Distribution, stability, bifurcations and catastrophe of steady rotation of a symmetrical heavy gyroscope with viscous-liquid-filled cavity

The number, the angles of orientation and the stability in Rumyantsev Movchan's sense of oblique steady rotations of a symmetric heavy gyroscope with a cavity completely filled with a uniform viscous liquid, possessing a fixed point 0 on its symmetric axis. are given for various values of the parameters. By taking the square of the upright component of the angular momentum M2 as a control parameter, three types of bifurcation diagrams of the steady rotations, two types of jumps and two kinds of local catastrophes, one being the symmetric reduced cusp type and the other being of the symmetric reduced butterfly type, are obtained. By taking account of the M2-damping owing to the moment of unavoidable faint friction, two different modes for the gyroscope, initially in a stable quasi-steady upright rotation with a nutation angle theta(s) equal to zero, to topple over are found.

On the non-linear stability theory of spinning solid bodies with liquid-filled cavities and its application to the columbus problem

In this paper, we first present a system of differential-integral equations for the largedisturbance to the general case that any arbitrarily shaped solid body with a cavity contain-ing viscous liquid rotates uniformly around the principal axis of inertia, and then develop aweakly non-linear stability theory by the Lyapunov direct approach. Applying this theoryto the Columbus problem, we have proved the consistency between the theory and Kelvin'sexperiments.

Liquid-filled microstructured polymer fibers as monolithic liquid-core array fibers

Liquid-filled microstructured polymer optical fibers (MPOFs) as monolithic liquid-core array fiber are proposed and prepared by injecting high-refractive-index liquid into the holes array of the MPOFs. One example for potential applications is demonstrated as a new kind of coherent imaging fiber. It provides great potential for applications in chemical sensing, biosensors, and endoscopy, particularly in bifunctional detection. (C) 2009 Optical Society of America

失重条件下对称充液陀螺的不稳定行为研究

对于质心固定的，充满粘性均匀液体的旋转对称陀螺在失重条件下绕对称长轴旋转态的小扰动不稳定及其极限行为进行了研究，所给出的定理3比以往的不稳定定理[4]为强，且反映的信息量多很多。关于初始大扰动后的渐近行为，对文[8]已给出但未严格证明的两条定理给出了严格证明，它由定理1和定理2所描述。

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.

刚性充液容器内竖直激励表面波研究进展

受外激励的充液刚性容器中流体的波动问题有实际的工程应用背景.竖直方向的受周期性外激励的充液容器的自由表面波问题--Faraday波问题是流体力学三大不稳定性难题之一(另外两个不稳定性问题是RayleighBénard对流和Taylor-Couette流).本文综述了在理想流体中和弱粘性流体中Faraday波的研究成果;介绍了作者在底部垂直激励的圆柱形容器中流体表面波图谱的实验研究和理论分析的结果.最后提出有待进一步研究的问题.

Pool boiling heat transfer of ultra-light copper foam with open cells

High speed visualizations and thermal performance studies of pool boiling heat transfer on copper foam covers were performed at atmospheric pressure, with the heating surface area of 12.0 mm by 12.0 mm, using acetone as the working fluid. The foam covers have ppi (pores per inch) from 30 to 90, cover thickness from 2.0 to 5.0 mm, and porosity of 0.88 and 0.95. The surface superheats are from -20 to 190 K, and the heat fluxes reach 140 W/cm(2). The 30 and 60 ppi foam covers show the periodic single bubble generation and departure pattern at low surface superheats. With continuous increases in surface superheats, they show the periodic bubble coalescence and/or re-coalescence pattern. Cage bubbles were observed to be those with liquid filled inside and vented to the pool liquid. For the 90 ppi foam covers, the bubble coalescence takes place at low surface superheats. At moderate or large surface superheats, vapor fragments continuously escape to the pool liquid. Boiling curves of copper foams show three distinct regions. Region I and II are those of natural convection heat transfer, and nucleate boiling heat transfer for all the foam covers. Region III is that of either a resistance to vapor release for the 30 and 60 ppi foam covers, or a capillary-assist liquid flow towards foam cells for the 90 ppi foam covers. The value of ppi has an important effect on the thermal performance. Boiling curves are crossed between the high and low ppi foam covers. Low ppi foams have better thermal performance at low surface superheats, but high ppi foams have better one at moderate or large surface superheats and extend the operation range of surface superheats. The effects of other factors such as pool liquid temperature, foam cover thickness on the thermal performance are also discussed.

Effect of liquid bridge volume on the instability in small-Prandtl-number half zones

A perturbation method is used to examine the linear instability of thermocapillary convection in a liquid bridge of floating half-zone filled with a small Prandtl number fluid. The influence of liquid bridge volume on critical Marangoni number and flow features is analyzed. The neutral modes show that the instability is mainly caused by the bulk flow that is driven by the nonuniform thermocapillary forces acting on the free surface. The hydrodynamic instability is dominant in the case of small Prandtl number fluid and the first instability mode is a stationary bifurcation. The azimuthal wave number for the most dangerous mode depends on the liquid bridge volume, and is not always two as in the case of a cylindrical liquid bridge with aspect ratio near 0.6. Its value may be equal to unity when the liquid bridge is relatively slender.

