二维可压缩流体Kelvin-Helmholtz不稳定性

利用高精度数值格式,研究了二维可压缩流体中的Kelvin-Helmholtz不稳定性,主要研究了可压缩性对Kelvin-Helmholtz稳定性增长率的影响.模拟定量的给出低Mach和高Mach数两种情况下,初始静压和对流Mach数以及Kelvin-Helmholtz不稳定性线性增长率的关系.模拟结果和自由剪切层以及混合层的实验结果以及理论分析一致.模拟表明,对流Mach数是描述流体可压缩性的合适参数,对流Mach数越小流体越不可压,Kelvin-Helmholtz不稳定性的线性增长率随对流Mach数的增加而减小. 关键词： Kelvin-Helmholtz不稳定性 可压缩流体 Mach数 超音速流体     

Preparation of carbon nanotubes-incorporated polymeric microspheres for electrorheological fluids

Electrically conducting polymeric microspheres having an average diameter of 92 μm were prepared from composites of multiwalled carbon nanotubes (MWCNTs) and suspension-polymerized poly(vinyl chloride) (PVC) particles. Cetyl trimethylammonium bromide and sodium dodecylbenzene sulfonate were selected as the surfactants to stably disperse the MWCNTs in water. Strong adhesion of MWCNTs on the surfaces of the PVC microspheres was observed from the images obtained by field emission scanning electron microscopy. The amount of MWCNTs adsorbed on the microspheres was approximately 2 wt.%, determined by thermogravimetric analysis. The electrical conductivity of these composite-microspheres was remarkably increased upto 1.5 × 10⁻⁴ S/cm compared with that of the pure PVC microspheres (less than 10⁻¹⁴ S/cm), because of the electrically conducting MWCNTs on their surfaces. These microspheres also showed an electrorheological (ER) effect under an electric field (1.8 kV/mm) owing to the interfacial polarization of the MWCNTs-adsorbed microspheres, when they were dispersed in silicone oil (20 wt.%). The MWCNT-adsorbed PVC microspheres formed linear structures by electric force; i.e. the individual microspheres were connected to neighboring microspheres.     

Criterion for long-wavelength electromagnetic instability of a homogeneous relativistic plasma

Electromagnetic instability of an unmagnetized homogeneous relativistic plasma with an anisotropic velocity distribution having a center of symmetry is analyzed. A stability criterion is derived for slowly varying long-wavelength perturbations. The criterion is formulated as a set of equalities that are not valid for ellipsoidal velocity distributions, but can be satisfied for other anisotropic distributions. The relativistic case is special only in that the rest mass is replaced with the relativistic one.     

Shear instability in fluids with a density-dependent viscosity

We present a shear instability, which can be triggered in compressible fluids with density-dependent viscosity at shear rates above critical. The instability mechanism is generic: It is based on density-dependent viscosity, compressibility, as well as flow two-(three-)dimensionality that provides coupling between streamwise and transversal velocity components and density variations. The only factor stabilizing the instability is fluid elasticity. The corresponding eigenvalue problem for a plane Couette flow is solved analytically in the limiting cases of large and small wave numbers.     

Hydromagnetic instability of streaming fluids in porous medium

The instability of the plane interface between two uniform, superposed, electrically conducting and counter-streaming fluids through a porous medium is considered in the presence of a horizontal magnetic field. In the absence of surface tension, perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming if perturbations in the direction of streaming are ignored. For perturbations in all other directions there exists instability for a certain wavenumber range. The instability of this system is postponed by the presence of magnetic field. The magnetic field and surface tension are able to suppress this Kelvin-Helmholtz instability for small wavelength perturbations and the medium porosity reduces the stability range given in terms of a difference between the streaming velocities and the Alfvén velocity.This research forms a part of the research project awarded to the first author (R.C.S.) by the University Grants Commission.     

Mean effects of turbulence on elliptic instability in fluids

Elliptic instability in fluids is discussed in the context of the Lagrangian-averaged Navier-Stokes-alpha (LANS-alpha) turbulence model. This model preserves the Craik-Criminale (CC) family of solutions consisting of a columnar eddy and a Kelvin wave. The LANS-alpha model is shown to preserve elliptic instability. However, the model shifts the critical stability angle. This shift increases (decreases) the maximum growth rate for long (short) waves. It also introduces a band of stable CC solutions for short waves.     

