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.

Squeeze-film Effects in MEMS Devices with Perforated Plates for Small Amplitude Vibration

Squeeze-film effects of perforated plates for small amplitude vibration are analyzed through modified Reynolds equation (MRE). The analytical analysis reckons in most important influential factors: compressibility of the air, border effects, and the resistance caused by vertical air flow passing through perforated holes. It is found that consideration of air compressibility is necessary for high operating frequency and small ratio of the plate width to the attenuation length. The analytical results presented in this paper agree with ANSYS simulation results better than that under the air incompressibility assumption. The analytical analysis can be used to estimate the squeeze-film effects causing damping and stiffness added to the system. Since the value of Reynolds number involved in this paper is low (< 1), inertial effects are neglected.

Temperature dependent photoluminescence of an In(Ga)As/GaAs quantum dot system with different areal density

We have systematically studied the temperature dependent photoluminescence of a self-assembled In(Ga)As/GaAs quantum dot (QD) system with different areal densities from similar to 10(9) to similar to 10(11) cm(-2). Different carrier channels are revealed experimentally and confirmed theoretically via a modified carrier equation model considering a new carrier transfer channel, i.e. continuum states ( CS). The wetting layer is demonstrated to be the carrier quenching channel for the low-density QDs but the carrier transfer channel for the high-density QDs. In particular, for the InGaAs/GaAs QDs with a medium density of similar to 10(10) cm(-2), the CS is verified to be an additional carrier transfer channel in the low temperature regime of 10-60 K, which is studied in detail via our models. The possible carrier channels that act on different temperature regimes are further discussed, and it is demonstrated that density is not a crucial factor in determining the carrier lateral coupling strength.

Isothermal crystallization kinetics of PEO in poly(ethylene terephthalate)-poly(ethylene oxide) segmented copolymers. I. Effect of the sofi-block length

The isothermal crystallization kinetics of poly(ethylene oxide) (PEO) block in two poly(ethylene terephthalate) (PET)-PEO segmented copolymers was studied with differential scanning calorimetry. The Avrami equation failed to describe the overall crystallization process, but a modified Avrami equation, the Q equation, did. The crystallizability of the PET block and the different lengths of the PEO block exerted strong influences on the crystallization process, the crystallinity, and time final morphology of the PEO block. The mechanism of nucleation and the growth dimension of the PEG block were different because of the crystallizability of time PET block and the compositional heterogeneity. The crystallization of the PEO block was physically constrained by the microstructure of time PET crystalline phase, which resulted in a lower crystallization rate. However, this influence became weak with the increase in the soft-block length. (C) 2000 John Wiley & Sons, Inc.

Isothermal and non-isothermal crystallization kinetics of syndiotactic polypropelene

Isothermal and non-isothermal crystallization kinetics of a syndiotactic polypropylene(sPP) sample synthesized by new metallocene catalyst at different annealing temperatures and different cooling rates have been investigated by using differential scanning calorimetry(DSC) and density analysis. The equilibrium melting temperature( T-m(0)) is 158 degrees C by Hoffman-Weeks method. The equilibrium heat of fusion(Delta H-m(0)) is 88J/g in terms of the density analysis and DSC methods. The lateral and end surface free energies derived from the Lauritzen-Hoffman spherulitic growth rate equation are sigma = 5.2erg/cm(2) and sigma(e) = 69erg/cm(2), respectively. The work of chain folding is determined to be q = 33.75kJ/mol. Modified Avrami equation and Ozawa equation can be used to describe the non-isothermal crystallization behavior. And a new and convenient approach by combining the Avrami equation and Ozawa equation in a same crystallinity is used to describe the non-isothermal behavior as well. The crystallization activation energies are evaluated to be 73.7kJ/mol and 73.1kJ/mol for isothermal crystallization and non-isothermal crystallization, respectively. The Avrami exponent n is 1.5 similar to 1.6 for isothermal crystallization procedure, while the Avrami exponent n,is 2.5 similar to 3.5 for non-isothermal crystallization procedure. This indicated the difference of nucleation and growth between the two procedures.

