Numerical study of bifurcation solutions of spherical Taylor-Couette flow

The steady bifurcation flows in a spherical gap (gap ratio sigma=0.18) with rotating inner and stationary outer spheres are simulated numerically for Re(c1)less than or equal to Re less than or equal to 1 500 by solving steady axisymmetric incompressible Navier-Stokes equations using a finite difference method. The simulation shows that there exist two steady stable flows with 1 or 2 vortices per hemisphere for 775 less than or equal to Re less than or equal to 1 220 and three steady stable flows with 0, 1, or 2 vortices for 1 220

Two-time scales inner solutions and motion of a geostrophic vortex

Based on the authors' previous work, in this paper the systematical analyses on the motion and the inner solutions of a geostrophic vortex have been presented by means of thematched asymptotic expansion method with multiple time scales (S/gh001/2 and α S/gh001/2) and space scales. It has been shown that the leading inner solutions to the core structure in two-time scales analyses are identified with the results in normal one-time scale analyses. The time averages of the first-order solutions on short time variable τ are the same as the first-order solutions obtained in one normal time scale analyses. The geostrophic vortex induces an oscillatory motion in addition to moving with the background flow. The period, amplitude andthe deviation from the mean trajectory depend on the core structure and the initial conditions. The velocity of the motion of vortex center varies periodically and the time average of the velocity on short time variable τ is equal to the value of the local mean velocity.

Asymptotic solutions to a class of nonlinear oscillation systems

In this paper, we present an asymptotic method for the analysis of a class of strongly nonlinear oscillators, derive second-order approximate solutions to them expressed in terms of their amplitudes and phases, and obtain the equations governing the amplitudes and phases, by which the amplitudes of the corresponding limit cycles and their behaviour can be determined. As an example, we investigate the modified van der Pol oscillator and give the second-order approximate analytical solution of its limit cycle. The comparison with the numerical solutions shows that the two results agree well with each other.

Extraction and separation of cadmium(II), iron(III), zinc(II), and europium(III) by Cyanex302 solutions using hollow fiber membrane modules

The mass transfer behaviors of Cd(II), Fe(III), Zn(II), and Eu(III) in sulfuric acid solution using microporous hollow fiber membrane (HFM) containing bis(2,4,4-trimethylpentyl)monothiophosphinic acid (commercial name Cyanex302) were investigated in this paper. The experimental results showed that the values of the mass transfer coefficients (K-w) decreased with an increase of H+ concentration and increased with an increase of extractant Cyanex302 concentration. The mass transfer resistance of Eu3+ was the largest because K-w value of Eu3+ was the smallest. The order of mass transfer rate of metal ions at low pH was Cd > Zn > Fe > Eu. Mixtures of Zn2+ and Eu3+ or of Zn2+ and Cd2+ were well separated in a counter-current circulation experiment using two modules connected in series at different initial acidity and concentration ratio. These results indicate that a hollow fiber membrane extractor is capable of separating the mixture compounds by controlling the acidity of the aqueous solution and by exploiting different mass transfer kinetics. The interfacial activity of Cyanex302 in sulfuric acid solution was measured and interfacial parameters were obtained according to Gibbs adsorption equation.

Probing the micellization of diblock and triblock copolymers of poly(L-lactide) and poly(ethylene glycol) in aqueous and NaCl salt solutions

The micelle formation of a series of amphiphilic block copolymers in aqueous and NaCl solutions was studied by a fluorescent probe technique using pyrene as a 'model drug'. These copolymers were synthesized from poly (ethylene glycol) (PEG) and L-lactide by a new calcium ammoniate catalyst. They had fixed PEG block lengths (44, 104 or 113 ethylene oxide units) and various poly(L-lactide) (PLLA) block lengths (15-280 lactide units). The critical micelle concentration (cmc) was found to decrease with increasing PLLA content. The distinct dissimilarity of the cmc values of diblock and triblock copolymers based on the same block length of PEG provided evidence for the different configurations of their micelles. It was also observed that the introduction of NaCl salt significantly contributed to a decrease in the cmcs of the copolymers with short PEG and PLLA blocks, while it had less influence on the cmcs of copolymers with long PEG or PLLA blocks. The dependence of partition coefficients ranging from 0.2x10(5) to 1.9x10(5) on the PLLA content in the copolymer and on the micelle configuration was also discussed.

