Bulk Viscosity Coefficient Research Articles

On the Breakdown of Regular Solutions with Finite Energy for 3D Degenerate Compressible Navier–Stokes Equations

In this paper, the three-dimensional (3D) isentropic compressible Navier–Stokes equations with degenerate viscosities (ICND) is considered in both the whole space and the periodic domain. First, for the corresponding Cauchy problem, when shear and bulk viscosity coefficients are both given as a constant multiple of the density’s power ( $$\rho ^\delta $$ with $$0<\delta <1$$ ), based on some elaborate analysis of this system’s intrinsic singular structures, we show that the $$L^\infty $$ norm of the deformation tensor D(u) and the $$L^6$$ norm of $$\nabla \rho ^{\delta -1}$$ control the possible breakdown of regular solutions with far field vacuum. This conclusion means that if a solution with far field vacuum of the ICND system is initially regular and loses its regularity at some later time, then the formation of singularity must be caused by losing the bound of D(u) or $$\nabla \rho ^{\delta -1}$$ as the critical time approaches. Second, when $$0<\delta \le 1$$ , under the additional assumption that the shear and second viscosities (respectively $$\mu (\rho )$$ and $$\lambda (\rho )$$ ) satisfy the BD relation $$\lambda (\rho )=2(\mu '(\rho )\rho -\mu (\rho ))$$ , if we consider the corresponding problem in some periodic domain and the initial density is away from the vacuum, it can be proved that the possible breakdown of classical solutions can be controlled only by the $$L^\infty $$ norm of D(u). It is worth pointing out that, except the conclusions mentioned above, another purpose of the current paper is to show how to understand the intrinsic singular structures of the fluid system considered now, and then how to develop the corresponding nonlinear energy estimates in the specially designed energy space with singular weights for the unique regular solution with finite energy.

Cosmic acceleration with bulk viscosity in modified f(Q) gravity

In this article, we have investigated the role of bulk viscosity to study the accelerated expansion of the universe in the framework of modified $f(Q)$ gravity. The gravitational action in this modified gravity theory has the form $f(Q)$, where $Q$ denote the non-metricity scalar. In the present manuscript, we have considered a bulk viscous matter-dominated cosmological model with the bulk viscosity coefficient of the form $\xi =\xi _{0}+\xi _{1}H+\xi _{2}\left( \frac{\dot{H}}{H}+H\right) $ which is proportional to the velocity and acceleration of the expanding universe. Two sets of limiting conditions on the bulk viscous parameters $\xi _{0},$ $\xi _{1},$ $% \xi _{2}$ and model parameter $\alpha $ arose here out of which one condition favours the present scenario of cosmic acceleration with a phase transition and corresponds to the universe with a Big Bang origin. Moreover, we have discussed the cosmological behaviour of some geometrical parameters. Then, we have obtained the best fitting values of the model parameters $\xi _{0},$ $\xi _{1},$ $\xi _{2}$ and $\alpha $ by constraining our model with updated Hubble datasets consisting of $57$ data points and recently released Pantheon datasets consisting of $1048$ data points which show that our obtained model has good compatibility with observations. Further, we have also included the Baryon Acoustic Oscillation (BAO) datasets of six data points with the Hubble \& Pantheon datasets and obtained slightly different values of the model parameters. Finally, we have analyzed our model with the statefinder diagnostic analysis and found some interesting results and are discussed in details.

Exploring new physics beyond the standard cosmology with Dark Energy Survey Year 1 Data

