Coaxial cylinder

Figure 2.3 Definition of variables for concentric cylinder viscometers (a) the rotating cylinder and (b) the coaxial cylinders.

These modes of operation ate used in conjunction with the two most popular energy analyzers, the cylindrical mirror analyzer (CMA) and the concentric hemispherical analyzer (CHA). The most common form of the CMA used today is the double-pass version diagramed in Eigute 21. This device consists of two perfectly coaxial cylinders of radii r and r. The outer cylinder is held at a potential of (— ) and the inner cylinder is held at ground. The... 

The Nametre Rotary B rotational viscometer measures torque in terms of the current needed to drive the d-c motor at a given speed while a material is under test. The standard sensors are coaxial cylinders or Brookfield disk-type spindles, but a cone—plate system is also available. The viscosity range for the coaxial cylinder sensors is 5 to 5 x 1(T mPa-s, and the maximum shear rate is 200. ... 

The birth of the field of carbon nanotubes is marked by the publication by lijima of the observation of multi-walled nanotubes with outer diameters as small as 55 A, and inner diameters as small as 23 A, and a nanotube consisting of only two coaxial cylinders [2]. This paper was important in making the connection between carbon fullerenes, which are quantum dots, with carbon nanotubes, which are quantum wires. FurtheiTnore this seminal paper [2] has stimulated extensive theoretical and experimental research for the past five years and has led to the creation of a rapidly developing research field. 

When the absorption relations are not dependent on temperature, the following approximations can be used (a = e = constant = 1 - p). For two coaxial cylinders and spheres,... 

Among the several known types of carbon fibres the discussion in this chapter is limited to the electric arc grown multi-walled carbon nanotubes (MWCNTs) as well as single-walled ones (SWCNTs). For MWCNT we restrict the discussion to the idealised coaxial cylinder model. For other models and other shapes we refer to the literature [1-6],... 

An image of an MWCNT obtained by using all available reflexions usually exhibits only prominently the oo.l lattice fringes (Fig. 4) with a 0.34 nm spacing, representing the "walls" where they are parallel to the electron beam. The two walls almost invariably exhibit the same number of fringes which is consistent with the coaxial cylinder model. 

This relation may be extended to any desired number n of coaxial cylinders. 

Figure 7.3. Laminar shear mixing in a coaxial cylinder arrangement...

This velocity profile is commonly called drag flow. It is used to model the flow of lubricant between sliding metal surfaces or the flow of polymer in extruders. A pressure-driven flow—typically in the opposite direction—is sometimes superimposed on the drag flow, but we will avoid this complication. Equation (8.51) also represents a limiting case of Couette flow (which is flow between coaxial cylinders, one of which is rotating) when the gap width is small. Equation (8.38) continues to govern convective diffusion in the flat-plate geometry, but the boundary conditions are different. The zero-flux condition applies at both walls, but there is no line of symmetry. Calculations must be made over the entire channel width and not just the half-width. 

By locating the anode entirely upstream from the ionized gas volume, collection of long range beta particles is minimized in the displaced coaxial cylinder design, and the direction of gas flow minimizes diffusion and convection of electrons to the collector electrode. However, the free electrons are sufficiently mobile that modest pulse voltages (e.g., 50 V) are adequate to cause the electrons to move against the gas flow and be collected during. this time. 

Figure 3.12 Schematic dlagrm of the coaxial cylinder. A, and the asymmetric (displaced coaxial cylinder), B, design.

Figure 5.30 illustrates schematically the cross-section of a CMA, and the principle of its operation. It consists of two coaxial cylinders, with the inner cylinder at ground potential and a potential of — V on the outer. The primary electron beam hits the sample surface and some of the Auger electrons generated will pass through the grid covered annular aperture in the inner cylinder. 

Hydraulic fracturing fluids are solutions of high-molecular-weight polymers whose rheological behavior is non-Newtonian. To describe the flow behavior of these fluids, it is customary to characterize the fluid by the Power Law parameters of Consistency Index (K) and Behavior Index (n). These parameters are obtained experimentally by subjecting the fluid to a series of different shear rates (y) and measuring the resultant shear stresses (t). The slope and Intercept of a log shear rate vs log shear stress plot yield the Behavior Index (n) and Consistency Index (Kv), respectively. Consistency Indices are corrected for the coaxial cylinder viscometers by ... 

