Velocity patterns

An alternative to traditional mass flow bin design is to use a patented BINSERT, which consists of a hopper-within-a-hopper below which is a single-hopper section (Fig. 15). The velocity pattern in such a unit is controded by the position of the bottom hopper. A completely uniform velocity profile can be achieved which results in an absolute minimum level of segregation. Alternatively, by changing the geometry at the bottom of the hopper, a velocity profile can be developed in which the center section moves faster than the outside, thus providing in-bin blending of the materials (7). 

Pickiug up the solids at the bottom of the tank depends upon the eddies and velocity fluctuations in the lower part of the tank and is a different criterion from the flow pattern required to keep particles suspended and moving in various velocity patterns throughout the remainder of the vessel This leads to the variables in the design equation and a relationship that is quite different when these same variables are studied in relation to complete uniformity throughout the mixing vessel. 

Figure 7-16. Velocity patterns observed in the side view of the blade passage for various casing treatments.

Flow measurement on supply terminals is difficult, as each terminal creates its own velocity pattern, and a reliable correlation between a local velocity and... 

The velocity patterns within a fixed bed reactor reflect the interactions between fluid elements... 

Garner and Haycock (G2) made quantitative measurements of the velocity pattern in drops falling through glycerine solutions, using a motion picture technique in which the camera fell with the drop. The refractive indices of their drop and field fluids were identical. There is no distortion due to bending of light beams in such cases. They found that no circulation was possible until the fall velocity exceeded 0.5 cm./sec. 

A number of initial velocity studies have been made with yeast hexokinase. All results to date indicate an intersecting initial velocity pattern in... 

In the limit e/Lw —> 0, only derivatives normal to the pore walls need to be considered. Straightforward integration yields the following velocity pattern in the boundary layer ... 

Analyzing in detail the fluid velocity patterns in oscillating tube flow, we have provided a new derivation of the Johnson et al. high-frequency development [6] and a new expression of the characteristic length A. Two different contributions to the dynamic permeability are now apparent. One stems from the boundary layer another stems from a perturbation potential flow in the... 

Fig. 7.41 Computation of the velocity pattern in the Kenics mixer, (a) the flow domain (b) the finite-element grid (c) the velocities at the cross section in the middle of an element (d) the same just after the transition. The contours in (c) and (d) are isolines of axial velocity, and the arrows show the lateral velocity. [Reprinted by permission from O. S. Galaktionov, P. D. Anderson, G. W. M. Peters, and H. E. H. Meijer, Analysis and Optimization of Kenics Mixers, Int. Polym. Process., 18,138-150, (2003).]...

Figure 5-23 has been used to correlate furnace performance data for a multitude of industrial furnaces and combustors. Typical operational domains for a variety of fuel-fired industrial furnaces are summarized in Table 5-7. The WSCC approach (or speckled furnace model) is a classic contribution to furnace design methodology which was first due to Hottel [op. cit.]. The WSCC model provides a simple furnace design template which leads to a host of more complex furnace models. These models include an obvious extension to a tanks-in-series model as well as multizone models utilizing empirical cold-flow velocity patterns. For more information on practical furnace design models, reference is made to Hottel and Sarofim (op. cit., Chap. 14). Qualitative aspects of process equipment have been treated in some detail elsewhere (Baukal, C. E., ed., The JohnZink Combustion Handbook, CRC Press, Boca Raton, Fla., 2001). 

Hartge, E. U., Rensner, D., and Werther, J. Solids concentration and velocity patterns in circulating fluidized beds, in Circulating Fluidized Bed Technology II (P. Basu and J. F. Large, eds.), p. 165. Pergamon Press, 1988. 

Initial velocity patterns obtained for the reduction of NAD by dihy-droplipoamide give a series of parallel lines (reciprocal plots). The K ... 

A third study of the kinetics of lipoamide dehydrogenase has utilized the enzyme isolated from rat liver (95). At 25°, the temperature of the two previous studies, when dihydrolipoamide was varied at fixed levels of NAD, the double reciprocal plots were concave down. At 37° this behavior was not observed. The detailed studies were carried out at the higher temperature. Rates were measured in both directions at pH 8.0, the pH optimum for the reduction of NAD. Under these conditions, initial velocity patterns for the forward and reverse reactions were a series of parallel lines. The Km for NAD was 0.52 mM, for dihydrolipoamide was 0.49 mAf, for NADH was 0.062 mM, and for lipoamide was... 