Abstract With the recent data from the first year of the Dark Energy Survey (DES Y1), we attempt to probe whether there is new physics beyond the standard cosmology and to reconcile the σ 8 tension between the DES Y1 and Planck datasets in three alternative cosmological models. Combining the galaxy clustering and weak gravitational lensing data from the DES Y1 with other cosmological observations including cosmic microwave background radiation, baryon acoustic oscillations, Type Ia supernovae (SNe Ia) and Planck lensing, we find that: (i) For the interacting dark energy model, we have an updated constraint on the modified matter expansion rate ϵ = − 0 . 00004 ± 0 . 00031 , which indicates that there is no hint of interaction between dark matter and dark energy in the dark sector of the universe; (ii) For the viscous dark energy model, up to now, the strictest constraint on the bulk viscosity coefficient η 0 . 00152 at the 2 σ confidence level is obtained; (iii) For the dynamical dark energy model, our constraint on the typical parameter β = − 0 . 04 ± 0 . 12 implies that there is still no evidence of dynamical dark energy. Meanwhile, we find the σ 8 tension can be effectively alleviated in the above three alternatives by constraining them with the DES Y1 and Planck datasets separately.

Cosmic acceleration in LRS bianchi type I space- time with bulk viscosity in general relativity

In present paper our intention to construct a locally rotational symmetric bianchi type I space time under framework of massless scalar field have flat potential. In existence of bulk viscosity the developed model provides inflationary solutions. The System of nonlinear Einstein field equations are solved by using suitable condition V(φ) = K (constant) and the bulk viscosity coefficient is inversely proportional to scalar of expansion i.e. ξθ = α yields the negative deceleration parameter, which favorable to cosmic accelerating universe in current scenario. The model isotropize at particular cases. The Proper volume for model increase with time represents eternal inflation of present universe. The physical and structural aspects of model are discussed in significantly manner.

COSMIC INFLATION IN BIANCHI TYPE IX SPACE WITH BULK VISCOSITY

In present paper we have constructed the Bianchitype-IX inflationary universe under framework of the effect of bulk viscosity and flat potential. To developed inflationary model we have consider the supplementary criteria that shear coefficient is directly proportional to expansion scalar which provides an appropriate relation with coefficients of metric $b=a^n$ where n is non-negative constant other than one.We conclude that rate of Higgs field decreases with time and proper volume V is increasing function of time which indicates that universe is expanded continuously. To find solutions of fields equations, we assume $ \xi \theta = \alpha$ (constant) as given by Brevik et al. where $\xi $is coefficient of bulk viscosity and $\theta$ expansion in model. The presence of bulk viscosity provides inflationary solution in current model. The model isotropize in special case. The cosmological parameters of model are also studied.

Multiscale simulations of interfacial slip for polymer melts under shear flow

The low shear rate interfacial slip behaviors of nonentangled bead–spring polymer melts are firstly simulated using a multiscale method without constitutive relations and wall slip hypotheses. Two orders of magnitude less computation compared with pure molecular dynamics simulations offers the present multiscale method unique capability to resolve the low shear rate slip problems for complex fluids, and to explore the impacts of bulk viscosity and interfacial friction coefficient on slip phenomenon detailedly. Variation of wall–fluid interaction (WFI) can lead to completely opposite trends of rate-dependent slip. For weak WFI, two distinct slip regimes including rate-independent regime and rapid increase regime can be found due to the competition between bulk viscosity and interfacial friction coefficient. For moderate WFI, the complete dominance of the bulk viscosity leads to a linear relation between the slip length and the bulk viscosity and two distinct regimes composed of rate-independent regime and rapid decrease regime.

Relaxation-time approximation with pair production and annihilation processes

We extend the Boltzmann equation in the relaxation time approximation to explicitly include transitions between particles forming an interacting mixture. Using the detailed balance condition as well as conditions of energy-momentum and current conservation, we show that only two independent relaxation time scales are allowed in such an interacting system. Dissipative hydrodynamic equations and the form of transport coefficients is subsequently derived for this case. We find that the shear and bulk viscosity coefficients, as well as the baryon charge conductivity are independent of the transition time scale. However, the bulk viscosity and conductivity coefficients that can be attributed to the individual components of the mixture depend on the transition time.

Viscosity of the magnetized strongly coupled one-component plasma.