Study on conical columns with different conical angles for semi-preparative liquid chromatography

The dynamic flow profiles and separation performances in conically shaped preparative liquid chromatographic columns (inlet i.d. larger than outlet i.d.) with three different angles (7, 10 and 15degrees) were studied and compared with cylindrical column of the same length and internal volume. The shapes of dynamic flow profiles were studied by on-column visualization method. The transparent chromatographic columns made of polymethyl methacrylate (PMMA), packed with C-18 bonded silica, were immerged into a cubic pool filled with glycerol to eliminate the cylindrical and conical lens effect. The flow profiles of colored iodine solution in the columns were observed clearly using cyclohexane as mobile phase since the refractive indices of C-18, column wall and the mobile phase are very close. In the conical column of 15degrees (20-7 mm i.d.) the mobile phase in the central region migrated slower than in wall region as it moved toward the column outlet, while in the conical column of 7degrees (17-11 mm i.d.) the mobile phase in the central region migrated faster than in wall region just like in cylindrical column. We found that a plug-like flow profile was generated in the conical column of 10degrees (18-9 mm i.d.) during the whole migration process. A carmine and brilliant blue mixture was used as a probe to test the separation ability of the columns. The resolutions of the two compounds on the conical column of 7, 10, 15degrees and on the cylindrical column were 0.6, 1.57, 1.29 and 0.8, respectively. (C) 2003 Elsevier B.V. All rights reserved.

One-Step Ionic Liquid-Assisted Electrochemical Synthesis of Ionic Liquid-Functionalized Graphene Sheet Directly from Graphite

Graphite, inexpensive and available in large quantities, unfortunately does not readily exfoliate to yield individual graphene sheets. Here a mild, one-step electrochemical approach for the preparation of ionic-liquid-functionalized graphite sheets with the assistance of an ionic liquid and water is presented. These ionic-liquid-treated graphite sheets can be exfoliated into functionalized graphene nanosheets that can not only be individuated and homogeneously distributed into polar aprotic solvents, but also need not be further deoxidized. Different types of ionic liquids and different ratios of the ionic liquid to water can influence the properties of the graphene nanosheets. Graphene nanosheet/polystyrene composites synthesized by a liquid-phase blend route exhibit a percolation threshold of 0.1 vol % for room temperature electrical conductivity, and, at only 4.19 vol %, this composite has a conductivity of 13.84 S m(-1), which is 3-15 times that of polystyrene composites filled with single-walled carbon nanotubes.

New Organic Sensitizer for Stable Dye-Sensitized Solar Cells with Solvent-Free Ionic Liquid Electrolytes

We report a high molar extinction coefficient metal-free sensitizer composed of a triarylamine donor in combination with the 2-(2,2'-bithiophen-5-yl)acrylonitrile conjugation unit and cyanoacrylic acid as an acceptor. In conjugation with a volatile acetonitrile-based electrolyte or a solvent-free ionic liquid electrolyte, we have fabricated efficient dye-sensitized solar cells showing a corresponding 7.5% or 6.1% efficiency measured under the air mass 1.5 global sunlight. The ionic liquid cell exhibits excellent stability during a 1000 h accelerated test under the light-soaking and thermal dual stress. Intensity-modulated photocurrent and photovolatge spectroscopies were employed along with the transient photoelectrical decay measurements to detail the electron transport in the mesoporous titania films filled with these two electrolytes.

Dewetting behavior of polystyrene film filled with (C6H5C2H4NH3)(2)PbI4

The dewetting behavior of thin (about 30 nm) polystyrene (PS) films filled with different amount of (C6H5C2H4NH3)(2)PbI4 (PhE-PbI4) on the silicon substrate with a native oxide layer was investigated. For different additive concentrations, PhE-PbI4 showed different spatial distributions in the PS films, which had a strong influence on the film wettability, dewetting dynamics, and mechanism. With 0.5 wt % additive, PhE-PbI4 formed a noncontinuous diffusion layer, which caused a continuous hole nucleation in the film. With about 1 wt % additive, a continuous gradient distribution layer of PhE-PbI4 formed in the film, which inhibited the dewetting.

A reversibly tunable colloidal photonic crystal via the infiltrated solvent liquid-solid phase transition

A reversibly tunable colloidal photonic crystal between two stop bands was realized by a liquid-solid phase transition of liquid infiltrated into the air voids of silica opals. The difference of the peak wavelengths of the two stop bands was dependent on the diameter of the silica opals and the difference of the refractive index of the filled solvent between the solid and liquid state. The reversibly tunable photonic crystals have good stability and reproducibility.

Studies on charge transfer across the micro-liquid/liquid interface supported at a double-barrel micropipette

In this paper, the charge transfer across the micro-liquid/liquid interface supported at the orifice of a double-barrel micropipette, namely, a theta-pipette, is reported. Simple ion transfer(TMA(+)), facilitated ion transfer (potassium ion transfer facilitated by DB18C6), and electron transfer (ferrocene and ferri/ferrocyanide system) have been investigated by cyclic voltammetry. The experimental results show that a very thin aqueous film, linking both barrels filled with the aqueous solution and the organic solution respectively, can spontaneously be formed on the outer glass surface of such a double-barrel micropipette to construct a micro-liquid/liquid interface, which provides the asymmetry of diffusion field. Such device is demonstrated experimentally which can be employed as one of the simplest electrochemical cells to investigate the charge transfer across the liquid/liquid interface.

Facilitated ion transfer across the micro-liquid /liquid interface supported at the tip of a silanized micropipette

Glass micropipettes with silanized inner walls can be filled with an organic solvent for voltammetric measurements in an aqueous solution. This arrangement was employed to investigate systematically the mechanism of facilitated potassium ion transfer by an ionophore dibenzo-18-crown-6 (DB18C6) across a micro-water/1.2-dichloroethane(W/DCE) interface supported at the tip of a silanized micropipette. Our experimental results verify that this facilitated ion transfer across the liquid/liquid interface did occur by an interfacial complexation-dissociation process (TIC-TID mechanism). The ratio of the diffusion coefficient of DB18C6 to that of its complexed ion in the DCE phase was calculated to be 1.74 +/- 0.07.