Motion surface

In the case of more or less axially mounted stirrers in vessels without baffles, the liquid is set in rotation, and generates a liquid vortex. As long as the vortex is not so deep that gas can be entrained by the stirrer, the vortex depth has no influence either on the stirrer power or on the mixing process. Naturally, the power number Ne and the mixing number nO depend upon whether the stirred tank is provided with baffles or not (see Fig. 1.36 and 3.3). 

As soon as the vortex reaches the stirrer head of a rapidly rotating stirrer (e.g. propeller or turbine stirrer) or the outer stirrer side of a slowly rotating stirrer (e.g. blade stirrer), gas is entrained in the liquid. Gas entrainment via vortex was 

The entrainment of gas in the liquid is undesirable in most mixing operations. In addition, the bearings and seals of stirrer shaft are subjected to exceptionally strong mechanical stress, due to the inhomogeneous gas/liquid mixture and the fact that the stirrer partly rotates in air and therefore the liquid bearing is absent. It is therefore of practical interest to know how a stirrer can be operated in an unbaffied vessel in such a way that vortex formation can be tolerated. 

The vortex formation involves on the one hand a lowering of the liquid level, which is characterized by the vortex depth h on the stirrer shaft, and on the other hand a liquid level increase h on the vessel wall, Fig. 1.21. The question concerning the relatively small liquid level increase h at the vessel wall compared with the vortex depth h is irrelevant. 

The vortex depth h on the stirrer shaft depends, for a given stirrer type and for geometric installation conditions D/d, h/d) upon the stirrer diameter d, the stirrer speed n, the liquid height H above the stirrer at rest, the physical properties of the liquid (density p, kinematic viscosity v) and the acceleration due to gravity, g  

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This interpretation is largely based on the results of cube models for the surface motion. It may also be that... 

The advent of lasers allowed optical interferometry to become a useful and accurate technique to determine surface motion in shocked materials. The two most commonly used interferometric systems are the VISAR (Barker and Hollenbach, 1972) and the Fabry-Perot velocity interferometer (Johnson and Burgess, 1968 Durand et al., 1977). Both systems produce interference fringe shifts which are proportional to the Doppler shift of the laser light reflected from the moving specimen surface. Both can accommodate a speci-... 

E. Eor radial flow turbine, locate 1.5D to 2.0D apart, with liquid coverage over the top impeller of minimum M to 3.0D, depending on surface motion desired. 

Another largely unexplored area is the change of dynamics due to the influence of the surface. The dynamic behavior of a latex suspension as a model system for Brownian particles is determined by photon correlation spectroscopy in evanescent wave geometry [130] and reported to differ strongly from the bulk. Little information is available on surface motion and relaxation phenomena of polymers [10, 131]. The softening at the surface of polymer thin films is measured by a mechanical nano-indentation technique [132], where the applied force and the path during the penetration of a thin needle into the surface is carefully determined. Thus the structure, conformation and dynamics of polymer molecules at the free surface is still very much unexplored and only few specific examples have been reported in the literature. 

Tears-of-Wine The surface motion of mixed liquids was described in ancient times [29], and scientifically in a paper by James Thompson, the brother of Lord Kelvin [30] in 1855. Recently Neogi [31], and Cazabat [32] reported on the formation of ordered stmctures in evaporating solutions of two liquids. The meniscus of wine in a glass is drawn upward on the glass surface and forms a thin film. Due to its... 

The Pt/Ru catalyst is the material of choice for the direct methanol fuel cell (DMFC) (and hydrogen reformate) fuel cell anodes, and its catalytic function needs to be completely understood. In the hrst approximation, as is now widely acknowledged, methanol decomposes on Pt sites of the Pt/Ru surface, producing chemisorbed CO that is transferred via surface motions to the active Pt/Ru sites to become oxidized to CO2... 

Using our procedures we cannot calculate the log L values for Steps 8 and 9 for Examples 3, 4, 9, and 10 because the reacting surface species in those steps are not the same as the gas phase species. But if we make the calculations for those steps assuming that the surface species are the same as the gas phase species, we obtain the following log L values for Steps 8 and 9, respectively—Example 3 23, 19 Example 4 14, 10 Example 9 20, 15 Example 10 18, 13. Thus, surface motion may be a factor in these examples. 

