Circulation times

As shown in the previous section, during plug flow in small channels, counter rotating vortices form in the phases with closed streamlines and a pattern symmetrical about the channel axis (Fig. 5.9). The rate of mixing inside the plug is quantified through the dimensionless circulation time, x, which relates the time for 

9 Schematic of the flow pattern inside the micro-channei of radius R in 3-D (Eq. 5.4.1) and 2-D (Eq. 5.4.2) referenee frames. The internal recirculation parameters are sketched inside a single water plug, projeeted onto the mid-xy plane (jt), where quantities in Eq. (5.4.2) are defined 

Assuming a fully developed laminar profile within the plug and the 3-D flow model in Fig. 5.9, the non-dimensional circulation time in cylindrical coordinates 

When a planar domain at the centre of the channel is considered (i.e. n plane in Fig. 5.9) and given the axisymmetric assumption, Eq. (5.4.1) is stiU valid with r simply substituted by y. Alternatively a 2-D definition of the non-dimensional circulation time can be obtained by rewriting Eq. (5.4.1), valid in the observation xy plane n (Fig. 5.9)  

A sample of the non-dimensional circulation time profile across the length of an aqueous plug in the 0.2 mm ID channel is shown in Fig. 5.10c, which was 

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Large tanks tend to develop a recirculation pattern from the impeller through the tank back to the impeller. This results in a behavior similar to that for a number of tanks in a series. The net result is that the mean circulation time is increased over what woiild be pre-dic ted from the impeller pumping capacity. This also increases the standard deviation of the circulation times around the mean. 

In gas-liquid systems, the tendency for an increase in the gas superficial velocity upon scale-up can further increase the overall circulation time. 

For any given process, one takes a qualitative look at the possible role of fluid shear stresses. Then one tries to consider pathways related to fluid shear stress that may affect the process. If there are none, then this extremely complex phenomenon can be dismissed and the process design can be based on such things as uniformity, circulation time, blend time, or velocity specifications. This is often the case in the blending of miscible fluids and the suspension of sohds. 

The overall circulating pattern, including the circulation time and the deviation of the circulation times, can never be neglected. No matter what else a mixer does, it must be able to circulate fluid throughout an entire vessel appropriately. If it cannot, then that mixer is not suited for the task being considered. 

There is the possibihty of misinterpretation of the difference between circulation time and blend time. Circulation time is primarily a function of the pumping capacity of the impeller. For axial-flow impellers, a convenient parameter, but not particularly physically accurate, is to divide the pumping capacity of the impeller by the cross-sectional area of the tank to give a superficial hquid velocity. This is sometimes used by using the total volume of flow from the impeller including entrainment of the tank to obtain a superficial hquid velociW. 

As the flow from an impeller is increased from a given power level, there will be a higher fluid velocity and therefore a shorter circulation time. This holds true when dealing with any given impeller. This is shown in Fig. 18-18, which shows that circulation time versus D/T decreases. A major consideration is when increasing D/T becomes too large and actually causes the curve to reverse. This occurs somewhere around 0.45, 0.05, so that using impellers of D/T ratios of 0.6 to 0.8... 

FIG. 18-18 Effect of D/T ratio on two different impellers on the circulation time and the hlend time. 

When comparing different impeller types, an entirely different phenomenon is important. In terms of circulation time, the phenomena shown in Figs. 18-18 and 18-19 stiU apply with the different impellers shown in Fig. 18-5. When it comes to blending another factor enters the picture. When particles A and B meet each other as a result of shear rates, there has to be sufficient shear stress to cause A and B to blend, react, or otherwise participate in the process. 

It turns out that in low-viscosity blending the acdual result does depend upon the measuring technique used to measure blend time. Two common techniques, wliich do not exhaust the possibilities in reported studies, are to use an acid-base indicator and inject an acid or base into the system that will result in a color change. One can also put a dye into the tank and measure the time for color to arrive at uniformity. Another system is to put in a conductivity probe and injecl a salt or other electrolyte into the system. With any given impeller type at constant power, the circulation time will increase with the D/T ratio of the impeller. Figure 18-18 shows that both circulation time and blend time decrease as D/T increases. The same is true for impeller speed. As impeller speed is increased with any impeller, blend time and circulation time are decreased (Fig. 18-19). 

However, when comparing different impeller types at the same power level, it turns out that impellers that have a higher pumping capacity will give decreased circulation time, but all the impellers, regardless of their pumping efficiency, give the same blend time at the... 

FIG. 18-19 Effect of impeller speed and power for the same diameter on circulation time and blend time for a particular impeller. 

FIG. 18-20 At constant power and constant impeller diameter, three different impellers give the same hlend time hut different circulation times. 

Figure 18-21 gives some data on the circulation time of the hehcal impeller. It has oeen observed that it takes about three circulation times to get one blend time being the visual uniformity of a dye added to the material. This is a macro-scale blending definition. 

FIG. 18-21 Effect of impeller speed on circulation time for a helical impeller in the Reynolds niimher arranged less than 10. 

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. 

Emulsions Almost eveiy shear rate parameter affects liquid-liquid emulsion formation. Some of the efrecds are dependent upon whether the emulsion is both dispersing and coalescing in the tank, or whether there are sufficient stabilizers present to maintain the smallest droplet size produced for long periods of time. Blend time and the standard deviation of circulation times affect the length of time it takes for a particle to be exposed to the various levels of shear work and thus the time it takes to achieve the ultimate small paiTicle size desired. 

Circulation time The time necessary for complete mixing of a tracer gas in a space. 

This scale-up criterion is based on achieving a constant pumping rate per unit volume with scale-up and therefore leads to similar macromixing on different scales, as the circulation time in the reactor remains constant. 

Finally, inadequate hole cleaning results in an overloading of the annulus with cuttings, especially in very high penetration rate, poor mud properties, and insufficient annular velocity or circulation time. Inadequate hole cleaning can also be experienced in deviated wells with the formation of cutting beds on the low side migrating in a sand dune fashion. 

A qualitative relationship between the drillpipe pressure, casing pressure and circulating time is shown in Figures 4-353a and 4-353b, respectively. 

Circulation time Precursors Specific growth rate... 

Gabizon, A., and Papahadjopoulos, D. (1988). Liposome formulations with prolonged circulation time in blood and enhanced uptake by tumors, Proc. Natl. Acad. Sci. USA, 85, 6949-6953. 

The Jing group investigated their poly(L-lysine)-6-poly(L-phenylalanine) vesicles for the development of synthetic blood, since PEG-lipid vesicles were previously used to encapsulate hemoglobin to protect it from oxidation and to increase circulation time. They extended this concept and demonstrated that functional hemoglobin could be encapsulated into their vesicles. The same polypeptide material was also used to complex DNA, which caused the vesicles to lose their... 

Various empirical equations are available for the circulation time constant, Xcirc> in stirred vessels, columns, etc. Usually the value of the time constant, however, will represent a mean value, owing to the stochastic nature of flow. 

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