Orr-Sommerfeld方程的Green函数和积分方程解法

本文提出了一种求解线性稳定性理论Orr-Sommerfeld方程的方法.我们首先定义了该方程的Green函数,并将它表达成矩阵形式;然后证明了Green函数的互易性;最后导出了等价于原方程的线性积分方程.该方法适用于两固壁间任意Reynolds数下各种主流速度分布的情况.

对流-扩散相互作用结构的不变性

本文提出并证明了不可压缩剪切层流中对流-扩散相互作用结构不变性诸定理:即二难剪切层流与其线性化及非线性扰动存在同一的对流-扩散相互作用结构,且物理尺度(指时间、空间和速度尺度)相同。给出十个推论,例如:对流-扩散相互作用可在剪切层流及其扰动场内“激发“快时间尺度和小空间尺度结构,线性化稳定性原理的约定对剪切流体系统成立等。应用题例导出计及时间-空间尺度效应和非平行流效应的广义Orr-Sommerfeld(GOS)方程,证实它有两个粘性解:阻尼层解和干扰层解;经典OS方程及其两个粘性解:边界层解和Heisenberg临界层解,Triple-deck稳定性理论基本方程及其两个粘性解,均是本文GOS方程及其两个粘性解的特例。

高雷诺数下平面Poiseuille流稳定性渐近分析

本文主要讨论高雷诺数下平面Poiseuille流稳定性问题.应用多层结构分析理论,求出了描述该流体稳定性的Orr-Sommerfeld方程特征值的较为合理的逼近式及相应的特征函数的渐近解析解.

强粘性剪切流稳定性方程组的简化及计算判据

研究强粘性剪切流稳定性方程组的物理尺度及其相互关系.同时,对强粘性剪切流稳定性方程组作GCS分析,从而解决强粘性剪切流稳定性方程组的某些计算问题.作为应用,给出Orr-Sommerfeld方程的一种新的简化形式.

Carbon-supported Pd nanocatalyst modified by non-metal phosphorus for the oxygen reduction reaction

A carbon-supported palladium catalyst modified by non-metal phosphorus(PdP/C) has been developed as an oxygen reduction catalyst for direct methanol fuel cells.The PdP/C catalyst was prepared by the sodium hypophosphite reduction method. The as-prepared Pd nanoparticles have a narrow size distribution with an average diameter of 2 nm. Energy dispersive X-ray analysis (EDX), X-ray photoelectron spectroscopy (XPS), and X-ray diffraction (XRD) results indicate that P enters into the crystal lattice of Pd and forms an alloy.

Pd nanoparticles supported on WO3/C hybrid material as catalyst for oxygen reduction reaction

Pd nanoparticles supported on WO3/C hybrid material have been developed as the catalyst for the oxygen reduction reaction (ORR) in direct methanol fuel cells. The resultant Pd-WO3/C catalyst has an ORR activity comparable to the commercial Pt/C catalyst and a higher activity than the Pd/C catalyst prepared with the same method. Based on the physical and electrochemical characterizations, the improvement in the catalytic performance may be attributed to the small particle sizes and uniform dispersion of Pd on the WO3/C, the strong interaction between Pd and WO3 and the formation of hydrogen tungsten bronze which effectively promote the direct 4-electron pathway of the ORR at Pd.

Development of durable carbon black/titanium dioxide supported macrocycle catalysts for oxygen reduction reaction

Carbon black and titanium dioxide supported iron tetraphenylporphyrin (FeTPP/TiO2/C) catalysts for oxygen reduction reaction (ORR) were prepared by sol-gel and precipitation methods followed by a heat-treatment at temperatures of 400-1000 degrees C. The FeTPP/C and TiO2/C were also studied for comparison. The FeTPP/TiO2/C pyrolyzed at 700 degrees C exhibits significantly improved stability while maintaining high activity towards ORR in comparison with the FeTPP/C counterpart. The electrochemical study combined with XRD, XPS, and SEM/EDX analyses revealed that the appropriate dispersion of TiO2 on the surface of FeTPP/TiO2/C catalysts, which depending on heat-treatment temperature, plays a crucial role in determining the activity and stability of catalysts.

A novel urchinlike gold/platinum hybrid nanocatalyst with controlled size

In this paper, we have explored a simple and new strategy to obtain quasimonodisperse Au/Pt hybrid nanoparticles (NPS) with urchinlike morphology and controlled size and Pt shell thickness. Through changing the molar ratios of Au to Pt, the Pt shell thickness of urchinlike Au/Pt hybrid NPs could be easily controlled; through changing the size of Au NPs (the size was easily controlled from similar to 3 to similar to 70 nm via simple heating of HAuCl4-citrate aqueous solution), the size of urchinlike Au/Pt hybrid NPs could be facilely dominated. It should be noted that heating the solution (100 degrees C) was very necessary for obtaining three-dimensional (3D) urchinlike nanostructures while H2PtCl6 was added to gold NPs aqueous solution in the presence of reductant (ascorbic acid). The electrocatalytic oxygen reduction reaction (ORR, a reaction greatly pursued by scientists in view of its important application in fuel cells) and the electron-transfer reaction between hexacyanoferrate(III) ions and thiosulfate ions of urchinlike Au/Pt hybrid NPs were investigated. It is found that the as-prepared urchinlike Au/Pt hybrid NPs exhibited higher catalytic activities than that of similar to Pt NPs with similar size.

