fluid model: one fluid being the neutron superfluid and the other a conglomerate of all charged components. We study to what extent the two-fluid dynamics might affect the robustness of the I-Love-Q relations by using a simple two-component polytropic model and a relativistic mean field model with entrainment for the equation-of-state. Our results depend crucially on the spin ratio Ωn/Ωp between the angular velocities of the neutron superfluid and the normal component. We find that the I-Love-Q relations can still be satisfied to high accuracy for superfluid neutron stars as long as the two fluids are nearly co-rotating Ωn/Ωp≈1. However, the deviations from the I-Love-Q relations increase as the spin ratio deviates from unity. In particular, the deviation of the Q-Love relation can be as large as O(10%) if Ωn/Ωp differ from unity by a few tens of percent. As Ωn/Ωp≈1 is expected for realistic neutron stars, our results suggest that the two-fluid dynamics should not affect the accuracy of any gravitational waveform models for neutron star binaries that employ the relation to connect the spin-induced quadrupole moment and the tidal deformability.

INFLATIONARY SCENARIO IN BRANS–DICKE THEORY FOR BIANCHI VI0 SPACE–TIME MODEL

2003 ◽  
Vol 12 (01) ◽  
pp. 129-143 ◽  
Author(s):  
SUBENOY CHAKRABORTY ◽  
ARABINDA GHOSH
Keyword(s):  
Equation Of State ◽  
Perfect Fluid ◽  
Analytical Solutions ◽  
Fluid Model ◽  
Space Time ◽  
Time Model ◽  
Exact Analytical Solutions ◽  
Exponential Expansion ◽  
Barotropic Equation ◽  
Space Time Model

We have investigated perfect fluid model in Brans–Dicke theory for Bianchi VI 0 space–time and have obtained exact analytical solutions considering barotropic equation of state. These solutions have been analyzed for different values of the parameters involved and some of them have shown a period of exponential expansion.

Heat Transfer Characteristics of Nitrogen in Supercritical Region Using Redlich-Kwong Equation of State

2019 ◽  
Vol 17 (10) ◽  
Author(s):  
Hussain Basha ◽  
G. Janardhana Reddy ◽  
N. S. Venkata Narayanan
Keyword(s):  
Heat Transfer ◽  
Thermal Expansion ◽  
Equation Of State ◽  
Thermal Expansion Coefficient ◽  
Expansion Coefficient ◽  
Physical Parameters ◽  
Heat Transfer Characteristics ◽  
Reduced Pressure ◽  
Supercritical Region ◽  
Transfer Characteristics

Abstract The present paper studies through numerical methods, the thermodynamic heat transfer characteristics of free convection flow of supercritical nitrogen over a vertical cylinder. In the present analysis, the values of volumetric thermal expansion coefficient ($\beta$) are evaluated based on Redlich-Kwong equation of state (RK-EOS) and Van der Waals equation of state (VW-EOS). The calculated analytical thermal expansion coefficient values using RK-EOS are very close to NIST data values in comparison with VW-EOS. A set of coupled nonlinear partial differential equations (PDEs) governing the supercritical fluid (SCF) flow are derived, converted into non-dimensional form with the help of suitable dimensionless quantities and solved using Crank-Nicolson implicit finite difference method. The simulations are carried out for nitrogen in the supercritical region. The obtained numerical data is expressed in terms of graphs and tables for various values of physical parameters. The increasing value of reduced temperature decreases the average Nusselt number and skin-friction coefficient, whereas amplifying value of reduced pressure enhance the heat transfer rate and wall shear stress in the SCF region. Present results are compared with the previous results and the two are found to be in good agreement, i. e. the numerically generated results found to be in agreement with existing results.

scholarly journals A two-fluid model for tissue growth within a dynamic flow environment

2008 ◽  
Vol 19 (6) ◽  
pp. 607-634 ◽  
Author(s):  
R. D. O'DEA ◽  
S. L. WATERS ◽  
H. M. BYRNE
Keyword(s):  
Cell Population ◽  
Culture Medium ◽  
Local Density ◽  
Fluid Model ◽  
Tissue Growth ◽  
Viscous Drag ◽  
Mechanical Environment ◽  
A Cell ◽  
Two Fluid Model ◽  
Tissue Construct

