Stormer-numerov approximation for numerical solutions of ordinary and partial differential equations

Stormer-Numerov approximations of high accuracy were developed for solutions of non-linear boundary value problems and nonlinear elliptic partial differential equations. The approximations can be easily adopted also for parabolic partial differential equations in one and more space dimensions and feature fourth-order accuracy. For boundary value problems only three nodes are necessary to obtain the desired fourth order accuracy. The finite difference formula for parabolic partial differential equations can be readily generalized to a nonequidistant mesh so that automatic regridding in space may be used. The Stomer-Numerov approximations are important for solution of problems where storage limitations and computer time expenditure preclude standard second order methods. Because of the fourth order approximations a low number of mesh points can be used for a majority of chemical engineering problems. The application of Stormer-Numerov approximations is illustrated on a number of examples.     

模数对无机富锌涂料和涂层性能的影响

硅酸钾富锌涂料是目前广泛使用的钢铁防腐蚀涂料。作为涂料粘结剂的高模数硅酸钾溶液对涂料和涂层的性能有重要影响。本研究考察了硅酸钾粘结剂的模数变化对涂料及涂层性能产生的影响。实验结果表明：粘结剂模数的提高可以提高固化后涂层的耐水性能，当粘结剂模数在5.0左右时，所得富锌涂层具有最佳的耐磨性能，但当粘结剂模数超过5.5时会造成涂料施工性能和贮存稳定性下降，涂层柔韧性降低，从而降低涂层的耐磨性能。     

Kinetics of cellobiose decomposition under subcritical and supercritical water in continuous flow system

The effects of reaction temperature, pressure and residence time were investigated with a flow apparatus. Cellobiose decomposition kinetics and products in suband supercritical water were examined at temperatures from 320 to 420 °C at pressures from 25 to 40 MPa, and at residence times within 3 sec. Cellobiose was found to decompose via hydrolysis and pyrolysis. The yield of desired hydrolysis product, glucose, was the maximum value of 36.8% at 320 °C, 35 MPa, but the amount of 5-(hydroxymethyl)furfural (HMF), fermentation inhibitor increased too because residence time increased in the subcritical region owing to decrease of reaction rate. Meanwhile, though the yield of glucose is low in the supercritical region, the yield of HMF decreased compared with the subcritical region; and at the minimum yield of HMF (380 °C, 25 MPa), the yield of glucose was 21.4%. The decomposition of cellobiose followed first-order kinetics and the activation energy for the decomposition of cellobiose was 51.05 kJ/mol at 40MPa.     

Electrochemical cell current requirements for toxic organic waste destruction in Ce(IV)-mediated electrochemical oxidation process

The electrochemical cell for cerium oxidation and reactor for organic destruction are the most important operation units for the successful working mediated electrochemical oxidation (MEO) process. In this study, electrochemical cells with DSA electrodes of two types, single stack and double stack connected in series, were used. The performances towards the electrochemical generation of Ce(IV) in nitric acid media at 80 °C were studied. The current-voltage curves and cerium electrolysis kinetics showed the dependence on number of cell stacks needed to be connected in series for the destruction of a given quantity of organic pollutant. The presence of an optimum region for Ce(III) oxidation with a contribution of oxygen evolution, especially at low Ce(III) concentration (high conversion ratios), was found. The cells were applied for the Ce(IV) regeneration during the organic destruction. The cell and reactor processes were fitted in a simple model proposed and used to calculate the current needed in terms of Ce(III) oxidation rate and the number of cell stacks required for maintaining Ce(IV)/Ce(III) ratio at the same level during the organic destruction. This consideration was based on the kinetic model previously developed by us for the organic destruction in the MEO process.     

含氟有机化合物氟化反应研究进展

介绍了含氟有机化合物的优点,一些常用的含氟有机化合物的分类和适用性,并介绍了主要的合成方法,按照合成物质的种类分为含氟非成环烷烃类、含氟环烷烃类及其衍生物和各自不同的应用.叙述了引入F原子或引入含氟端基的方法:电化学反应法、聚合反应法和其它反应法.     

