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.

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.

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.

A Study of Eddy Viscosity Coefficient in Numerical Tidal Simulation

Based on the fluid motion equations, the physical meaning of eddy viscosity coefficient and the rationality of the Boussinesq hypothesis are discussed in this paper. The effect of the coefficient on numerical stability is analyzed briefly. A semi-enclosed rectangular sea area, with an orthogonal spur dike, is applied in a 2-D numerical model to study the effect of horizontal eddy viscosity coefficient (A(H)), The computed result shows that A(H) has little influence on the tidal level and averaged flow velocity, but has obvious influence on the intensity and the range of return flow around near the spur dike. Correspondingly, a wind-driven current pool and an annular current are applied in a 3-D numerical model respectively to study the effect of vertical eddy viscosity coefficient (A(V)). The computed result shows that the absolute value of A(V) is inversely proportional to that of horizontal velocity, and the vertical gradient value of A(V) determines the vertical distribution of horizontal velocity, The distribution form of A(V) is theoretically recommended as a parabolic type, of which the maximum value appears at 0.5 H.

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.

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.

On the micropolar flow in a circular pipe: the effects of the viscosity coefficients

This paper considers the stationary flow of incompressible micropolar fluid through a thin cylindrical pipe governed by the pressure drop between pipe’s ends. Its goal is to investigate the influence of the viscosity coefficients on the effective flow. Depending on the magnitude of viscosity coefficients with respect to the pipe’s thickness, it derives different asymptotic models and discusses their properties.

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.

Measurement of Diffusion Coefficients of Air in Silicone Oil and in Hydraulic Oil

A piston-cylinder apparatus was established to measure the solubility and diffusivity of air in dimethyl silicone oils and in hydraulic oils based on the PVT state equation of air and the solution of unsteady one-dimensional diffusion equation.The measured diffusivity-temperature relation can be well fitted by the Arrhenius equation for engineering applications.The correlation between the solute diffusivity D and solvent viscosity μ is examined.In terms of Eyring＇s activation theory,the activation in the air-silicone-oil diffusion process is quite different from that in the momentum transport of the silicone oil：the activation entropy of the former is positive while that of latter is negative.However,the activation enthalpies of the two processes are in the same order of magnitude,which leads to the observation that Dμ/T is roughly constant.

Experimental Study on the Viscosity of Soft Cohesive Sediments Around A Vibrating Pillar

Offshore structures are subject to environmental loads such as waves,currents,or wind,which may induce cyclic lateral vibration at the foundations.These cyclic vibration loadings may affect the rheological property of the sediments adjacent to the foundation and the stability of the structures.This is especially true when the structures are founded on cohesive sedimentary bed.In this study,the viscosity of soft cohesive sediments adjacent to a vibrating pillar was considered,and as a primary index of the rheological characteristics of the sediments.The investigation was performed using the sinking ball method.The experimental findings indicated that the viscosity of cohesive sediments decrease with increase of the liquidity index and vibration intensity.A simple semi-empirical formula was proposed.The structures of the cohesive sediments were destroyed due to the mechanical vibration,and the sediments were fluidized during vibration loads.The shear strength of the cohesive sediments decreased with increased vibration intensity,not only because of the increased pore water pressure but also the decreased viscosity of cohesive sediments following sediment fluidization.

Viscosity testing method of ultra-low temperature drilling fluids for polar glacier drilling

According to the working environment of the polar glacier core drilling, a separatory funnel capillary viscometer which can be used for testing the viscosity of liquids under ultra-low temperature conditions was de- signed. This viscometer has a simple structure and it is easy to operate, which can meet the testing requirements of different temperature conditions. The viscosity of the dimethyl silicone oil KF-96L-2.0cs was measured under different temperatures using this designed viseometer, and it is found that the viscometer coefficient K changes linearly with temperature. This testing method has relatively high test accuracy and its relative error is less than 4%, which can be used to test the viscosity of the different liquids in ultra-low temperature conditions.

Molecular dynamics simulation of self-diffusion coefficients for liquid metals

The temperature-dependent coefficients of self-diffusion for liquid metals are simulated by molecular dynamics meth ods based on the embedded-atom-method （EAM） potential function. The simulated results show that a good inverse linear relation exists between the natural logarithm of self-diffusion coefficients and temperature, though the results in the litera ture vary somewhat, due to the employment of different potential functions. The estimated activation energy of liquid metals obtained by fitting the Arrhenius formula is close to the experimental data. The temperature-dependent shear-viscosities obtained from the Stokes-Einstein relation in conjunction with the results of molecular dynamics simulation are generally consistent with other values in the literature.

