光滑粒子动力学方法中粒子分布与数值稳定性分析

光滑粒子动力学(SPH)作为一种拉格朗日型无网格粒子方法,已经成功地应用于包括含多相流动界面以及移动边界的可压缩和不可压缩流体运动的研究中.通过对Poiseuille流动的深入研究,探索了SPH方法中粒子分布对计算精度的影响,揭示了一种因为粒子不规则分布而导致的数值不稳定现象.研究显示,这种数值不稳定性起源于SPH方法粒子近似过程中的不连续性.使用了一种新的粒子近似格式以确保SPH方法中粒子近似的连续性.计算结果表明,这种新的粒子近似格式对于规则和不规则的粒子分布都能得到稳定精度的结果.

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

Kinetic study of the 2-methyl-3-methoxy-4-phenylbutanoic acid produced by oxidation of microcystin in aqueous solutions

Microcystins (MCs) are a family of related cyclic hepatotoxic heptapeptides, of which more than 70 types have been identified. The chemically unique nature of the C20 beta-amino acid, (2S, 3S, 8S, 9S)-3-amino-9-methoxy-2,6,8-trimethyl-10-phenyldeca4,6-dienoic acid (Adda), portion of the MCs has been exploited to develop a strategy to analyze the entirety. Oxidation of MCs causes the cleavage of MC Adda to form 2-methyl-3-methoxy-4-phenylbutanoic acid (MMPB). In the present study, we investigated the kinetics of MMPB produced by oxidation of the most-often-studied MC variant, MC-LR (L = leucine, R = arginine), with permanganate-periodate. This investigation allowed insight regarding the influence of the reaction conditions (concentration of the reactants, temperature, and pH) on the conversion rate. The results indicated that the reaction was second order overall and first order with respect to both permanganate and MC-LR. The second-order rate constant ranged from 0.66 to 1.35 M/s at temperatures from 10 to 30 degrees C, and the activation energy was 24.44 kJ/mol. The rates of MMPB production can be accelerated through increasing reaction temperature and oxidant concentration, and sufficient periodate is necessary for the formation of MMPB. The initial reaction rate under alkaline and neutral conditions is higher than that under acidic conditions, but the former decreases faster than the latter except under weakly acidic conditions. These results provided new insight concerning selection of the permanganate-periodate concentration, pH, and temperature needed for the oxidation of MCs with a high and stable yield of MMPB.

Study on the hydrolysis/precipitation behavior of Keggin Al-13 and Al-30 polymers in polyaluminum solutions

The hydrolysis/precipitation behaviors of Al3+, Al-13 and Al-30 under conditions typical for flocculation in water treatment were investigated by studying the particulates' size development, charge characteristics, chemical species and speciation transformation of coagulant hydrolysis precipitates. The optimal pH conditions for hydrolysis precipitates formation for AlCl3, PAC(A113) and PAC(A130) were 6.5-7.5, 8.5-9.5, and 7.5-9.5, respectively. The precipitates' formation rate increased with the increase in dosage, and the relative rates were AlCl3 >> PAC(A130) > PACA113. The precipitates' size increased when the dosage increased from 50 mu M to 200 mu M, but it decreased when the dosage increased to 800 AM. The Zeta potential of coagulant hydrolysis precipitates decreased with the increase in pH for the three coagulants. The isoelectric points of the freshly formed precipitates for AlCl3, PAC(A113) and PAC(A130) were 7.3, 9.6 and 9.2, respectively. The Zeta potentials of AlCl3 hydrolysis precipitates were lower than those of PAC(A113) and PAC(A130) when pH > 5.0. The Zeta potential of PAC(A130) hydrolysis precipitates was higher than that of PACA113 at the acidic side, but lower at the alkaline side. The dosage had no obvious effect on the Zeta potential of hydrolysis precipitates under fixed pH conditions. The increase in Zeta potential with the increase in dosage under uncontrolled pH conditions was due to the pH depression caused by coagulant addition. Al-Ferron research indicated that the hydrolysis precipitates of AlCl3 were composed of amorphous AI(OH)3 precipitates, but those of PACA113 and PACA130 were composed of aggregates of Al-13 and Al-30, respectively. Al3+ was the most un-stable species in coagulants, and its hydrolysis was remarkably influenced by solution pH. Al-13 and Al-30 species were very stable, and solution pH and aging had little effect on the chemical species of their hydrolysis products. The research method involving coagulant hydrolysis precipitates based on Al-Ferron reaction kinetics was studied in detail. The Al species classification based on complex reaction kinetic of hydrolysis precipitates and Ferron reagent was different from that measured in a conventional coagulant assay using the Al--Ferron method. The chemical composition of Al-a, Al-b and Al-c depended on coagulant and solution pH. The Al-b measured in the current case was different from Keggin Al-13, and the high Alb content in the AlCl3 hydrolysis precipitates could not used as testimony that most of the Al3+ Was converted to highly charged Al-13 species during AlCl3 coagulation.