Fig. 26 Schematic illustration of model for hexagonal triple coaxial cylinder structure observed in PS- -PI- -PDMS-6-P2VP. From [91]. Copyright 2002 American Chemical Society...

There are two main types of viscometer rotary instruments and tubular, often capillary, viscometers. When dealing with non-Newtonian fluids, it is desirable to use a viscometer that subjects the whole of the sample to the same shear rate and two such devices, the cone and plate viscometer and the narrow gap coaxial cylinders viscometer, will be considered first. With other instruments, which impose a non-uniform shear rate, the proper analysis of the measurements is more complicated. 

Oscillatory shearing is used to characterize viscoelastic fluids using coaxial cylinders or cone and plate instruments. 

The following measurements were made on the inner cylinder of a coaxial cylinders viscometer having inner and outer diameters of 24 mm and 26 mm, and an effective cylinder length of 35 mm. Using these data, determine the values of the shear stress, shear rate and apparent viscosity of the sample. 

The experimental data obtained from these patterns allows the determination of the atomic structure of both high- and low-symmetric crystals. Since the crystals of a plate texture are all oriented with a particular plane parallel to the support, the properties of the reciprocal lattice require that its points will be distributed exclusively along straight lines perpendicular to the support (Fig. 10), independent of the symmetry of the crystals forming the texture. As a result the rings of the reciprocal lattice lie on coaxial cylinders whose axis is texture axis. This distribution of the rings is the most important characteristic of the reciprocal lattice of plate textures. 

Figure 10. Distribution of reciprocal lattice points of a plate texture along straight lines parallel to the texture axis and perpendicular to the face lying on the support (a) and distribution of circular scattering regions of the reciprocal lattice of a texture on coaxial cylinders.

Separation of EMCL and IMCL in proton muscle spectra is possible due to the different geometrical arrangement of these lipid compartments resulting in different bulk magnetic susceptibility (BMS). EMCL are nestled in long fatty septa along the muscle fibre bundles or fasciae, and can thus be described in a simplified way as coaxial cylinders. IMCL are located in a roughly spherical... 

Capillary pipette Falling sphere Parallel plate Falling coaxial cylinder Stress relaxation Rotating cylinder Tensile creep... 

Figure 10.5 Becquerel phosphoscope with (a) coaxial cylinders (b) a pair of rotating sectors mounted cn a common shaft.

For convenience, a mathematically simple arrangement is considered. It consists of a fluid layer of finite constant thickness, confined by two rigid parallel planes of infinite extension. Steady laminar shear flow is created in this layer by fixing one plane in space and moving the other one with constant speed in a direction parallel to both planes. In this way, a truly uniform and time independent shear rate q is created in the liquid. The magnitude of this shear rate is simply given by the ratio of the said speed to the mutual distance of the planes. Experimentally such an arrangement is approximated e.g. by the use of two coaxial cylinders. When the gap between the inner surfaces of these cylinders is made small compared with their radii, the above mentioned situation can be realized to a sufficient extent. 

Flow birefringence of polymer solutions is, in general, measured with the aid of an apparatus of the Couette type, containing two coaxial cylinders. One of these cylinders is rotated at constant speed, the other is kept in a fixed position. The light beam for the birefringence measurement is directed through the annular gap between these cylinders, in a direction parallel with the axis of the apparatus. In this way, the difference of principal refractive indices An is measured just in the above defined plane of flow (1—2 plane). 

At this stage of the discussion it must be emphasized that Philippoff (53, 54) has published a considerable amount of work carried out on solutions. For the determination of shear recovery he used a special coaxial cylinder apparatus. He arrived at the embarassing conclusion that Lodge s equation (2.11) is not valid, but that the equation of "solid state theory , i.e. eq. (2.12) is in accordance with the experimental results. Fig. 2.3 gives some of the results recently published by Philippoff and Stratton (55) for a 4.15 wt. per cent solution of polyisobutylene... 

L-100 (Mw — 1.4 0.1 x 10 , Mw/Mn — 2.2)4 in medicinal white oil as a rather high viscous solvent (1.50 poise at 25° C). In this figure the directly measured shear recovery (s ) (open triangles) is plotted against shear stress pzl of the preceding shear flow. From flow birefringence measurements (in a coaxial cylinder apparatus) and normal thrust measurements (in a cone-and-plate apparatus) values of normal stress difference (pn — p22) were calculated. These values were transformed with the aid of eq. (2.12) into recoverable shears s. The full circles (from... 

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