A fiber-array probe technique for measuring the viscosity of a substance under shock compression

A fiber-array probe is designed to measure the damping behavior of a small perturbed shock wave in an opaque substance, by which the effective viscosity of substance under the condition of high temperature and high pressure can be constrained according to the flyer-impact technique. It shows that the measurement precision of the shock arrival time by using this technique is within 2 ns. To easily compare with the results given by electrical pin technique, the newly developed method is used to investigate the effective viscosity of aluminum （Al）. The shear viscosity coefficient of A1 is determined to be 1700 Pa.s at 71 GPa with a strain rate of 3.6× 10^6 s-1, which is in good agreement with the results of other methods. The advantage of the new technique over the electrical pin one is that it is applicable for studying the non-conductive substances.

MODELING A SOLID BOUNDARY AS A FLUID OF INFINITE VISCOSITY

A new approach to model viscosity in the conservation of momentum equations is presented and discussed. Coefficient of viscosity is modeled in such a way that it reaches asymptotically to infinity at the solid boundary but still yields a finite value for the shear stress at the solid wall. Basic objective of this research is to show that certain combinations of higher order normal velocity gradients become zero at the solid boundary. Malled solutions for the Couette flow and Poiseuille flow between two parallel plates are obtained by modeling the coefficient of viscosity in a novel way. Also, viscous drag computed by our model is expected to yield higher values than the values predicted by the existing models, which matches closely to the experimental data.

Intradiffusion, density and viscosity studies in binary liquid systems of acetylacetone + DMF/DMSO/benzene at 303.15 K and 333.15 K

Intradiffusion coefficients of acetylacetone(AcAc) and DMF/DMSO/benzene in binary systems over the entire concentration range at 303.15 K were determined by 1H diffusion-order spectroscopy(DOSY) nuclear magnetic resonance(NMR) method based pulse field gradient(PFG).The densities and viscosities of the above three binary systems at 303.15 K were also studied and employed to calculate the excess molar volumes(V^E) and deviations in viscosity(△η).Besides,experiments were carried out at 333.15 K for the system of AcAc+DMF.The solvent and temperature effect upon the difference in D between enol and keto tautomers,the tautomeric equilibrium and excess properties(V^E and △η) were discussed as well.Isotherms of V^E as a function of mole fraction of AcAc(χ_1) show positive deviations in benzene but negative deviations in DMF and DMSO,whereas isotherms of △ηas a function of χ_1 record positive deviations in DMF but negative in benzene and DMSO.V^E values show more negative and △η values are less positive in the system of AcAc+DMF at 333.15 K compared to 303.15 K.The V^E and △η were fitted to a Redlich-Kister type equation and the measured results were interpreted concerning molecular interactions in the solutions.

Concentration and temperature dependence of viscosity of uranium solutions in H2O and 3mol／L HNO3

Viscosities of uranium solutions in H2O and 3 mol/L HNO3 medium were measured by Ubbelhode flow vis-cometer in the concentration range of 0.5%3.0% from 10 篊 to 30 篊 at 5 篊 interval. Viscosity data were interpreted in terms of an empirical equation; h =aoexp(boM+coM2). Values of coefficients ao, bo and co were calculated for all the three systems studied. Flow activation energies and thermodynamic parameters were also evaluated.

Anomalous Viscosity of Vortex Hall States in Graphene

We study temperature effect on anomalous viscosity of Graphene Hall fluid within quantum many-vortex hydrodynamics. The commonly observed filling fraction, in the range is considered. An expression for anomalous viscosity dependent on a geometric parameter-Hall expansion coefficient is obtained at finite temperatures. It arises from strained induced pseudo-magnetic field in addition to an anomalous term in vortex velocity, which is responsible for renormalization of vortex-vortex interactions. We observed that both terms greatly modify the anomalous viscosity as well as an enhancement of weakly observed v fractions. Finite values of the expansion coefficient produce constant and infinite viscosities at varying temperatures. The infinities are identified as energy gaps and suggest temperatures at which new stable quantum hall filling fractions could be seen. This phenomenon is used to estimate energy gaps of already measured fractional Quantum Hall States in Graphene.

Viscosity Indices of Rapeseed Oil

In this article, viscosity indices was presented for a number of vegetable oils, crude rapeseed oil, degummed rapessed oil, rapeseed oil dry, rapeseed oil bleache and refined rapeseed oil using two methods. Viscosity indices were calculated from the measured viscosity at 40℃ and 100℃ using ASTM D （American Society for Testing and Materials ） 2270 and method graphically using ASTM D 341. The viscosity-temperature coefficients for vegetable oils were calculated from the measured viscosity at 40℃ and 100℃.