Mixing flow number

The pumping number is a function of impeller type, the impeller/tank diameter ratio (D/T), and mixing Reynolds number Re = pND /p.. Figure 3 shows the relationship (2) for a 45° pitched blade turbine (PBT). The total flow in a mixing tank is the sum of the impeller flow and flow entrained by the hquid jet. The entrainment depends on the mixer geometry and impeller diameter. For large-size impellers, enhancement of total flow by entrainment is lower (Fig. 4) compared with small impellers. 

There are three types of mixing flow patterns that are markedly different. The so-called axial-flow turbines (Fig. 18-3) actually give a flow coming off the impeller of approximately 45°, and therefore have a recirculation pattern coming back into the impeller at the hub region of the blades. This flow pattern exists to an approximate Reynolds number of 200 to 600 and then becomes radial as the Reynolds number decreases. Both the RlOO and A200 impellers normally require four baffles for an effective flow pattern. These baffles typically are V12 of the tank diameter and width. 

This is probably the most important dimensionless group used to represent the actual flow during mixing in a vessel. Flow Number, Nq (or pumping number) ... 

R, = Reynolds number = No = d np/H Nqd = discharge flow number = qu/nd p - pressure qq = discharge flow rate ejq = mixing time... 

Mixing concepts, fundamentals, 297 Actual motor horsepower, 307 Axial flow, 291 Baffle diagrams, 318 Baffles, 311 Calculations, 297 Characteristic curves, 306 Draft lubes, 309, 312, 313 Entrainment, 309 Flow number, 298 Flow patterns, 309-313 Flow, 298... 

Numbering-up can be performed in two ways (Figure 1.4). External numhering-up is referred to as the connection of many devices in a parallel fashion [8] (a similar, but less elaborate, definition was already provided in [9, 10] see also [11] for a realized industrial example). A device in the sense as it is used here is defined as a functional element, e.g. a micro-mixing flow configuration such as an interdigital... 

As a further disadvantage, it is known concerning operation in many parallel micro channels that mixed flow patterns and even drying of the channels can occur [9, 10]. This comes from phase maldistribution to the channels. To overcome this problem, first solutions for phase equipartition have been proposed recently, but so far have not been applied for the mixers described here, but instead for mini-packed reactors, having feed sections similar to the mixers [11,12]. Nevertheless, numbering-up of dispersive-acting micro devices generally seems to be more complicated than for two-phase contactors (see Section 5.1.1). 

For a well-mixed flow system at steady state, the fractional conversion Xa is the ratio of the number of moles of A converted to the moles A fed to the system... 

Fig. 36. The spatial variation of agglomerate sizes in simulations of erosion in the journal bearing flow. Initially there are 10000 agglomerates consisting of 400-500 aggregates. The grey scale represents the number of aggregates in the agglomerates, (a) Poorly mixed flow after four periods, (b) Well-mixed flow after one period (Hansen, el al. 1998).

Consider a system of N mixed flow reactors connected in series. Though the concentration is uniform in each reactor, there is, nevertheless, a change in concentration as fluid moves from reactor to reactor. This stepwise drop in concentration, illustrated in Fig. 6.3, suggests that the larger the number of units in series, the closer should the behavior of the system approach plug flow. This will be shown to be so. 

This is the conversion expression for second-order reaction of a macrofluid in a mixed flow reactor. The integral, represented by ei(a) is called an exponential integral. It is a function alone of a, and its value is tabulated in a number of tables of integrals. Table 16.1 presents a very abbreviated set of values for both ei(jc) and Ei(jc). We will refer to this table later in the book. 

One of the significant limitations of the use of first- and second-generation superplasticizers in ready-mixed flowing concrete is the rapid decrease in the initially achieved high workability and this constitutes one of the chief constraints to their wider acceptance. Therefore, a number of major producers of admixtures have sponsored active research to improve the workability retention characteristics of their superplasticizers. Some recent developments [48] have shown promise, among these are materials based on acrylate polymers (AP). The AP-based materials are reported to be more effective than SNF- or SMF-based surplasticizers in terms of water reduction, slump increase and slump retention. Figure 7.19 shows the remarkable improvement in the retention of workability produced by the AP type superplasticizer compared to an SNF type. 

The classic analysis of reactors involves two idealized flow patterns— plug flow and mixed flow. Though real reactors never fully follow these flow patterns, in many cases, a number of designs approximate these ideals with negligible error. However, deviation from ideality can be considerable. Typically, in a reaction vessel, we can have several immediate cases closer to plug or mixed flow. Of course, nonideal flow concerns all types of reactors used in heterogeneous processes, i.e. fixed beds, fluidized beds, continuous-flow tank reactors, and batch reactors. However, we will focus on fixed beds and batch reactors, which are the common cases. 

Electric-force mixing is adequate for mixing flows at very low Reynolds number (-1). By lamination of two fluids with different electric conductivity and/or permittivity in a micro mixer, a steep cross-sectional gradient of the respective properties can be established [91]. The electric field may be parallel or perpendicular to the fluid interface, which is also a boundary where electric properties abruptly... 

The disadvantages are that (1) they are not suitable for services that are dirty, abrasive, viscous, or mixed-flow (gas with liquid droplets, liquid with vapor bubbles), or that have low Reynolds numbers (below 20,000) (2) the available choices in materials of construction are limited (3) the pulse resolution (number of pulses per gallon or liter) drops off in larger sizes (4) the pressure drop is high (two velocity heads) and (5) substantial straight runs are required, both upstream and downstream. 

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