The viscosity tensor of the magnetized one-component plasma, consisting of five independent shear viscosity coefficients, a bulk viscosity coefficient, and a cross coefficient, is computed using equilibrium molecular dynamics simulations and the Green-Kubo relations. A broad range of Coulomb coupling and magnetization strength conditions are studied. Magnetization is found to strongly influence the shear viscosity coefficients when the gyrofrequency exceeds the Coulomb collision frequency. Three regimes are identified as the Coulomb coupling strength and magnetization strength are varied. The Green-Kubo relations are used to separate kinetic and potential energy contributions to each viscosity coefficient, showing how each contribution depends upon the magnetization strength. The shear viscosity coefficient associated with the component of the pressure tensor parallel to the magnetic field, and the two coefficients associated with the component perpendicular to the magnetic field, are all found to merge to a common value at strong Coulomb coupling.

Observational constraints of bulk viscous Friedmann–Robertson–Walker cosmology with hybrid expansion law

In this work, we study bulk viscous Friedmann–Robertson–Walker cosmologies with hybrid expansion law. The bulk viscous theory of dissipative effects described by Eckart theory, truncated Israel–Stewart theory and full Israel–Stewart theory are implemented here. The hybrid expansion law model of scale factor is a general analytic type of evolution from which one can recover power-law and exponential expansion as a special cases. Hybrid expansion law model are applied to describe the present accelerating phase and early phases of evolution. We have determined the cosmological parameters such as Hubble parameter, deceleration parameter, jerk parameter, energy density, bulk viscous pressure and coefficient of bulk viscosity of the universe to construct physically acceptable cosmological model. We have considered both flat and closed space–time of Friedmann–Robertson–Walker cosmology to implement hybrid expansion law with dissipative effect. The variations of the coefficient of bulk viscosity with cosmic evolution are studied here in Eckart, truncated and full Israel–Stewart theory for flat and closed space–time to obtain physically acceptable hybrid expansion models driven by viscosity. We have also estimated observational constraints of the parameters of hybrid expansion law model by considering recent observational data set. We further reveal possible connections of our models with [Formula: see text] tension problem.

Degenerate Bogdanov\u2013Takens bifurcations in a bulk viscous cosmology

Using the dynamical system theory we show that the Friedmann–Robertson–Walker (FRW) cosmological model with bulk viscous fluid in the presence of cosmological constant is equivalent to a degenerate two dimensional Bogdanov–Takens normal form. The equation of state parameter, omega , the bulk viscosity coefficient, xi , and the cosmological constant, Lambda , define the necessary parameters for unfolding the degenerate Bogdanov-Takens system. The fixed points of the system are discussed together with the variation of their stability properties upon changing the relevant parameters omega , Lambda and xi . The variation of the stability properties are visualized by the appropriate bifurcation diagrams. Phase portrait for finite domain and global phase portrait are displayed and the issue of the structural stability is discussed. Typical issues such as late acceleration or inflation that can be induced by viscosity and could have relevance to observational cosmology are also discussed.

Shock wave structure in non-ideal dilute gases under variable Prandtl number

This paper investigates the structure of normal shock waves for a planar steady flow of non-ideal dilute gases under variable viscosity and thermal conductivity using the Navier–Stokes–Fourier approach to the continuum model. The gas is assumed to follow the simplified van der Waals equation of state along with the power-law temperature-dependent coefficients of shear viscosity, bulk viscosity, and thermal conductivity. A closed system of nonlinear differential equations having a variable Prandtl number ( $$\Pr $$ ) is formulated. Exact analytical solutions of the shock wave structure in non-ideal gases are derived for $$\Pr \rightarrow \infty $$ and $$\Pr \rightarrow 0$$ limits, and the corresponding profiles for velocity and temperature are obtained. For $$\Pr \rightarrow 0$$ , an isothermal shock is encountered for high Mach numbers. It appears sooner in non-ideal gases. The solution profiles for $$\Pr =2/3$$ are obtained numerically and compared with the corresponding profiles for $$\Pr \rightarrow 0$$ , 3/4, and $$\infty $$ under the same initial conditions. Qualitative agreement is obtained with the theoretical and experimental results for the shock wave structure. The inverse shock thickness is computed for different values of $$\Pr $$ , and it is found that the inverse shock thickness increases with an increase in the Prandtl number. The bulk viscosity, the non-idealness parameter, the specific heat ratio, the power-law index, and the pre-shock Mach number have a significant effect on the shock wave structure.