Low temperature preparation of ceria solid solutions doubly doped with rare-earth and alkali-earth and their properties as solid oxide fuel cells

A series of solid electrolytes, (Ce(0.8)Ln(0.2))(1 - x)MxO2 - delta(Ln = La, Nd, Sm, Gd, M:Alkali-earth), were prepared by amorphous citrate gel method. XRD patterns indicate that a pure fluorite phase is formed at 800 degreesC. The electrical conductivity and the AC impedance spectra were measured. XPS spectra show that the oxygen vacancies increase owing to the MO doping, which results in the increase of the oxygen ionic transport number and conductivity. The performance of ceria-based solid electrolyte is improved. The effects of rare-earth and alkali-earth ions on the electricity were discussed. The open-circuit voltages and maximum power density of planar solid oxide fuel cell using (Ce0.8Sm0.2)(1 - 0.05)Ca0.05O2 - delta as electrolyte are 0.86 V and 33 mW . cm(-2), respectively.

Sol-gel synthesis and properties of Ce1-xGdxO2-x/2 solid solutions

A series of solid electrolytes Ce1-xGdxO2-x/2(x=0 similar to0.6) was prepared by sol-gel method. The structure, thermal expansion coefficient and electrical properties of the solid solutions were systematically studied. XRD data showed that a complete cubic fluorite structure was formed at 160 degreesC. The purity of the product prepared by the sol-gel method is higher, the grain size is uniformly smaller. They were easily sintered into highly dense ceramic pellets at 1 300 degreesC. The sintering temperature was significantly lower than that by traditionally high temperature solid phase reaction method. The thermal expansion coefficient of Ce0.8Gd0.2O1.9, determined from high- temperature XRD data, is 8. 125 X 10(-6) K-1. Impedance spectra analyses showed that the grain-boundary resistance of the solid electrolyte prepared by sol-gel method was reduced or even eliminated. The conductivity of Ce0.8Gd0.2O1.9 is 5.26 X 10(-3) S/cm at 600 degreesC. The activation energy (E-a) is 0.82 eV.

Electrochemical behavior of a series of undecatungstozincates monosubstituted by first-row transition metals, ZnW11M(H2O)O-39(n-) (M = Cr, Mn, Fe, Co, Ni, Cu or Zn)

The electrochemical behavior of a series of undecatungstozincates monosubstituted by first-row transition metals, ZnW11M(H2O)O-39(n-) (M=Cr, Mn, Fe, Co, Ni, Cu or Zn), was investigated systematically and comparably in aqueous solutions by electrochemical and in situ UV-visible-near-IR spectroelectrochemical methods. These compounds exhibit not only successive reduction processes of the addenda atoms (W) in a negative potential range, but some of them also involve redox reactions originating from the substituted transition metals (M) such as the reduction of Fe-III and Cu-II at less negative potentials and the oxidation of Mn-II at a more positive potential. Some interesting results and phenomena, especially of the transition metals, were found for the first time. Moreover, possible reaction mechanisms are proposed based on the experimental results.

Studies on extracting solutions of endohedral rare-earth metallofullerenes by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

Thirteen extracting solutions of rare-earth metallofullerenes containing La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm and Yb respectively have been investigated by means of matrix-assisted laser desorption/ionization time-of-night, mass spectrometry. The influences of the positive-ion/negative-ion mode, laser intensity, matrix and mass discrimination to the analytical results are studied, based on which the optimal analytical conditions have been determined. The results show that the extracting solutions contain large quantities of rare-earth metallofullerenes brs;des empty fullerenes, On the basis of comparing their relative intensities, the different structure stabilities and solubilities of metallofullerenes with different rare-earth metals encapsulated into the fullerene cages, as well as some possible reasons to those differences, are discussed.

Anisotropic thermopiezoelectric solids with an elliptic inclusion or a hole under uniform heat flow

The two-dimensional problem of a thermopiezoelectric material containing an elliptic inclusion or a hole subjected to a remote uniform heat flow is studied. Based on the extended Lekhnitskii formulation for thermopiezoelectricity, conformal mapping and Laurent series expansion, the explicit and closed-form solutions are obtained both inside and outside the inclusion (or hole). For a hole problem, the exact electric boundary conditions on the hole surface are used. The results show that the electroelastic fields inside the inclusion or the electric field inside the hole are linear functions of the coordinates. When the elliptic hole degenerates into a slit crack, the electroelastic fields and the intensity factors are obtained. The effect of the heat how direction and the dielectric constant of air inside the crack on the thermal electroelastic fields are discussed. Comparison is made with two special cases of which the closed solutions exist and it is shown that our results are valid.