We study the growth of a tissue construct in a perfusion bioreactor, focussing on its response to the mechanical environment. The bioreactor system is modelled as a two-dimensional channel containing a tissue construct through which a flow of culture medium is driven. We employ a multiphase formulation of the type presented by G. Lemon, J. King, H. Byrne, O. Jensen and K. Shakesheff in their study (Multiphase modelling of tissue growth using the theory of mixtures.J. Math. Biol.52(2), 2006, 571–594) restricted to two interacting fluid phases, representing a cell population (and attendant extracellular matrix) and a culture medium, and employ the simplifying limit of large interphase viscous drag after S. Franks in her study (Mathematical Modelling of Tumour Growth and Stability. Ph.D. Thesis, University of Nottingham, UK, 2002) and S. Franks and J. King in their study (Interactions between a uniformly proliferating tumour and its surrounding: Uniform material properties.Math. Med. Biol.20, 2003, 47–89).The novel aspects of this study are: (i) the investigation of the effect of an imposed flow on the growth of the tissue construct, and (ii) the inclusion of a mechanotransduction mechanism regulating the response of the cells to the local mechanical environment. Specifically, we consider the response of the cells to their local density and the culture medium pressure. As such, this study forms the first step towards a general multiphase formulation that incorporates the effect of mechanotransduction on the growth and morphology of a tissue construct.The model is analysed using analytic and numerical techniques, the results of which illustrate the potential use of the model to predict the dominant regulatory stimuli in a cell population.

BRANS–DICKE THEORY IN BIANCHI III MODEL AND INFLATIONARY SCENARIO

2002 ◽  
Vol 11 (03) ◽  
pp. 391-404 ◽  
Author(s):  
NARAYAN CHANDRA CHAKRABORTY ◽  
SUBENOY CHAKRABORTY
Keyword(s):  
Equation Of State ◽  
Perfect Fluid ◽  
Analytical Solutions ◽  
Fluid Model ◽  
Space Time ◽  
Exact Analytical Solutions ◽  
Inflationary Scenario ◽  
Bianchi Iii ◽  
Barotropic Equation

Brans–Dicke theory with perfect fluid model has been considered in Bianchi III space–time and exact analytical solutions are presented with barotropic equation of state. These solutions have been analyzed and some of them have shown the properties of inflationary scenario.

scholarly journals Incorporation of Fluid Compressibility into the Calculation of the Stationary Mode of Operation of a Hydraulic Device at High Fluid Pressures

2021 ◽  
Vol 17 (2) ◽  
pp. 195-209
Author(s):  
V. A. Tenenev ◽  
◽  
T. Raeder ◽  
A. A. Chernova ◽  
◽  
...  
Keyword(s):  
Equation Of State ◽  
Incompressible Fluid ◽  
Numerical Method ◽  
Fluid Model ◽  
Local Approximation ◽  
Critical Parameters ◽  
Stationary Mode ◽  
High Fluid ◽  
Comparison Of The Results ◽  
Valve Operation

This paper is concerned with assessing the correctness of applying various mathematical models for the calculation of the hydroshock phenomena in technical devices for modes close to critical parameters of the fluid. We study the applicability limits of the equation of state for an incompressible fluid (the assumption of constancy of the medium density) to the simulation of processes of the safety valve operation for high values of pressures in the valve. We present a scheme for adapting the numerical method of S. K. Godunov for calculation of flows of incompressible fluids. A generalization of the method for the Mie – Grüneisen equation of state is made using an algorithm of local approximation. A detailed validation and verification of the developed numerical method is provided, and relevant schemes and algorithms are given. Modeling of the hydroshock phenomenon under the valve actuation within the incompressible fluid model is carried out by the openFoam software. The comparison of the results for the weakly compressible

Thermodynamic excess functions of regular and related solutions according to some equations of state based on the perturbed hard sphere model

1973 ◽  
Vol 26 (10) ◽  
pp. 2071 ◽  
Author(s):  
DK Astin ◽  
ID Watson
Keyword(s):  
Equation Of State ◽  
Hard Sphere ◽  
Equations Of State ◽  
Fluid Model ◽  
Quantitative Agreement ◽  
Excess Functions ◽  
Hard Sphere Model ◽  
Thermodynamic Excess Functions ◽  
Two Fluid Model ◽  
Two Fluid

The excess thermodynamic functions of 12 mixtures, each representative of a certain type of system, have been calculated by means of the van der Waals, Frisch,1 and Carnahan and Starling2 equation of state, in conjunction with one-fluid and two-fluid models of conformal mixtures. In addition, the equation of state of hard sphere mixtures of Mansoori et al.3 has been used. Though none of the approaches give quantitative agreement for any of the systems considered, they all give a qualitative account which broadly reflect the trends in behaviour. In the cases where it is appropriate to comment on the qualitative accuracy the two-fluid model, used with either the Frisch or Carnahan and Starling equation of state, shows a slight superiority to the others.

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