Yieldlike constitutive transition in shear flow of entangled polymeric fluids

We describe an unexpected constitutive transition in entangled polymer solutions. At and beyond a critical stress, the initial spatially homogeneous and well-entangled sample transforms from its entangled (coiled) state into a fully disentangled (stretched) state over a period during which the resulting shear rate increases in a spatially inhomogeneous fashion. In the mode of controlled shear rate, the sample exhibits a stress plateau over three decades. Flow birefringence and normal stress observations unravel additional features of these flow phenomena.     

Direct visualization of continuous simple shear in non-Newtonian polymeric fluids

Using a particle tracking velocimetric technique, we show direct evidence of nonlinear velocity profiles during simple-shear flow of an entangled polymer solution, offering new insight into the origins of such characteristics as stress overshoot. Upon a startup shear by imposing a constant velocity on one of the two surfaces that confine the sample, the velocity field evolves from the initial linearity across the gap to a final state with a shear rate gradient. The unexpected deviation from the widely assumed linear variation of the velocity along the gap direction is most plausibly due to the entangled polymer's ability to disentangle in the presence of high shear that can orient the polymer chains leading to anisotropy in their mutual constraint.     

General mechanism for the meandering instability of rivulets of Newtonian fluids

A rivulet flowing down an inclined plane often does not follow a straight path, but starts to meander spontaneously. Here we show that this instability is the result of two key ingredients: fluid inertia and anisotropy of the friction between rivulet and substrate. Meandering only occurs if the motion normal to the instantaneous flow direction is more difficult than parallel to it. We give a quantitative criterion for the onset of meandering and confirm it by comparing to the flow of a rivulet between two glass plates which are wetted completely. Above the threshold, the rivulet follows an irregular pattern with a typical wavelength of a few cm.     

Lyapunov instability of two-dimensional fluids: Hard dumbbells

We generalize Benettin's classical algorithm for the computation of the full Lyapunov spectrum to the case of a two-dimensional fluid composed of linear molecules modeled as hard dumbbells. Each dumbbell, two hard disks of diameter sigma with centers separated by a fixed distance d, may translate and rotate in the plane. We study the mixing between these qualitatively different degrees of freedom and its influence on the full set of Lyapunov exponents. The phase flow consists of smooth streaming interrupted by hard elastic collisions. We apply the exact collision rules for the differential offset vectors in tangent space to the computation of the Lyapunov exponents, and of time-averaged offset-vector projections into various subspaces of the phase space. For the case of a homogeneous mass distribution within a dumbbell we find that for small enough d/sigma, depending on the density, the translational part of the Lyapunov spectrum is decoupled from the rotational part and converges to the spectrum of hard disks. (c) 1998 American Institute of Physics.     

Nonlinear Rayleigh-Taylor instability in magnetic fluids between two parallel plates

A nonlinear stage of the two-dimensional Rayleigh-Taylor instability for two magnetic fluids of finite thickness is studied by including the effect of surface tension between the two fluids. The system is subjected to a tangential magnetic field. The method of multiple scale perturbations is used in order to obtain uniformly valid expansions near the cutoff wavenumber separating stable and unstable deformations. Two nonlinear Schrödinger equations are obtained, one of which leads to the determination of the cutoff wavenumber. The other Schrödinger equation is used to analyze the stability of the system. It is found that if a finite-amplitude disturbance is stable, then a small modulation to the wave is also stable. It is also found that the tangential magnetic field plays a dual role in the stability criterion. Finally, the magnetic permeability constants of the fluid affect the stability conditions.     

Propagation and modulational instability of Rossby waves in stratified fluids

Perturbation analysis and scale expansion are used to derive the (2+1)-dimensional coupled nonlinear Schrödinger (CNLS) equations that can describe interactions of two Rossby waves propagating in stratified fluids. The (2+1)-dimensional equations can reflect and describe the wave propagation more intuitively and accurately. The properties of the two waves in the process of propagation can be analyzed by the solution obtained from the equations using the Hirota bilinear method, and the influence factors of modulational instability are analyzed. The results suggest that, when two Rossby waves with slightly different wave numbers propagate in the stratified fluids, the intensity of bright soliton decreases with the increases of dark soliton coefficients. In addition, the size of modulational instable area is related to the amplitude and wave number in y direction.     