Viscous universe with cosmological constant

We investigated a bulk viscous fluid universe with cosmological constant Λ by assuming that the bulk viscosity to be proportional to the Hubble parameter. We found that for an expanding universe, the (relative) matter density will be always greater than a nonzero constant and tends to this nonzero constant in the future. We show that the bulk viscosity model has a significantly better fitting to the combined SNe Ia + CMB + BAO + H(z) data than the ΛCDM model. Generally, the evolution or values of some cosmological parameters predicted by the bulk viscosity model do not deviate significantly from which are obtained from the ΛCDM model since the bulk viscosity coefficient obtained from the astronomical observational data is so small. We also made a statefinder analysis of the bulk viscosity model and found that the evolution of the {r, s} parameters behaves in such a way that 0 < s < 1, 0.945 < r < 1, indicating the bulk viscosity model is different from the ΛCDM model and the other “dark energy” model.

Frequency Dispersion of the Coefficient of Shear Viscosity and the Magnetic Viscous Effect in Magnetic Liquids

Dynamic expressions for bulk and shear viscosity coefficients are obtained on the basis of statistical theory and a model of a two-component system. The dependence of the coefficients of shear viscosity of magnetic fluids based on water, kerosene, and undecane on the frequency and magnitude of an external magnetic field is calculated from the selection of potential energies for intermolecular and dipole–dipole interactions, the radial distribution functions, and the effect of an external magnetic field. The regions of frequency dispersion for the coefficients of shear viscosity of the studied fluids are determined, and the magneto–viscous effect in magnetic fluids is considered.

Numerical Simulations of Shock Waves in Viscous Carbon Dioxide Flows Using Finite Volume Method

An efficient numerical tool for studying shock waves in viscous carbon dioxide flows is proposed. The developed theoretical model is based on the kinetic theory formalism and is free of common limitations such as constant specific heat ratio, approximate analytical expressions for thermodynamic functions and transport coefficients. The thermal conductivity, viscosity and bulk viscosity coefficients are expressed in terms of temperature, collision integrals and internal energy relaxation times. Precomputed in the wide temperature range thermodynamic functions and transport coefficients are implemented to the numerical code which is used for the simulations of the shock wave structure. Including the bulk viscosity to the kinetic model results in the increasing shock width and improves the agreement with experimental data.

Bulk Viscosity of a Suspension of Silicon Oxide Nanoparticles

Data on the bulk viscosity of an aqueous suspension of SiO2 nanoparticles (Ludox TM-50) have been obtained for the first time using an acoustic spectrometer. A wide range of nanoparticle mass concentrations (from 1 to 50 wt %) has been investigated. Spectra of the ultrasound attenuation coefficient and coefficients of longitudinal and dynamic viscosities have been measured. Dependences of the dynamic and bulk viscosity coefficients of the suspensions on the nanoparticle concentration have been obtained.

Some properties and implications of the creation pressure and the generalized equilibrium: modification of the adiabatic index, cosmological perturbations