Structural characteristics and redox behaviors of Ce1-xCuxOy solid solutions

Nanosized Ce1-xCuxOy materials were prepared by complexation-combustion method. The structural characteristics and redox behaviors were investigated using X-ray diffraction (XRD), temperature programmed reduction (H-2-TPR), UV-Vis, and Raman spectroscopies. In XRD patterns, no evidence of CuO diffraction peaks are observed for the Ce1-xCuxOy samples calcinated at 650 degreesC for 5 h, until the Cu/(Ce + Cu) ratio is higher than 0.4. The stepwise decrease of the 2theta value of CeO2 in Ce1-xCuxOy with the increasing of Cu concentration suggests that the CU2+ ions incorporate into the CeO2 lattice to form Ce1-xCuxOy solid solutions for low Cu/(Ce + Cu) ratios (x less than or equal to 0.1). The CuO phase begins to segregate from the solid solutions with the further increasing of Cu/(Ce+Cu) ratio. The Raman mode at 1176 cm(-1) ascribed to the enhanced defects appears for CeO2 and the Ce0.9Cu0.1Oy solid solution. Compared with CeO2 alone, the Raman mode of cubic CeO2 shifts from 462 to 443 cm(-1) for the Ce0.9Cu0.1Oy solid solution. The H-2 consumption of the fresh Ce0.95Cu0.05Oy is 1.65 times higher than that needed to reduce CuO to Cu, and it increases to 2.4 after a reoxidation of the partially reduced Ce0.95Cu0.05Oy at 300 degreesC, which indicates that the CeO2 phase is also extensively reduced. Compared with the high Cu/(Ce+Cu) ratio sample Ce0.7Cu0.3Oy, the Ce0.9Cu0.1Oy solid solution shows high and stable redox property even after different reoxidation temperatures. When the reoxidation temperature exceeds 200 degreesC, the a peak (similar to170 degreesC) ascribed to the reduction of surface oxygen disappears, and the P peak (similar to190 degreesC) ascribed to the reduction of Cu2+ species and the partial reduction of bulk CeO2 shifts to higher temperatures with the H-2 consumption 1.16 times higher than that for fresh sample. The result demonstrates that the redox property of the CeO2 is Significantly improved by forming the Ce1-xCuxOy solid solutions.

Preparation and evaluation of a proton exchange membrane based on oxidation and water stable sulfonated polyimides

A series of novel oxidation and water stable sulfonated polyimides (SPIs) were synthesized from 4,4'-binaphthyl-1,1',8,8'-tetracarboxylic dianhydride (BTDA), and wholly aromatic diamine 2,2'-bis(3-sulfobenzoyl) benzidine (2,2'-BSBB) for proton exchange membrane fuel cells. These polyimides could be cast into flexible and tough membranes from m-cresol solutions. The copolymer membranes exhibited excellent oxidative stability and mechanical properties due to their fully aromatic structure extending through the backbone and pendant groups. Moreover, all BTDA-based SPI membranes exhibited much better water stability than those based on the conventional 1,4,5,8-naphthalenecarboxylic dianhydride. The improved water stability of BTDA-based polyimides was attributed to its unique binaphthalimide structure. The SPI membranes with ion exchange capacity (IEC) of 1.36-1.90 mequiv g(-1) had proton conductivity in the range of 0.41 x 10(-1) to 1. 12 x 10(-1) S cm(-1) at 20 degrees C. The membrane with IEC value of 1.90 mequiv g(-1) displayed reasonably higher proton conductivity than Nafion((R)) 117 (0.9 x 10(-1) S cm(-1)) under the same test condition and the high conductivity of 0.184 S cm(-1) was obtained at 80 degrees C. Microscopic analyses revealed that well-dispersed hydrophilic domains contribute to better proton conducting properties. These results showed that the synthesized materials might have the potential to be applied as the proton exchange membranes for PEMFCs.

