GLOBAL SOLUTIONS TO 1D COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND FREE-BOUNDARY

This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.

GLOBAL CLASSICAL SOLUTION TO THE CAUCHY PROBLEM OF THE 3-D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

In this paper, we consider the global existence of classical solution to the 3-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient λ(ρ)provided that the initial energy is small in some sense. In our result, we give a relation between the initial energy and the viscosity coefficient μ, and it shows that the initial energy can be large if the coefficient of the viscosity μ is taken to be large, which implies that large viscosity μ means large solution.

STABILITY OF VISCOUS SHOCK WAVES FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density- dependent viscosity. The nonlinear stability of the viscous shock waves is shown for certain class of large initial perturbation with integral zero which can allow the initial density to have large oscillation. Our analysis relies upon the technique developed by Kanel~ and the continuation argument.

FREE BOUNDARY VALUE PROBLEM FOR THE CYLINDRICALLY SYMMETRIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

In this paper, we investigate the free boundary value problem （FBVP） for the cylindrically symmetric isentropic compressible Navier-Stokes equations （CNS） with density- dependent viscosity coefficients in the case that across the free surface stress tensor is balanced by a constant exterior pressure. Under certain assumptions imposed on the initial data, we prove that there exists a unique global strong solution which tends pointwise to a non-vacuum equilibrium state at an exponential time-rate as the time tends to infinity.

COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

The global existence of solutions to the equations of one-dimensional compressible flow with density-dependent viscosity is proved. Specifically,the assumptions on initial data are that the modulo constant is stated at x=∞ ＋and x=-∞ ,which may be different ,the density and velocity are in L^z ,and the density is bounded above and below away from zero. The results also show that even under these conditions, neither vacuum states nor concentration states can be formed in finite time.

Investigations on the Equation of State of Neutron Star Matter with Density-dependent Relativistic Mean-field Model

The neutron star as a supernova remnant is attracting high attention recently due to the gravitation wave detection and precise measurements about its mass and radius.In particular,the compact object with a mass of 2.50-2.67 M_(⊙)observed by LIGO Scientific and Virgo collaborations in GW190814,as well as the recent report of a light compact object with a mass and radius of M=0.77_(-0.17)^(+0.20)M_(⊙)and R=10.4_(-0.78)^(+0.86)km within the supernova remnant HESS J1731-347,have posed a great challenge to the investigations into the supranuclear matter.In the inner core of a neutron star,the strangeness degrees of freedom,such as the hyperons,can be present to form a hyperon star.In this work,the neutron star consisting of nucleons and leptons,and the hyperonic star including the hyperons will be studied in the framework of the density-dependent relativistic mean-field(DDRMF)model.Some popular DDRMF parameterizations will be adopted to investigate the properties of nuclear matter and the mass,radius,tidal deformability,and other properties of neutron star and hyperonic stars.We find that the maximum masses of neutron star calculated by DD-MEX,DD-MEX1,DD-MEX2,DD-MEXY and DD-LZ1 sets can be around 2.5-2.6 MM_(⊙)because they can produce quite stiff equations of state(EOSs)due to the strong repulsive contributions from vector potentials at high densities.Moreover,by investigating the influence of the crust EOS and core EOS on the neutron stars,we find that the observational data from HESS J1731-347 suggest the requirement of a crust EOS with a higher L parameter and a core EOS with a lower L parameter,and the M-R relations from the constructed EOSs can also be consistent with the observables of PSR J0740+6620,PSR J0030+0451 from NICER and the GW170817 event.With the inclusion of hyperons,the hyperonic star matter becomes softer compared to the neutron star matter,but the massive hyperonic star can also be obtained with DDRMF parameter sets if the vector meson coupling constants are strong.

LOCAL WELL-POSEDNESS TO THE CAUCHY PROBLEM OF THE 3-D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity μ is a positive constant and the bulk viscosity λ（ρ） = ρ^β with β≥0. Note that the initial data can be arbitrarily large to contain vacuum states.