If a flow in the tank is turbulent, either because of high power levels or low viscosity, then a typical velocity pattern at a point would be illustrated by Fig. 3. The velocity fluctuation i can be changed into a root mean square value (RMS), which has great utility in estimating the intensity of turbulence at a point. So in addition to the definitions above, based on average velocity point, we also have the same quantities based on the root mean square fluctuations at a point. We re interested in this value at various rates of power dissipation, since energy dissipation is one of the major contributors to a particular value of RMS v. ... 

Fig. 11. Typical computational results obtained by Lapin and Liibbert (1994) with a mixed Eulerian-Lagrangian approach. Liquid phase velocity pattern (left) and the bubble positions (right) in a wafer column (diameter, 1.0 m height, 1.5 m) where the bubbles are generated uniformly over its entire bottom. (Reprinted from Chemical Engineering Science, Volume 49, Lapin, A. and Liibbert, A., Numerical simulations of the dynamics of two-phase gas-liquid flows in bubble columns, p. 3661, copyright 1994 with permission from Elsevier Science.)...

Enzyme kinetics is an important tool for assaying enzyme activities and for determining enzyme mechanisms. Although other techniques can provide useful information on enzyme mechanisms, the kinetics has to be the ultimate arbiter because it looks at the reaction while it is taking place. Initial velocity patterns, inhibition patterns, patterns of isotopic exchange, pH profiles, and isotope effects are all kinetic tools that allow one to determine kinetic mechanisms, chemical mechanisms, and transition state structures. 

The approach outlined above is sufficient when there is only one substrate or in an assay where one varies only the concentration of one substrate. However, where two or more substrates exist and one wants to know the order of their combination with the enzyme, one needs to determine an initial velocity pattern. One varies the concentrations of one substrate at several different levels of a second substrate and determines the initial velocities for the different reaction mixtures. It is, of course, necessary to have the same enzyme level in each reaction or correct the rates to constant enzyme concentration. 

Three initial velocity patterns are commonly observed. When both substrates have to add to the enzyme before any products... 

Equation 6 describes an intersecting initial velocity pattern where 1/v is plotted versus 1/A at different values of B, whereas Equation 6 describes the pattern where 1/v is plotted versus 1/B at different values of A (Fig. 1). Both the slopes and the intercepts of the reciprocal plots are functions of the other substrate concentration, and replots of slopes or intercepts versus the reciprocal of the other substrate concentration allow determination of all kinetic constants. 

Figure 1 Reciprocal plots with A varied at different levels of B (intersecting initial velocity pattern) or different levels of I (noncompetitive inhibition pattern).

The constant term is missing, which leads to a parallel initial velocity pattern (Fig. 2) regardless of which substrate concentration is varied ... 

The third type of initial velocity pattern results from a mechanism in which 1) the substrates add in obligatory order and 2) the off-rate constant for the first substrate to bind exceeds the turnover number (V/Et or kcat) sufficiently that its binding is at equilibrium, which is called an equilibrium ordered initial velocity pattern (Fig. 3). The rate equation is... 

The determination of kinetic mechanisms requires more than just initial velocity patterns, and inhibition studies are usually required. Several types of inhibitors are useful. The products are substrates in the reverse reaction and thus have some affinity for the enzyme and will give inhibition unless their inhibition constants exceed their solubility. Dead-end inhibitors are molecules that play musical chairs with the substrates for open portions of the active site but do not react. Substrates may act as dead-end inhibitors by combining at points in the mechanism where they are not intended and thus cause substrate inhibition. The inhibition patterns caused by these inhibitors are useful in distinguishing between different kinetic mechanisms. 

Figure 10.4. Ultraceutrifugatiou Studies of ATCase. Sedimentation velocity patterns of (A) native ATCase and (B) the enzyme after treatment withp-hydroxymercuribenzoate show that the enzyme can be dissociated into regulatory and catalytic subunits. [After J. C. Gerhart and H. K. Schachman. Biochemistry 4(1965) 1054.]...

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