Criterion for instability of oxide film growth with respect to formation of cracks

If the rate of oxidation along metal grain boundaries is higher than that in the perfect metal, the oxide growth in these regions is accompanied by deformation of the oxide film and creation of strongly non-uniform stresses. The latter is shown to result in formation of cracks if h >l (γ/lE)^1/5, where h is the oxide-film thickness, l the metal-grain size, γ the oxide surface energy, and E the oxide Young modulus. The criterion derived is applied to interpret the transition from the parabolic to linear regime of oxidation of Zr alloys.     

The instability of streaming fluids with fine dust in porous medium

The instability of the plane interface between two uniform, superposed, and streaming fluids permeated with suspended particles through porous medium is considered. The effect of a uniform horizontal magnetic field on the problem is also studied. In the absence of surface tension, perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming if perturbations in the direction of streaming are ignored, whereas for perturbations in all other directions there exists instability for a certain wavenumber range. The instability of the system is postponed by the presence of magnetic field. The magnetic field and surface tension are able to suppress this Kelvin-Helmholtz instability for small wavelength perturbations and the medium porosity reduces the stability range given in terms of a difference in streaming velocities and the Alfvén velocity. The suspended particles do not affect the above results.     

Heterogeneity and the role of normal stresses during the extensional thinning of non-Brownian shear-thickening fluids

We contrast the extensional and shear dynamics of non-Brownian suspensions as a function of particle concentration. We show that the thinning rate selected during the viscoelastic pinch-off of a liquid bridge is related to the shear rate at which normal stresses become positive, which differs from the shear rate at the onset of shear thickening. By tracking particles, we demonstrate that the extensional flow is heterogeneous, with local variations of the volume fraction consistent with self-dilution. This nonuniform structure is the cause of the buckling of the threads formed after breakup.     

The dispersion of polymeric materials with the use of supercritical fluids

The dispersion of polyisobutylene was studied on a Thar RESS-100-2 test bench over the temperature and pressure ranges 45–120°C and 100–350 bar; 30–1000 nm particles were obtained. Particle size could be controlled by varying process parameters. A procedure for modifying polymer particles during rapid expansion of supercritical solutions was suggested. Modification suppressed agglomeration and caused particle coating with a modifier (NaCl). The use of supercritical fluid antisolvents was shown to be promising for the dispersion of polymers to nanosized particles. An experimental bench for performing such processes was described. A procedure for trapping nanoparticles prepared using antisolvents was suggested. Particles with sizes of 10 to 150 nm were obtained in the dispersion of polystyrene in the toluene-polystyrene-supercritical carbon dioxide system at 40–150 bar and temperatures of 40 and 100°C.     

Hydromagnetic parametric resonance instability of two superposed conducting fluids in porous medium

Rayleigh–Taylor instability of a heavy fluid supported by a lighter one through porous medium, in the presence of a uniform, horizontal and oscillating magnetic field is studied. The fluids are taken as viscous (obeying Darcy's law), uniform, incompressible, and infinitely conducting. The amplitude of the oscillating part of the field is taken to be small compared with its steady part. The dispersion relation is obtained in the form of a third-order differential equation, with time as the independent variable and with periodic coefficients, for the vertical displacement of the surface of separation of the two fluids from its equilibrium position. The oscillatory magnetic field of frequency ω$\omega$ and steady part _H0$H_0$ has a stabilizing influence on a mode of disturbance which is unstable in a steady magnetic field of strength _H0$H_0$. It is found that the oscillatory magnetic field and porosity of the porous medium have stabilizing effects, while the medium permeability has a destabilizing influence on the considered system. For a constant value of any of these physical parameters, the system has been found to be unstable (for small wavenumbers) as well as stable afterwards after a definite wavenumber value. The marginal stability case of parametric resonance holds when _M1=_M2=0$M_1=M_2=0$ (and hence m=0$m=0$), in which the characteristic exponents, and the corresponding solutions for u$u$ break down, is also investigated in detail. It is found, to order ?$?$, that the effect of an oscillating magnetic field has no stabilizing influence on a disturbance which is marginally stable in the steady magnetic field; while to order ?²${?}^2$, and when the magnetic field oscillates, a resonance between this mode of disturbances and the oscillating field leads to instability when _ρ2>_ρ1${\rho }_2>{\rho }_1$. It is found also, in this resonant case, that all the constant or varied physical parameters, mentioned above, have destabilizing influences on the considered system. Finally, the other two resonance points appear in non-porous media (i.e., when m=±iω$m=\pm \mathrm{i}\omega$ and m=±2iω$m=\pm 2\mathrm{i}\omega$), are disappeared here due to the presence of the porous medium.