Polyelectrolyte-functionalized ionic liquid for electrochemistry in supporting electrolyte-free aqueous solutions and application in amperometric flow injection analysis

As a green process, electrochemistry in aqueous solution without a supporting electrolyte has been described based on a simple polyelectrolyte-functionalized ionic liquid (PFIL)-modified electrode. The studied PFIL material combines features of ionic liquids and traditional polyelectrolytes. The ionic liquid part provides a high ionic conductivity and affinity to many different compounds. The polyelectrolyte part has a good stability in aqueous solution and a capability of being immobilized on different substrates. The electrochemical properties of such a PFIL-modified electrode assembly in a supporting electrolyte-free solution have been investigated by using an electrically neutral electroactive species, hydroquinone ( HQ) as the model compound. The partition coefficient and diffusion coefficient of HQ in the PFIL film were calculated to be 0.346 and 4.74 X 10(-6) cm(2) s(-1), respectively. Electrochemistry in PFIL is similar to electrochemistry in a solution of traditional supporting electrolytes, except that the electrochemical reaction takes place in a thin film on the surface of the electrode. PFILs are easily immobilized on solid substrates, are inexpensive and electrochemically stable. A PFIL-modified electrode assembly is successfully used in the flow analysis of HQ by amperometric detection in solution without a supporting electrolyte.

Preparation, structure and oxide ion conductivity in Ce6-xYxMoO15-delta (x=0.1-1.4) solid solutions

The Ce6-xYxMoO15-delta solid solution with fluorite-related structure have been characterized by differential thermal analysis/thermogravimetry (DTA/TG), X-ray diffraction (XRD), IR, Raman, scanning electric microscopy (SEM) and X-ray photoelectron spectroscopy (XPS) methods. The electric conductivity of samples is investigated by Ac impedance spectroscopy. An essentially pure oxide-ion conductivity of the oxygen-deficiency was observed in pure argon, oxygen and air. The highest oxygen-ion conductivity was found in Ce5.5Y0.5MoO15-delta ranging from 5.9 X 10(-5)(S cm(-1)) at 300 degrees C to 1.3 X 10(-2)(S cm(-1)) at 650 degrees C, respectively. The oxide-ion conductivities remained stable over 80 h-long test at 800 degrees C. These properties suggested that significant oxide-ionic conductivity exists in these materials at moderately elevated temperatures.

On improving the phase stability and thermal expansion coefficients of lanthanum cerium oxide solid solutions

The phase stability of lanthanum cerium oxide (La2Ce2O7), which is stable up to 1400 degrees C, and the thermal expansion coefficient of La2Ce2O7 doped with Ta2O5 or WO3 were studied. The thermal expansion coefficient of La2Ce2O7 below 400 degrees C was increased by adding more CeO2 or doping with either Ta2O5 or WO3.

Fracture mechanics of piezoelectric materials

This paper presents an analysis of crack problems in homogeneous piezoelectrics or on the interfaces between two dissimilar piezoelectric materials based on the continuity of normal electric displacement and electric potential across the crack faces. The explicit analytic solutions are obtained for a single crack in an infinite piezoelectric or on the interface of piezoelectric bimaterials. For homogeneous materials it is found that the normal electric displacement D-2, induced by the crack, is constant along the crack faces which depends only on the remote applied stress fields. Within the crack slit, the perturbed electric fields induced by the crack are also constant and not affected by the applied electric displacement fields. For bimaterials, generally speaking, an interface crack exhibits oscillatory behavior and the normal electric displacement D-2 is a complex function along the crack faces. However, for bimaterials, having certain symmetry, in which an interface crack displays no oscillatory behavior, it is observed that the normal electric displacement D-2 is also constant along the crack faces and the electric field E-2 has the singularity ahead of the crack tip and has a jump across the interface. Energy release rates are established for homogeneous materials and bimaterials having certain symmetry. Both the crack front parallel to the poling axis and perpendicular to the poling axis are discussed. It is revealed that the energy release rates are always positive for stable materials and the applied electric displacements have no contribution to the energy release rates.

Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

Damping of Vertically Excited Surface Wave in Weakly Viscous Fluid

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.

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.