The Flow Pattern

The advantage of single-pass over cross-flow filtration is that it is an easier system to operate and can be cost effective, particularly if the product to be filtered is expensive, because very tittle of the initial fluid is lost during filtration. However, because the flow pattern of the fluid is directly through the filter, filter life maybe too short for the fluid being filtered. The minimum flow rate needed downstream of the filter must also be considered, especially when there are time constraints to the process. In some situations it may be more advantageous to use a cross-flow system where higher flow rates may be easier to obtain. 

The mesophase pitch is then extmded and melt spun through spinnerettes into fibers. The flow pattern of the mesophase during fiber formation has a strong influence on the morphology of the fiber (52—54) and can result in fibers with radial, onion-skin, or random microstmctures. Commercially available PBCFs have a round cross section, but this can be easily modified by changing the cross section of the spinnerette holes. Multilobal and C-shaped fibers have been produced with exceptional mechanical properties (55). 

Experimental techniques to visualize flows have been extensively used to define fluid flow in pipes and air flow over lift and control surface of airplanes. More recently this technology has been appHed to the coating process and it is now possible to visualize the flow patterns (16,17). The dimensions of the flow field are small, and the flow patterns both along the flow and inside the flow are important. Specialized techniques such as utilizing small hydrogen bubbles, dye injection, and optional sectioning, are required to visualize these flows. 

The flow pattern efficiency depends solely upon the shape of the velocity profile in the circulating gas. In terms of the integrals appearing in the gradient equation, the flow pattern efficiency is given by equation 86. 

To evaluate the flow pattern efficiency, a knowledge of the actual hydrodynamic behavior of the process gas circulating in the centrifuge is necessary. Primarily because of the lack of such knowledge, the flow pattern efficiency has been evaluated for a number of different assumed isothermal centrifuge velocity profiles. 

The Optimum Velocity Profile. The optimum velocity profile (41), that is the velocity profile that yields the maximum value for the flow pattern efficiency, is one in which the mass velocitypv is constant over the radius of the centrifuge except for a discontinuity at the wall of the centrifuge (r = rP). This optimum velocity profile is shown in Figure 14a. For this case the following values for the separation parameters of the centrifuge are obtained... 

The value of the flow pattern efficiency is shown as a function of the spacing between the streams ia Figure 15a. It can be seen that the flow pattern efficiency is a maximum when the position of the upflowiag stream is chosen such that /T2 is equal to 0.5335. For this particular case the flow pattern efficiency assumes the value 6p = 0.8145. 

Fig. 15. (a) Values of the flow-pattern efficiency for the two-sheU model, (b) The dependence of the flow-pattern efficiency on the dimensionless... 

These simple velocity profiles do not indicate directly any dependence of the flow pattern efficiency upon the rotational speed of the centrifuge. A dependence on speed is to be expected on the basis of the argument that at high speeds the gas in the centrifuge is crowded toward the periphery of the rotor and that the effective distance between the countercurrent streams is thereby reduced. It can be seen from the two-sheU model that, as the position of upflowing stream approaches the periphery, the flow pattern efficiency drops off from its maximum value. 

The separation parameters have been calculated for a centrifuge in which the behavior of the circulating gas is described by Martin s equation. The flow pattern efficiency is shown in Figure 15(b) as a function of the dimensionless parameter M, where M is equal to (ME /2RT). In this case the maximum flow pattern efficiency attainable is 0.956. 

For upflow in helieally eoiled tubes, the flow pattern, pressure drop, and holdup can be predicled by the correlations of Banerjee,... 

For a given impeller and tank geometiy, the impeller Reynolds number determines the flow pattern in the tank ... 

Dispersion In tubes, and particiilarly in packed beds, the flow pattern is disturbed by eddies diose effect is taken into account by a dispersion coefficient in Fick s diffusion law. A PFR has a dispersion coefficient of 0 and a CSTR of oo. Some rough correlations of the Peclet number uL/D in terms of Reynolds and Schmidt numbers are Eqs. (23-47) to (23-49). There is also a relation between the Peclet number and the value of n of the RTD equation, Eq. (7-111). The dispersion model is sometimes said to be an adequate representation of a reaclor with a small deviation from phig ffow, without specifying the magnitude ol small. As a point of superiority to the RTD model, the dispersion model does have the empirical correlations that have been cited and can therefore be used for design purposes within the limits of those correlations. 

The half-pipe jacket is used when high jacket pressures are required. The flow pattern of a liquid heat-transfer fluid can be controlled and designed for effective heat transfer. The dimple jacket offers structural advantages and is the most economical for high jacket pressures. The low volumetric capacity produces a fast response to temperature changes. 

For Reynolds numbers greater than 2000 baffles are commonly used with turbine impelTers and with on-centerhne axial-flow impellers. The flow patterns illustrated in Figs. 18-15 and 18-16 are quite different, but in both cases the use of Baffles results in a large top-to-bottom circulation without vortexing or severely unbalanced fluid forces on the impeller shaft. 

In the region of laminar flow (Vr < 10), the same power is consumed by the impeller whether baffles are present or not, and they are seldom required The flow pattern may be affected by the baffles, but not always advantageously. When they are needed, the baffles are usually placed one or two widths radially off the tank wall, to allow fluid to circulate behind them and at the same time produce some axial deflection of flow. 

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. 

Solid-Liquid Mass Transfer There is potentially a major effect of both shear rate and circulation time in these processes. The sohds can either be fragile or rugged. We are looking at the slip velocity of the particle and also whether we can break up agglomerates of particles which may enhance the mass transfer. When the particles become small enough, they tend to follow the flow pattern, so the slip velocity necessary to affect the mass transfer becomes less and less available. 

Many times solids are present in one or more phases of a solid-hquid system. They add a certain level of complexity in the process, especially if they tend to be a part of both phases, as they normally will do. Approximate methods need to be worked out to estimate the density of the emulsion and determine the overall velocity of the flow pattern so that proper evaluation of the suspension requirements can be made. In general, the solids will behave as though they were a fluid of a particular average density and viscosity and won t care much that there is a two-phase dispersion going on in the system. However, if solids are being dissolved or precipitated by participating in one phase and not the other, then they will be affected by which phase is dispersed or continuous, and the process will behave somewhat differently than if the solids migrate independently between the two phases within the process. 

A distinc tion is to be drawn between situations in which (1) the flow pattern is known in detail, and (2) only the residence time distribution is known or can be calculated from tracer response data. Different networks of reactor elements can have similar RTDs, but fixing the network also fixes the RTD. Accordingly, reaction conversions in a known network will be unique for any form of rate equation, whereas conversions figured when only the RTD is known proceed uniquely only for hnear kinetics, although they can be bracketed in the general case. 

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