GLOBAL SOLUTIONS TO A 3D AXISYMMETRIC COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY

In this paper,we consider the 3D compressible isentropic Navier-Stokes equations when the shear viscosityμis a positive constant and the bulk viscosity is λ(ρ)=ρ^(β) with β>2,which is a situation that was first introduced by Vaigant and Kazhikhov in[1].The global axisymmetric classical solution with arbitrarily large initial data in a periodic domain Ω={(r,z)|r=√x^(2)+y^(2),(x,y,z)∈R^(3),r∈I⊂(0,+∞),-∞<z<+∞} is obtained.Here the initial density keeps a non-vacuum state ρ>0 when z→±∞.Our results also show that the solution will not develop the vacuum state in any finite time,provided that the initial density is uniformly away from the vacuum.

Efficient and reversible separation of NH_(3) by deep eutectic solvents with multiple active sites and low viscosities

The efficient separation and collection of ammonia(NH_(3))during NH_(3) synthesis process is essential to improve the economic efficiency and protect the environment.In this work,ethanolammonium hydrochloride(EtOHACl)and phenol(PhOH)were used to prepare a novel class of deep eutectic solvents(DESs)with multiple active sites and low viscosities.The NH_(3) separation performance of EtOHACl+PhOH DESs was analyzed completely.It is figured out that the NH_(3) absorption rates in EtOHACl+PhOH DESs are very fast.The NH_(3) absorption capacities are very high and reach up to 5.52 and 10.74 mol·kg1 at 11.2 and 100.4 kPa under 298.2 K,respectively.In addition,the EtOHACl+PhOH DESs present highly selective absorption of NH_(3) over N_(2) and H_(2) and good regenerative properties after seven cycles of absorption/desorption.The intrinsic separation mechanism of NH_(3) by EtOHACl+PhOH DESs was further revealed by spectroscopic analysis and quantum chemistry calculations.

ZERO DISSIPATION LIMIT TO RAREFACTION WAVES FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH SELECTED DENSITY-DEPENDENT VISCOSITY

This paper is devoted to studying the zero dissipation limit problem for the one-dimensional compressible Navier-Stokes equations with selected density-dependent viscosity.In particular,we focus our attention on the viscosity taking the formμ(ρ)=ρ^(ϵ)(ϵ>0).For the selected density-dependent viscosity,it is proved that the solutions of the one-dimensional compressible Navier-Stokes equations with centered rarefaction wave initial data exist for all time,and converge to the centered rarefaction waves as the viscosity vanishes,uniformly away from the initial discontinuities.New and subtle analysis is developed to overcome difficulties due to the selected density-dependent viscosity to derive energy estimates,in addition to the scaling argument and elementary energy analysis.Moreover,our results extend the studies in[Xin Z P.Comm Pure Appl Math,1993,46(5):621-665].

Non-formation of vacuum states for Navier-Stokes equations with density-dependent viscosity

We consider the Cauchy problem, free boundary problem and piston problem for one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. Using the reduction to absurdity method, we prove that the weak solutions to these systems do not exhibit vacuum states, provided that no vacuum states are present initially. The essential re- quirements on the solutions are that the mass and energy of the fluid are locally integrable at each time, and the Lloc1-norm of the velocity gradient is locally integrable in time.

Viscosity and structure relationship with equimolar substitution of CaO with MgO in the CaO–MgO–Al_(2)O_(3)–SiO_(2)slag melts

Currently,the Al_(2)O_(3)content in the high-alumina slag systems within blast furnaces is generally limited to 16wt%–18.5wt%,making it challenging to overcome this limitation.Unlike most studies that concentrated on managing the MgO/Al_(2)O_(3)ratio or basicity,this paper explored the effect of equimolar substitution of MgO for CaO on the viscosity and structure of a high-alumina CaO-MgO-Al_(2)O_(3)-SiO_(2)slag system,providing theoretical guidance and data to facilitate the application of high-alumina ores.The results revealed that the viscosity first decreased and then increased with higher MgO substitution,reaching a minimum at 15mol%MgO concentration.Fourier transform infrared spectroscopy(FTIR)results found that the depths of the troughs representing[SiO_(4)]tetrahedra,[AlO_(4)]tetrahedra,and Si-O-Al bending became progressively deeper with increased MgO substitution.Deconvolution of the Raman spectra showed that the average number of bridging oxygens per Si atom and the X_(Q^(3))/X_(Q^(2))(X_(Q^(i))is the molar fraction of Q^(i) unit,and i is the number of bridging oxygens in a[SiO_(4)]tetrahedral unit)ratio increased from 2.30 and 1.02 to 2.52 and 2.14,respectively,indicating a progressive polymerization of the silicate structure.X-ray photoelectron spectroscopy(XPS)results highlighted that non-bridging oxygen content decreased from 77.97mol% to 63.41mol% with increasing MgO concentration,whereas bridging oxygen and free oxygen contents increased.Structural analysis demonstrated a gradual increase in the polymerization degree of the tetrahedral structure with the increase in MgO substitution.However,bond strength is another important factor affecting the slag viscosity.The occurrence of a viscosity minimum can be attributed to the complex evolution of bond strengths of non-bridging oxygens generated during depolymerization of the[SiO_(4)]and[AlO_(4)]tetrahedral structures by CaO and MgO.