Numerical Solutions for the Transient Flow in the Homogenous Closed Circle Reservoirs

There are many fault block fields in China. A fault block field consists of fault pools. The small fault pools can be viewed as the closed circle reservoirs in some case. In order to know the pressure change of the developed formation and provide the formation data for developing the fault block fields reasonably, the transient flow should be researched. In this paper, we use the automatic mesh generation technology and the finite element method to solve the transient flow problem for the well located in the closed circle reservoir, especially for the well located in an arbitrary position in the closed circle reservoir. The pressure diffusion process is visualized and the well-location factor concept is first proposed in this paper. The typical curves of pressure vs time for the well with different well-location factors are presented. By comparing numerical results with the analytical solutions of the well located in the center of the closed circle reservoir, the numerical method is verified.

Finite Element Solutions for Plane Strain Mode I Crack with Strain Grading Effect

In this paper, a new phenomenological theory with strain gradient effects is proposed to account for the size dependence of plastic deformation at micro- and submicro-length scales. The theory fits within the framework of general couple stress theory and three rotational degrees of freedom omega(i) are introduced in addition to the conventional three translational degrees of freedom mu(i). omega(i) is called micro-rotation and is the sum of material rotation plus the particles' relative rotation. While the new theory is used to analyze the crack tip field or the indentation problems, the stretch gradient is considered through a new hardening law. The key features of the theory are that the rotation gradient influences the material character through the interaction between the Cauchy stresses and the couple stresses; the term of stretch gradient is represented as an internal variable to increase the tangent modulus. In fact the present new strain gradient theory is the combination of the strain gradient theory proposed by Chen and Wang (Int. J. Plast., in press) and the hardening law given by Chen and Wang (Acta Mater. 48 (2000a) 3997). In this paper we focus on the finite element method to investigate material fracture for an elastic-power law hardening solid. With remotely imposed classical K fields, the full field solutions are obtained numerically. It is found that the size of the strain gradient dominance zone is characterized by the intrinsic material length l(1). Outside the strain gradient dominance zone, the computed stress field tends to be a classical plasticity field and then K field. The singularity of stresses ahead of the crack tip is higher than that of the classical field and tends to the square root singularity, which has important consequences for crack growth in materials by decohesion at the atomic scale. (C) 2002 Elsevier Science Ltd. All rights reserved.

Diffusive Wave Solutions for Open Channel Flows with Uniform and Concentrated Lateral Inflow

The diffusive wave equation with inhomogeneous terms representing hydraulics with uniform or concentrated lateral inflow intoa river is theoretically investigated in the current paper. All the solutions have been systematically expressed in a unified form interms of response function or so called K-function. The integration of K-function obtained by using Laplace transform becomesS-function, which is examined in detail to improve the understanding of flood routing characters. The backwater effects usuallyresulting in the discharge reductions and water surface elevations upstream due to both the downstream boundary and lateral infloware analyzed. With a pulse discharge in upstream boundary inflow, downstream boundary outflow and lateral inflow respectively,hydrographs of a channel are routed by using the S-functions. Moreover, the comparisons of hydrographs in infinite, semi-infiniteand finite channels are pursued to exhibit the different backwater effects due to a concentrated lateral inflow for various channeltypes.

Governing Equations and Numerical Solutions of Tension Leg Platform with Finite Amplitude Motion

It is demonstrated that when tension leg platform (TLP) moves with finite amplitude in waves, the inertia force, the drag force and the buoyancy acting on the platform are nonlinear functions of the response of TLP. The tensions of the tethers are also nonlinear functions of the displacement of TLP. Then the displacement, the velocity and the acceleration of TLP should be taken into account when loads are calculated. In addition, equations of motions should be set up on the instantaneous position. A theoretical model for analyzing the nonlinear behavior of a TLP with finite displacement is developed, in which multifold nonlinearities are taken into account, i.e., finite displacement, coupling of the six degrees of freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. Based on the theoretical model, the comprehensive nonlinear differential equations are deduced. Then the nonlinear dynamic analysis of ISSC TLP in regular waves is performed in the time domain. The degenerative linear solution of the proposed nonlinear model is verified with existing published one. Furthermore, numerical results are presented, which illustrate that nonlinearities exert a significant influence on the dynamic responses of the TLP.

Closed form solutions of T-stress in plane elasticity crack problems

The T-stress is considered as an important parameter in linear elastic fracture mechanics. In this paper, several closed form solutions of T-stress in plane elasticity crack problems in an infinite plate are investigated using the complex potential theory. In the line crack case, if the applied loading is the remote stress or the concentrated forces, the T-stress can be derived from the basic field. Here, the basic field is defined as the field caused by the applied loading in the infinite plate without the crack. For the circular are crack, the T-stress can be abstracted from a known solution. For the cusp crack problems, the T-stress can be separated from the obtained stress solution for which the conformal mapping technique is used.