Raspberry-like Hierarchical Au/Pt Nanoparticle Assembling Hollow Spheres with Nanochannels: An Advanced Nanoelectrocatalyst for the Oxygen Reduction Reaction

In this contribution, we for the first time report the synthesis of raspberry-like hierarchical Au/Pt nanoparticle (NP) assembling hollow spheres (RHAHS) with pore structure and complex morphology through one in situ sacrificial template approach without any post-treatment procedure. This method has some clear advantages including simplicity, quickness, high quality, good reproducibility, and no need of a complex post-treatment process (removing templating). Furthermore, the present method could be extended to other metal-based NP assembling hollow spheres. Most importantly, the as-prepared RHAHS exhibited excellent electrocatalytic activity for oxygen reduction reaction (ORR). For instance, the present RHAHS-modified electrode exhibited more positive potential (the half-wave potential at about 0.6 V), higher specific activity, and higher mass activity for ORR than that of commercial platinum black (CPB). Rotating ring-disk electrode (RRDE) voltarnmetry demonstrated that the RHAHS-modified electrode could almost catalyze a four-electron reduction of O-2 to H2O in a 0.5 M air-saturated H2SO4 solution.

Electrochemical designing of Au/Pt core shell nanoparticles as nanostructured catalyst with tunable activity for oxygen reduction

Au/Pt core shell nanoparticles (NPs) have been prepared via a layer-by-layer growth of Pt layers on An NPs using underpotential deposition (UPD) redox replacement technique. A single UPD Cu monolayer replacement with Pt(11) yielded a uniform Pt film on Au NPs, and the shell thickness can be tuned by controlling the number of UPD redox replacement cycles. Oxygen reduction reaction (ORR) in air-saturated 0.1 M H2SO4 was used to investigate the electrocatalytic behavior of the as-prepared core shell NPs. Cyclic voltammograms of ORR show that the peak potentials shift positively from 0.32 V to 0.48 V with the number of Pt layers increasing from one to five, suggesting the electrocatalytic activity increases with increasing the thickness of Pt shell. The increase in electrocatalytic activity may originate mostly from the large decrease of electronic influence of Au cores on surface Pt atoms. Rotating ring-disk electrode voltammetry and rotating disk electrode voltammetry demonstrate that ORR is mainly a four-electron reduction on the as-prepared modified electrode with 5 Pt layers and first charge transfer is the rate-determining step.

The real role of carbon in Pt/C catalysts for oxygen reduction reaction

A new electrocatalysis of carbon materials for oxygen reduction reaction (ORR) on Pt/C catalysts was discovered. It was found that there exist two kinds of electroactive sites on these supports of carbon materials, which can effectively electrocatalyze the reduction of peroxide intermediated from oxygen reduction on Pt, as this provides continuous driving force to move the equilibrium toward the production of peroxide from ORR.

Effect of borohydride as reducing agent on the structures and electrochemical properties of Pt/C catalyst

In this paper, we found that boron deposited on the surface of support when sodium borohydride used as reducing agent during the preparation of Pt/C catalyst. The deposition of boron markedly reduces particle size of Pt, raises electrochemical active surface (EAS) area of catalyst and electrochemical activity for hydrogen evolution or oxygen reduction reaction (ORR) compared with which prepared using other reducing agents (hydrogen and formaldehyde).

Electrochemical impedance spectroscopy analysis for oxygen reduction reaction in 3.5% NaCl solution

The electrochemical impedance spectroscopy (EIS) at different potentials has been used to study the oxygen reduction reaction (ORR) in 3.5% NaCl solution on glassy carbon (GC) electrode in this work. Results show that ORR consists of three two-electron reaction steps and both superoxide ion (O-2(-)) and hydrogen peroxide (H2O2), which are produced by ORR, obstruct the diffusion of oxygen to the surface of the electrode and make the EIS results change into a transmissive finite diffusion process with the real part contraction and a reflective finite diffusion process from a semi-infinite diffusion process. The values of electron transfer resistance (R-t) and diffusion resistance (R-d) were calculated from EIS. O-2(-) influenced strongly on the Rt values and induced a maximum at -0.45 V.

The electrochemical reduction reaction of dissolved oxygen on Q235 carbon steel in alkaline solution containing chloride ions

Cyclic voltammetry, electrochemical impedance spectroscopy, and rotating disk electrode voltammetry have been used to study the effect of chloride ions on the dissolved oxygen reduction reaction (ORR) on Q235 carbon steel electrode in a 0.02 M calcium hydroxide (Ca(OH)(2)) solutions imitating the liquid phase in concrete pores. The results indicate that the cathodic process on Q235 carbon steel electrode in oxygen-saturated 0.02 M Ca(OH)(2) with different concentrations of chloride ions contain three reactions except hydrogen evolution: dissolved oxygen reduction, the reduction of Fe(III) to Fe(II), and then the reduction of Fe(II) to Fe. The peak potential of ORR shifts to the positive direction as the chloride ion concentration increases. The oxygen molecule adsorption can be inhibited by the chloride ion adsorption, and the rate of ORR decreases as the concentration of chloride ions increases. The mechanism of ORR is changed from 2e(-) and 4e(-) reactions, occurring simultaneously, to quietly 4e(-) reaction with the increasing chloride ion concentration.