Preparation and characterization of eugenol‐grafted chitosan hydrogels and their antioxidant activities

The hydrogels composed of chitosan and eugenol were prepared to enhance and sustain antioxidant activities. The vinyl groups of eugenol monomer were directly grafted on the amino groups of chitosan, using ceric ammonium nitrate. The graft of eugenol onto chitosan was confirmed by using Fourier‐transform infrared and proton nuclear magnetic resonance spectroscopies. Results from the swelling behavior, thermal stability, and wide‐angle X‐ray diffraction revealed that the equilibrium water content decreased with increase of graft yields, because of the hydrophobicity of eugenol, although the introduction of eugenol as a side chain disturbed the ordered arrangement of chitosan's crystalline structure. The eugenol‐grafted chitosan hydrogels showed lower pH sensitivity in comparison with chitosan alone, because the amino groups, which were pH sensitive, of chitosan were grafted with eugenol. The scavenging activity of the tested hydrogels increased with graft yield of eugenol, because phenolic groups in the eugenol could play a major role as potent free‐radical terminators, in the results of improved antioxidant activity in eugenol‐grafted chitosan hydrogel in comparison with chitosan alone. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 99:3500–3506, 2006     

Catalytic characteristics of various rubber-reinforcing carbon blacks in decomposition of methane for hydrogen production

Carbon black has recently been reported to act as an effective catalyst for methane decomposition and to exhibit stable catalytic behavior despite carbon deposition, and thus it can be used for CO₂-free production of hydrogen from natural gas. In this work, various carbon blacks with different primary particle size were investigated with respect to methane decomposition under atmospheric pressure from 1123 to 1223 K. Catalytic characteristics, such as activity, activation energy and reaction order, were investigated and compared. It was observed that with decreasing primary particle size (or increasing specific surface area), the specific activity increased and the activation energy decreased. The reaction orders for various pelletized, rubber-reinforcing carbon blacks were 0.6–0.7, about the same regardless of the primary particle size, while they were near 1 for fluffy carbon blacks. Fluffy carbon black showed higher activity and activation energy than the pelletized carbon black of the same primary particle size. Changes of the surface morphology during carbon deposition were observed by TEM. Variations of the number of active sites were discussed in regard of the primary particle size, carbon deposition and binder. The presence of different types of active sites was also suggested.     

A visual study on flame behavior in tone-excited non-premixed jet flames

A visualization study on the effect of forcing amplitude in tone-excited jet diffusion flames has been conducted. Visualization techniques are employed using optical schemes, which are a light scattering photography. Flame stability curve is attained according to Reynolds number and forcing amplitude at a fuel tube resonant frequency. Flame behavior is globally grouped into two from attached flame to blown-out flame according to forcing amplitude; one sticks the tradition flame behavior which has been observed in general jet diffusion flames and the other shows a variety of flame modes such as the flame of a feeble forcing amplitude where traditionally well-organized vortex motion evolves, a fat flame, an elongated flame, and an in-burning flame. Particular attention is focused on an elongation flame, which is associated with a turnabout phenomenon of vortex motion, and on a reversal of the direction of vortex roll-up. It is found that the flame length with forcing amplitude is the direct outcome of the evolution process of the formed inner flow structure. Especially the negative part of the acoustic cycle under the influence of a strong positive pressure gradient causes the shapes of the fuel stem and fuel branch part and even the direction of vortex roll-up to dramatically change.     

Morphology and mechanical properties of liquid crystalline copolyester and poly(ethylene 2,6-naphthalate) blends

Blends of poly(ethylene 2,6-naphthalate) (PEN) and a liquid crystalline copolyester (LCP), poly(benzoate-naphthoate), were prepared in a twin-screw extruder. Specimens for mechanical testing were prepared by injection molding. The morphology and mechanical properties were investigated by scanning electron microscopy (SEM) and an Instron tensile tester. SEM studies revealed that finely dispersed spherical domains of the liquid crystalline polymer (LCP) were formed in the PEN matrix, and the inclusions were deformed into fibrils from the spherical droplets with increasing LCP content. The morphology of the blends was found to be affected by their composition and a distinct skin-core morphology was found to develop in the injection molded samples of these blends. Mechanical properties were improved with increasing LCP content, and synergistic effects have been observed at 70 wt% LCP content whereas the elongation at break was found to be reduced drastically above 10 wt% of LCP content. This is a characteristic typical of chopped-fiber-filled composites. The improvement in mechanical properties is likely due to the reinforcement of the PEN matrix by the fibrous LCP phase as observed by scanning electron microscopy. The tensile and modulus mechanical behavior of the LCP/PEN blends was very similar to those of the polymeric composite, and the tensile strength and flexural modulus of the LCP/PEN 70/30 blend were two times the value of PEN homopolymer and exceeded those of pure LCP, suggesting LCP acts as a reinforcing agent in the blends.     

Intricate CSTR dynamics

Various dynamical characters of continuous stirred tank reaclors (CSTR) are introduced with respect to the effects of reaction types, extra thermal capacitance, periodic forcing, and coupling of CSTRs. The subject includes the classical dynamics of two-dimensional model and the variety of complex dynamics in three or higher dimensional systems such as periodic bifurcations to torus or chaos, aperiodic oscillations on invariant torus, and universal dynamics of alternating periodic-chaotic sequences with k.2^v-cycles for every natural number k. Particularly this review intends to bring about the problems that the engineers must be prepared to encounter in solving various physical systems including chemically reacting systems.