Modified Simplified Rate Equation Model of Flowing Chemical Oxygen-Iodine Laser and its Application

A modified simplified rate equation (RE) model of flowing chemical oxygen-iodine laser (COIL), which is adapted to both the condition of homogeneous broadening and inhomogeneous broadening being of importance and the condition of inhomogeneous broadening being predominant, is presented for performance analyses of a COIL. By using the Voigt profile function and the gain-equal-loss approximation, a gain expression has been deduced from the rate equations of upper and lower level laser species. This gain expression is adapted to the conditions of very low gas pressure up to quite high pressure and can deal with the condition of lasing frequency being not equal to the central one of spectral profile. The expressions of output power and extraction efficiency in a flowing COIL can be obtained by solving the coupling equations of the deduced gain expression and the energy equation which expresses the complete transformation of the energy stored in singlet delta state oxygen into laser energy. By using these expressions, the RotoCOIL experiment is simulated, and obtained results agree well with experiment data. Effects of various adjustable parameters on the performances of COIL are also presented.

Modified Simplified Rate Equation Model of Flowing Chemical Oxygen-Iodine Laser and its Application

A modified simplified rate equation (RE) model of flowing chemical oxygen-iodine laser (COIL), which is adapted to both the condition of homogeneous broadening and inhomogeneous broadening being of importance and the condition of inhomogeneous broadening being predominant, is presented for performance analyses of a COIL. By using the Voigt profile function and the gain-equal-loss approximation, a gain expression has been deduced from the rate equations of upper and lower level laser species. This gain expression is adapted to the conditions of very low gas pressure up to quite high pressure and can deal with the condition of lasing frequency being not equal to the central one of spectral profile. The expressions of output power and extraction efficiency in a flowing COIL can be obtained by solving the coupling equations of the deduced gain expression and the energy equation which expresses the complete transformation of the energy stored in singlet delta state oxygen into laser energy. By using these expressions, the RotoCOIL experiment is simulated, and obtained results agree well with experiment data. Effects of various adjustable parameters on the performances of COIL are also presented.

New doubly periodic waves of the (2+1)-dimensional double sine-Gordon equation

New exact solutions of the (2 + 1)-dimensional double sine-Gordon equation are studied by introducing the modified mapping relations between the cubic nonlinear Klein-Gordon system and double sine-Gordon equation. Two arbitrary functions are included into the Jacobi elliptic function solutions. New doubly periodic wave solutions are obtained and displayed graphically by proper selections of the arbitrary functions.

Preparation and optical property of a novel hydrophobic anti-reflection coating for KDP crystal

A novel inorganic-organic hybrid hydrophobic anti-reflection silica film used for laser crystal was obtained by sol-gel process. The film consisted of silica sols mixed with a small amount of polymethyl methacrylate (PMMA) or polystyrene (PS). The optical transparency, hydrophobic property and surface morphology of the film were characterized by UV-VIS-NIR spectrophotometer; contact angle instrument and Scanning Electron Microscopy (SEM), respectively. The results showed that the anti-reflection coating had good hydrophobility and optical transparency from 400 nm to 1200 nm. The contact angle reached to 130-140 degrees. SEM images indicated the hydrophobic films modified with PMMA or PS had compact structure compared to the pure silica sol film. (C) 2008 Elsevier B.V. All rights reserved.

Electrochemistry of hydroquinone derivatives at metal and iodine-modified metal electrodes

The difference in the electrochemical behavior of hydroquinone and pyrocatechol. at platinum and gold surfaces was analyzed using voltammetry and attenuated total reflection Fourier transform infrared spectroscopy. The results show that the hydroquinone derivatives are adsorbed on a gold surface with vertical orientation, which makes the electron transfer between the bulk species and the electrode surface easier than that in the case of flat adsorption of hydroquinone derivatives that occurs at a platinum electrode. The formation of the vertical conformation and the rapid process of electron transfer were also confirmed by quantum chemistry calculations. In addition, the pre-adsorbed iodine on the electrodes played a key role on the adsorbed configuration and. electron transfer of redox species.

Theoretical estimation of thermodynamic properties of the system PS/PPO on the basis of modified combining rule of Sanchez-Lacombe lattice fluid model

The three scaling parameters described in Sanchez-Lacombe lattice fluid theory (SLLFT), T*, P* and rho* of pure polystyrene (PS), pure poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) and their mixtures are obtained by fitting corresponding experimental pressure volume-temperature data with equation-of-state of SLLFT. A modified combining rule in SLLFT used to match the volume per mer, v* of the PS/PPO mixtures was advanced and the enthalpy of mixing and Flory-Huggins (FH) interaction parameter were calculated using the new rule. It is found that the difference between the new rule and the old one presented by Sanchez and Lacombe is quite small in the calculation of the enthalpy of mixing and FH interaction parameter and the effect of volume-combining rule on the calculation of thermodynamic properties is much smaller than that of energy-combining rule. But the relative value of interaction parameter changes much due to the new volume-based combining rule. This effect can affect the position of phase diagram very much, which is reported elsewhere [Macromolecules 34 (2001) 6291]