Equal surface motion is related most often to vortex formation. The depth of the vortex is related by geometric similarity and equal Froude number = DN fg... 

The rate and characteristics of surface evolution depend on the particular transport mechanisms that accomplish the necessary surface motion. These can include surface diffusion, diffusion through the bulk, or vapor transport. Kinetic models of capillarity-induced interface evolution were developed primarily by W.W. Mullins [1-4]. The models involving surface diffusion, which relate interface velocity to fourth-order spatial derivatives of the interface, and vapor transport, which relate velocity to second-order spatial derivatives, derive from Mullins s pioneering theoretical work. 

The effect of various factors—the forms and dimensions of the igniting surface, motion of the fuel, etc.—are reduced to their effect on the conditions of heat transfer. 

S) P-4 Pitched-blade turbine Blending, Heat transfer-Dispersion, Surface motion, Solid suspension, np - 5. Nq - 0.7 (turbulent)... 

Xiang and Sabatier [149] used a scanning laser Doppler vibrometer (LDV) to detect acoustic-to-seismic surface motion. This technique exploits airborne acoustic waves penetrating the ground and causing seismic motion. When an anti-personnel landmine... 

Although apparently simple, there is a lot of subtlety in this model. The most important parameter in determining the translational energy dependence of the activation energy is AE. If we reduce AE, then the slope of E (Elmm) increases, which is found in the results of the full quantum dynamics calculations the slope is greater for the J 0 -> 4 transition than for J 0 - 6. AE is the shift in the threshold due to the thermal motion, it is the amount of energy surface motion contributes to aid the dissociation or rovibrational excitation. Why this should vary from one particular transition to... 

For propagation in an isotropic medium or along a pure-mode direction of a crystal (e.g., a plane of symmetry). Equation 3.38 reduces to a Rayleigh wave, characterized by having no transverse component Ux = 0. Since Uy and Uz are 90° out of phase, the particles move in an elliptical orbit in the sagittal plane die surface motion resembles that of the ocean under the influence of a passing wave. 

Protein rate processes are strongly affected by hydration. The dry protein shows greatly reduced internal motions, measured by Moss-liauer spectroscopy, neutron scattering, fluorescence spectroscopy, and other methods. Surface motions, monitored by spin probes or spin or Mossbauer labels, are similarly frozen in the dry protein. The following paragraphs comment on the appearance of motion characteristic of the hydrated protein and on the coupling between protein and solvent motions. 

There appears to be no single pattern describing the hydration dependence of enzyme activity. Lysozyme activity is correlated with the unfreezing of surface motion at 0.25 A and also with the onset of surface percolation. There are changes in activity above 0.38 A, such as the changes found for rotational motion of TEMPONE. The hydration threshold for chymotrypsin activity, at 0.12 A, is substantially lower than that for lysozyme. A correlation with percolation is an attractive, but untested, possibility. 

We start from the experimental observation that lysozyme powders exhibit a single critical hydration level for the onset of enzyme activity and the onset of surface motions, displayed in the dynamics of a spin... 

These results have important implications. For example, metal surfaces are often used to speed up particular reactions. The motions on the metal surface could significantly influence the way that reactants interact with the surface. Also, a lot of effort is now being expended to construct tiny machines (called nanoscale devices) by assembling individual atoms on a solid surface. These devices could be literally torn apart by excess surface motions. ... 

NPT ensemble anti used the shell-model to describe polarizability. All simulation runs were performed at atmospheric pressure and in the temperature range 10 - 1100 K. For all three surfaces at both 300 and 1100 K it was found that the surface mean square displacements are generally larger for the oxide ions than for the cations and that the out-of-plane surface motion is usually larger than the in-plane surface motion. At room temperature, the oxygen mean square displacements at the (111) surface arc a factor 1.2 larger than in the bulk, a factor 1.6 for the (Oil) surface and approximately five limes larger at the metastable (001) surface compared to the bulk. The effect of the presence of a surface on the ion dynamics (and on the structure for (011)) persists all the way to the slab centers, even for these rather thick slabs. 

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