Quasi-solid rotation

Two additional parameters are the angular position of the point at which the film thickness is maximum, 0rot, and the ratio of the maximum thickness of the film to its mean thickness e. The zone of large Re and small Fr is shaded in Fig. 4.22 in the right bottom. The existence of circular closed flow lines proves to be impossible hence, a stable solution of the hydrodynamic problem is also impossible. The zone of quasi-solid rotation A is marked in the top left comer film flow is absent here and 1 < e < 1.01. This zone is reached either at Fr = const by decreasing Re (due to an increase in viscosity) or at Re = const by increasing Fr (through an increase in to). Two transient zones are marked with the numbers 1 and 2 in the lower unstable zone of Fig. 4.22. In zone 1, the... 

Figure 4.23. Different possible flow modes in rotary processing of polyester resin 1 - quasi-solid rotation 2 - stable hydrocyst 3 - rotation in an annular (ring-shaped) layer, 4 - cascade flow. [Adapted, by permission, from I. L. Throne, I. Gianchandani, Potym. Eng. Sci., 20 (1980), 913.]...

At k = —1, the flow is spinning, obeying the law of circulation constancy (potential rotation) at k = 0, the spin angle is constant, i.e. does not depend on radius and at k = 1, the rotation obeys the laws of solid body rotation (a quasi-solid rotation). To ensure that rotation obeys (19.8), the blades of the swirler at the exit should have a certain dependence of the spin angle on the radius. The question... 

Quasi-solid rotation (k = 1). In this case we have ... 

A different situation arises for hydrocyclones, in which the density of the disperse phase is only moderately greater than the density of the continuous phase. Therefore, for hydrocyclones, < 1, and their CE (Eig. 19.4, b) is small and essentially depends on the profile of the tangential flow velocity. From the three laws of swirling considered above, the greatest efficiency is provided by the law of quasi-solid rotation. 

Organic solids have received much attention in the last 10 to 15 years especially because of possible technological applications. Typically important aspects of these solids are superconductivity (of quasi one-dimensional materials), photoconducting properties in relation to commercial photocopying processes and photochemical transformations in the solid state. In organic solids formed by nonpolar molecules, cohesion in the solid state is mainly due to van der Waals forces. Because of the relatively weak nature of the cohesive forces, organic crystals as a class are soft and low melting. Nonpolar aliphatic hydrocarbons tend to crystallize in approximately close-packed structures because of the nondirectional character of van der Waals forces. Methane above 22 K, for example, crystallizes in a cubic close-packed structure where the molecules exhibit considerable rotation. The intermolecular C—C distance is 4.1 A, similar to the van der Waals bonds present in krypton (3.82 A) and xenon (4.0 A). Such close-packed structures are not found in molecular crystals of polar molecules. 

Crystal lattices have symmetry elements such as rotation axes, mirror planes, inversion points, and combinations of these. A crystalline lattice has translation symmetry, except for quasi-crystals or icosahedral phases, which have lattices with point symmetry elements only. Glasses are amorphous solids that do not have any symmetry element in their lattices. 

The nuclear resonant inelastic and quasi-elastic scattering method has distinct features favorable for studies concerning the microscopic dynamics (i.e., lattice vibration, diffusion, and molecular rotation) of materials. One advantageous feature is the ability to measure the element-specific dynamics of condensed matter. For example, in solids the partial phonon density of states can be measured. Furthermore, measurements under exotic conditions -such as high pressure, small samples, and thin films - are possible because of the high brilliance of synchrotron radiation. (For the definition of brilliance, see O Sect. 50.3.4.5 of Chap. 50, Vol. 5, on Particle Accelerators. ) This method is applicable not only to solids but also to liquids and gases, and there is no limitation concerning the sample temperature. 

The centrifugal flows considered in this chapter are those dominated by rotatioa The azimuthal component of the velocity is preponderant, that is, Ur ue and Uz Ue in the cylindrical coordinate system. In such a configuration, the flow tends to become two-dimensional in a plane perpendicular to the Oz axis. The Ur and Ue components of the velocity are quasi-independent from coordinate z. The proof of this property goes beyond the scope of this chapter. Our goal is to describe the centrifugation of solid particles in a rotating flow. We simply choose to consider steady-state axisymmetric fluid flows, whose velocity and pressure fields possess the following kinematic characteristics ... 

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