In-situ microscopic FT-IR spectroelectrochemical investigation of polythiophene film modified electrode

A polythiophene film was electrochemically deposited on a Pt micro-plate electrode and investigated by cyclic voltammetry and in-situ reflection microscopic FTIR spectroscopy. The FTIR analysis showed that the electropolymerization of thiophene on the Pt surface was affected Lv the surface adsorption processes of thiophene molecules. Two adsorption modes were identified. Two structure models of the polythiophene chain were observed simultaneously. It was proposed that the good conductibility of the polythiophene film was originated from a co-vibratory equilibrium of the link part of model I and model II.

Thermodynamics of blends of poly(ethylene oxide) with poly(methyl methacrylate) and poly(vinyl acetate): prediction of miscibility based on Flory solution theory modified by Hamada

Flory solution theory modified by Hamada et al. (Macromolecules, 1980, 13, 729) was used to predict the miscibility of blends of poly(ethylene oxide) with poly(methyl methacrylate) (PEO-aPMMA) and with poly(vinyl acetate) (PEO-PVAc). Interaction parameters of a PEO-aPMMA blend with the weight ratio of PEO/aPMMA = 50/50 at the temperature range of 393-433 K and PEO-PVAc blends with different compositions and temperatures were calculated from the determined equation-of-state parameters based on Flory solution theory modified by Hamada ed al. Results show that interaction parameters of the PEO-aPMMA blend are negative and can be comparable with values obtained from neutron-scattering measurements by Ito et al. (Macromolecules, 1987, 20, 2213). Also, interaction parameters and excess volumes of PEO-PVAc blends are negative and increase with enhancing the content of PEO and the temperature. (C) 1998 Elsevier Science Ltd. All rights reserved.

Synthesis, characterization and ionic conductivity of solid polymer electrolytes based on modified alternating maleic anhydride copolymer with oligo(oxyethylene) side chains

Three comb polymers (CP) based on modified alternating methyl vinyl ether/maleic anhydride copolymer with oligo-oxyethylene side chains of the type -O(CH2CH2O)(n)CH3 were synthesized and characterized, and the ionic conductivity of CP/salt complexes is reported. The conductivity of these complexes was about 10(-5)-10(-6) S cm(-1) at room temperature. The conductivity, which displayed non-Arrhenius behaviour, was analysed using the Vogel-Tammann-Fulcher equation. The conductivity maxima appear at lower salt concentration, when CP has longer side chains. Infrared (i.r.) was used to study the cation-polymer interaction. I.r. results also indicate that the ester in CP might decompose at 140 degrees C and reproduce the maleic anhydride ring. (C) 1997 Elsevier Science Ltd.

KINETIC-STUDY OF ELECTROCATALYTIC REDUCTION OF HYDROGEN-PEROXIDE AT IRON(III) PORPHYRIN MODIFIED GLASSY-CARBON ELECTRODE IN ALKALINE-MEDIUM USING THE ROTATION-SCAN METHOD

Reduction of hydrogen peroxide at a glassy carbon (GC) electrode modified with sigma-bonded pyrrole iron(III) octaethylporphyrin complex, (OEP)Fe(Pyr), was studied by cyclic voltammetry and a rotating disk electrode. In 0.1N NaOH solution, it is shown that such an (OEP)Fe(Pyr)/GC electrode has a significant catalytic activity towards hydrogen peroxide reduction (E(D) = -0.80 V, k = 0.066 cm s(-1)); however, the electrode stability is low. The deactivation is observed when the reaction charge (Q) is passing through the (OEP)Fe(Pyr)/GC disk electrode. A linear rotation scan method is applied to study the kinetic process by determining the disk electrochemical response (i(D)) to rotation rate (omega) at a definite disk potential (E(D)). Considering that the number of adsorbed electroreduced catalyst molecules (Red) varies according to the disk potential, a factor theta(= Gamma(Red)/(Gamma(Red) + Gamma(Ox))) is introduced to describe the electrode surface area fraction for electroreduced species. The obtained Koutecky-Levich equation is applicable whatever the potential is.