Characteristic mixing time

Example 3 Mixing Time Characteristics for Liquid Mixtures... 

From this, the mixing time characteristics results to... 

This results in a mixing time characteristics incorporating six numbers ... 

This relevance list yields in the two parametric mixing time characteristics... 

Figure 13 Mixing time characteristics of three slowly rotating stirrers (leaf, frame, crossbeam stirrer) in a vessel with and without baffles. To correlate the data in order to emphasize the similarity, n6 values of the crossbeam stirrer were multiplied by 0.7 and of the leaf stirrer by 1.25. Source From Ref. 14.

To gain information on minimum mixing work (P6 = min) necessary for homogenization, the mixing time characteristics, as well as the power... 

Mixing time characteristic of the Nauta cone and screw mixer... 

The mixing time characteristic of the Nauta mixer is given in Figure 16. It can be shown that the type of material has a negligible influence (proof that the density p is irrelevant indeed). Likewise, the number b/ has no effect within the used range. In contrast, the influence of the parameter l/d is very pronounced. The process equation reads ... 

The impact, which the introduction of intermediate quantities can have on the relevance list, will be demonstrated in the following by one elegant example. Example 3 Mixing-Time Characteristics for Liquid Mixtures with Differences in Density and Viscosity. The mixing time 0 necessary to achieve a molecular homogeneity of a liquid mixture—normally measured by decolorizatiorr methods—depends, in material systems without differences in density and viscosity, on only four parameters stirrer diameter d, density p, kinematic viscosity v, rotational speed ti ... 

Example 5.2 Mixing-Time Characteristics of a Stirrer. Mixing time 0 is the time necessary to completely homogenize an admixture with the liquid contents of the vessel. It can easily be determined visually by a decolorization reaction (neutralization, redox reaction in the presence of a color indicator). The relevance list of this task consists of the target quantity (mixing time 0) and of the same parameters as in the case of mixing power—on condition that (contrary to Example 3) both liquids have similar physical properties) ... 

For the three stirrer types treated in this example, the mixing-time characteristics are presented in Fig. 10. 

This 5-parametric dimensional space leads to the 2-parametric mixing time characteristic ... 

This leads to a mixing time characteristic consisting of six pi-numbers ... 

In order to design and dimension stirrers for the homogenization of liquid mixtures - and this is by far the most common task when it comes to stirring - it is vital to know the power characteristic and the mixing time characteristic of the type of stirrer in question. If this information is available for various types of stirrers, it is possible to determine both the best type of stirrer for the given mixing task and the optimum operating conditions for this particular type. 

Fig. 26 Mixing time characteristic of a blade stirrer For installation conditions see Fig. 27 from [57].

Fig. 38 Mixing time characteristic of a plow-share mixer.

Fig. 22. Mixing-time characteristics of the stirrer types in Fig. 21 (curve h for 21h without baffles curve hs for 21h with baffles, etc.). (Reprinted with permission from the publisher, VCH Publishers, Inc., after Zlokarnik and Judat, 1988.)...

By way of example, in Fig. 3.3 the mixing time characteristic of a blade stirrer is... 

Fig. 3.3 Mixing time characteristic of blade stirrer according to Fig. 2.1c in the form of nS = /(Re). Geometrical conditions ...

In Fig. 3.5 the mixing time characteristics n0gg = f(Re) for the stirrer types with... 

Fig. 3.5 Mixing time characteristics of the stirrer types represented in Fig. 2.1 under given installation conditions from [611]. (The nD values for the cross-beam and the gate stirrer are by the factor given in the table higher than that of the blade stirrer, b - baffled tank)...

For helical ribbon stirrers not only the power characteristic but also the mixing time characteristic is clearly dependent upon the size of the helical surface (single or double helix pitch 0.5 or 1.0). For the range Re < 100 it was found that ... 

Fig. 3.6 Mixing time characteristics for different H/D ratios the top graph holds for the cross-beam stirrer, the bottom for the propeller stirrer, after Fig. 2.1a and h, resp. from [611]... 

Fig. 3.7 Mixing time characteristics for cross-beam stirrers at H/D = 1 in material systems with density and viscosity differences from [616]. 

Fig, 3.8 Mixing time characteristics for a pitched-blade stirrer in baffled tanks with Newtonian and non-Newtonian fluids in the conventional representation. For legend see Fig. 3.9 from [384]. 

Finally mixing time characteristics were mentioned [535], which were determined with seven different designs of helical ribbon stirrers, in which the gap... 

It should be emphasized that in this diagram only those stirrers are exemplary represented, whose geometric conditions are given in Fig. 2.1 and whose power and mixing time characteristics are presented in Fig. 2.2 and Fig. 3.5. To ascertain which stirrer type is actually the most suitable for a particular homogenization operation, a whole range of stirrer types must be evaluated and documented while changing their parameters (number of stirrer elements, pitch of the blades or stirrer vanes) and particularly their installation conditions (H/D, D/d, h/d etc.), which vastly exceeds the scope of this book. [0.19] is recommended literature in this connection. 

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