Incompressible Limit of the Oldroyd-B Model with Density-Dependent Viscosity

This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ Rd, d = 2 or 3 via incompressible limit, in which the initial data is “well-prepared” and the velocity field enjoys the slip boundary conditions. The main idea is to derive the uniform energy estimates for nonlinear systems and corresponding incompressible limit.

Densities and viscosities for ionic liquids [BMIM][BF4] and [BMIM][Cl] and their binary mixtures at various temperatures and atmospheric pressure

The density and viscosity of 1-butyl-3-methylimidazolium tetrafluoroborate[BMIM][BF4]and 1-butyl-3-methylimidazolium chloride[BMIM][Cl]and their binary mixtures within the temperatures from 303.15 K to323.15 K and at ambient pressure were determined in this work.The temperature dependences of density and viscosity were satisfactorily described with the linear model and the Vogel-Tammann-Fulcher type equation,respectively.The molar volume and viscosity of binary IL mixtures were predicted through ideal mixing rules showing that almost null deviations for IL mixtures were observed and their mixing was remarkably close to linear ideal behavior in the molar volumes,while comparatively large errors in viscosity occurred.Additionally,the molar volume of the investigated pure ILs and their mixtures could well be predicted by a predictive model presented by Valderrama et al.(Fluid Phase Equilib.,275(2009)145).

Analysis of the rates of emulsification in intraocular silicone oil tamponades of differing viscosities

AIM:To investigate the rates of emulsification in silicone oil(SO)tamponades of differing viscosities used during pars plana vitrectomy(PPV)in the treatment of complicated vitreoretinal diseases.METHODS:This study was a prospective randomized clinical trial.Totally 290 cases with greater likelihoods of secondary detachment were included and randomly grouped into either Siluron 2000(n=143)or Siluron 5000(n=147)SO tamponades with 23-gauge PPV.Patient followups and data analyses were conducted 1,3,6,and 12 mo post-surgery.RESULTS:The time of the SO emulsification ranged from 1 to 17 mo,with a mean of 7.3±4.2 mo.The Siluron 5000 group showed a slower emulsification rate in comparison to the Siluron 2000 group.The Siluron 2000 group took a shorter time to show signs of emulsification,necessitating earlier SO removal.However,there were no significant differences in the occurrence of complications,including secondary retinal detachment,cataract,corneal abnormality,high intraocular pressure and hypotony.CONCLUSION:The Siluron 2000 SO tamponade shows a faster rate of emulsification than the Siluron 5000 SO,necessitating earlier removal.Both groups show similar results in terms of anatomical success and visual acuity outcome,and there is no significant difference between the SOs regarding the occurrence of complications.

Numerical investigation of variable viscosities and thermal stratification effects on MHD mixed convective heat and mass transfer past a porous wedge in the presence of a chemical reaction

An analysis is presented to investigate the effects of variable viscosities and thermal stratification on the MHD mixed convective heat and mass transfer of a viscous, incompressible, and electrically conducting fluid past a porous wedge in the presence of a chemical reaction. The wall of the wedge is embedded in a uniform nonDarcian porous medium in order to allow for possible fluid wall suction or injection. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically with finite difference methods. Numerical calculations up to the thirdorder level of truncation are carried out for different values of dimensionless parameters. The results are presented graphically, and show that the flow field and other quantities of physical interest are significantly influenced by these parameters. The results are compared with those available in literature, and show excellent agreement.