The creation pressure, due to constant specific entropy particle production, vanishes for a fluid where the sum of the energy density and the isotropic pressure is zero; for example in an empty space–time with the cosmological constant interpreted as vacuum energy density. Within the framework of relativistic thermodynamics theories, the energy–momentum tensor of a linear barotropic fluid with constant specific entropy particle production and in generalized equilibrium can be written as the effective energy–momentum tensor of a perfect linear barotropic fluid where the adiabatic index is a homographic function of the initial adiabatic index. This function shows that by adding constant specific entropy particle production to a phantom fluid, the effective perfect fluid will be without phantom property, whereas there are some fluids that with specific entropy particle production have phantom property. This transformation is useful for obtaining the behaviour of the scale factor of cosmological models. By solving the equation that comes from the entropy production equation, then the transport equation in the framework of the Muller-Israel-Stewart second-order causal relativistic thermodynamics, assuming constant specific entropy particle production and the generalized equilibrium, we obtain the bulk viscosity coefficient ζ and the relaxation time τ. The relation ζ ∝ $$ \rho^{{\frac{1}{2}}} $$ between ζ and the energy density ρ is predicted in spatially flat homogeneous and isotropic (FLRW) cosmological model for any value of the constant state parameter. The gauge–invariant energy density contrast and velocity perturbations of the previous cosmological model in the matter-dominated era with isentropic particle production are studied. The modes of these perturbations are decaying faster than the corresponding modes for the perfect fluid perturbations in the particle number conservation case. Then the isentropic, usually called adiabatic, gauge–invariant energy density contrast and velocity perturbations in case of a perfect linear barotropic fluid with particle number conservation are studied, in particular for negative values of the constant state parameter.

Single trajectory transport coefficients and the energy landscape by molecular dynamics simulations.

The Green-Kubo (GK) method is widely used to calculate the transport coefficients of model liquids by Molecular Dynamics (MD) simulation. A reformulation of GK was proposed by Heyes et al. [J. Chem. Phys. 150, 174504 (2019)], which expressed the shear viscosity in terms of a probability distribution function (PDF) of "single trajectory (ST) viscosities," called "viscuits." This approach is extended here to the bulk viscosity, thermal conductivity, and diffusion coefficient. The PDFs of the four STs expressed in terms of their standard deviations (calculated separately for the positive and negative sides) are shown by MD to be statistically the same for the Lennard-Jones fluid. This PDF can be represented well by a sum of exponentials and is independent of system size and state point in the equilibrium fluid regime. The PDF is not well reproduced by a stochastic model. The PDF is statistically the same as that derived from the potential energy, u, and other thermodynamic quantities, indicating that the transport coefficients are determined quantitatively by and follow closely the time evolution of the underlying energy landscape. The PDFs of out-of-equilibrium supercooled high density states are quite different from those of the equilibrium states.

A Magnetized Dark Energy Type R/W Model with Polytropic Equation of State in Brans-Dicke Theory

In this paper, we study the spatially homogeneous Robertson-Walker cosmological models with magnetized isotropic dark energy like fluid in the scalar-tensor theory of gravitation proposed by Brans-Dicke. Variable cosmological constant ᴧ and Polytropic equation of state have been used to find exact solutions of the models with volumetric expansion and power-law relation. The Physical and dynamical behaviors of the models have been discussed using some physical quantities like energy density, pressure, and coefficient of bulk viscosity.

Numerical simulations of shock waves in viscous carbon dioxide flows using finite volume method

An efficient numerical tool for studying shock waves in viscous carbon dioxide flows is proposed. The developed theoretical model is based on the kinetic theory formalism and is free of common limitations such as constant specific heat ratio, approximate analytical expressions for thermodynamic functions and transport coefficients. The thermal conductivity, viscosity and bulk viscosity coefficients are expressed in terms of temperature, collision integrals and internal energy relaxation times. Precomputed in the wide temperature range thermodynamic functions and transport coefficients are implemented to the numerical code which is used for the simulations of the shock wave structure. Including the bulk viscosity to the kinetic model results in the increasing shock width and improves the agreement with experimental data.

Объемная вязкость суспензии наночастиц оксида кремния

Data on the bulk viscosity of an aqueous suspension of SiO2 nanoparticles (Ludox TM-50) were obtained using an acoustic spectrometer for the first time. A wide range of mass concentrations of nanoparticles (from 1 to 50 wt.%) was considered. The spectra of the attenuation coefficient of ultrasound and the coefficients of longitudinal and dynamic viscosity were measured. The dependences of the dynamic and bulk viscosity coefficients of the suspensions on the nanoparticle concentration were obtained.