Densities and Viscosities of the Ionic Liquid [C4mim][PF6]＋ N,N-dimethylformamide Binary Mixtures at 293.15 K to 318.15 K

Viscosities and densities for 1-butyl-3-methylimidazolium hexafluorophosphate （[C4mim][PF6]） and N, N-dimethylformamide （DMF） binary mixtures have been measured at the temperature range from 293.15 K to 318.15 K. It is shown that the viscosities and densities decrease monotonously with temperature and the content of DMF. Various correlation methods including Arrhenius-like equation, Sedclon et al.＇s equation, Redlich-Kister equation with four parameters, and other empirical equations were applied to evaluate these experimental data. A model based on an equation of state Ior estimating the viscosity of mixtures containing ionic liquids were proposed by coupling with the excess Gibbs free energy model of viscosity, which can synchronously calculate the viscosity and the molar volume. The results show that the model gives a deviation of 8.29% for the viscosity, and a deviation of 1.05% for the molar volume when only one temperature-independent adjustable parameter is adopted. The correlation accuracy is further improved when two parameters or one temperature-dependent parameter is used.

Flow characteristics of liquid with pressure-dependent viscosities in microtubes

It is obvious that the pressure gradient along the axial direction in a pipe flow keeps constant according to the Hagen-Poiseuille equation. However, recent experiments indicated that the distribution of the pressure seemed no longer linear for liquid flows in microtubes driven by high pressure （1-30MPa）. Based on H-P equation with slip boundary condition and Bridgman＇s relation of viscosity vs. static pressure, the nonlinear distribution of pressure along the axial direction is analyzed in this paper. The revised standard Poiseuille number with the effect of pressure-dependent viscosity taken into account agrees well with the experimental results. Therefore, the dependence of the viscosity on the pressure is one of the dominating factors under high driven pressure, and is represented by an important property coefficient α of the liquid.

A Generalized Correlation for Characterization of Lubricating Base-oils from Their Viscosities

Lubricating mineral base oils are normally extracted from lube-oil cuts with furfural solvent.Aromatic content in the raffinate phase from extraction process is an essential parameter that affects the quality of the lubricating base-oils.For determination of aromatic content by the usual ASTM D3238 method,density,refractive index and molecular weight of the raffinate are required.In this work,a new generalized correlation is developed for de-termination the aromatic content by using only the measured viscosity of lubricating oil.With a mole fraction of aromatic compounds,the kinematic viscosity may be obtained at any temperature between 60-100°C along with their molecular weight and refractive index.

A Laboratory Study of the Effect of Temperature on Densities and Viscosities of Binary and Ternary Blends of Soybean Oil, Soy Biodiesel and Petroleum Diesel Oil

The depletion of world petroleum reserves and the increased environmental concerns have stimulated the search for alternative sources for petroleum based fuel. The possibility of using vegetable oils as fuel has been recognized, however, due to its high viscosities and low volatilities makes it inefficient for most combustion engines and thus the need to get them chemically altered or transesterified to obtain fatty alkyl esters of the oil (biodiesel). In this study, binary and ternary blends of biodiesel were produced and the effect of temperature on their viscosity and density was investigated. Biodiesel was produced from soybean oil by transesterification of the oil with methanol using potassium hydroxide as a catalyst at a temperature of 60℃ in a batch reactor. Binary and ternary blends of the soy-biodiesel were prepared with soy bean oil and petroleum diesel fuel, respectively. Viscosities and densities of the binary and ternary blends were measured at different temperatures of 20℃ to 90℃ as to determine the effect of temperature on viscosities and densities of the blends. The properties of the soy-biodiesel produced were compared with ASTM standard and found to be within the limits. The results show that the viscosities and densities of both the binary and ternary blends are temperature dependent. The viscosities of binary and ternary blends decreased nonlinearly with temperature, while their densities decreased linearly with temperature. The variation of temperature with viscosity and density of the blends was correlated and the polynomial equation offered the best correlation between temperature and viscosity, while linear equation gave the best correlation between temperature and density. In conclusion, the efficiency of binary and ternary blends of biodiesel in combustion engines is dependent on the viscosity and density of the blends which are invariably temperature dependent.