Zwietering correlation

Albal et al. (1983) have shown that the Zwietering correlation does not work well in an unconventional agitated vessel. Zlokarnik and Judat (1969) studied... 

What is the minimum agitator speed to suspend the solids In stirred tanks, there is always an impeller speed below which settling solids will tend to accumulate on the bottom of the vessel. This speed is different for different types of impellers and for identical impellers located at different clearances from the bottom of the vessel. It also depends on the properties of the solid and liquid phases. The minimum speed may be estimated for certain impeller and tank geometries using the Zwietering correlation. It is advisable, however, to determine this value experimentally for processes where solid-liquid mixing is deemed critical. See Section 10-2.2 for details. 

SOLUTION (a) For this simple dissolution a high efficiency impeller will be used (see below for the rationale). From Table 10-3 select an A-310 impeller with diameter, D, equal to the half the vessel diameter, T (i.e., D = T/2, 24 in. or 0.61 m and located at T/4 from the vessel bottom). First, calculate Njs using the Zwietering correlation. 

The impeller speed recommended will in general be higher than Njs, the speed required for the just suspended state estimated by the Zwietering correlation. The speed required should be based on experimental data. For quick estimates of the speed and power requirements for complete uniformity, the ratios in Table 10-2 may be applied to the estimated value of Njs. 

Various correlations are provided for calculating the minimum speed of the agitator Nmin to keep a given solid in suspension. Zwietering [40] developed the following equation ... 

As homogeneous suspension in nonaerated stirred vessels can hardly be achieved, even with very high stirrer speeds, mainly Nc, needed for complete suspension, is of interest for the design purposes. This value, by definition, is characterized by the just-suspended criterion, i.e., the state where only a small fraction of the solids remains at the bottom of the reactor for one second at maximum (Einenkel, 1979). Zwietering (1958) proposed the following correlation to predict Nc, the minimum rotational speed of agitation required for the complete suspension ... 

Joosten et al. (1977) and Kolar (1967) also studied suspension of solids in stirred vessels. The correlations of Baldi et al. (1978) and Zwietering (1958) are based on data over a wide range of conditions and are also in good agreement with each other. Baldi et al. (1978) also proposed a new model to explain the mechanism of complete suspension of solid particles in cylindrical flat-bottomed stirred vessels. According to this model the suspension of particles at rest on certain zones of the tank bottom is mainly due to turbulent eddies of a scale of the order of the particle size. The model leads to an expression... 

Zwietering s (1958) correlation, as modified by others, is recommended for prediction of Njs for off-bottom suspension. The dimensionless correlation is... 

The attainment of the solids just-suspended regime is essential to ensure that all solids are suspended off the tank bottom, thus ensuring that their surface area is fully exposed to the fiuid. Therefore, the ability to determine or predict the minimum impeller speed, Ajs, for the just-suspended state is a critical step in any solid-liquid mixing operation. Techniques for measuring Ajs are discussed elsewhere.In addition, Ajs has been the subject of significant studies and correlations are available to predict it. The most widely used equation for the determination of Ajs is the Zwietering equation... 

Chowdhury has pointed out regions of interest where Zwietering s correlation is not as reliable. They include 1) solids loading below 2% (v/v) 2) high Jp/r values and 3) high solids loading (>15%, v/v). 

Zwietering s correlation is based on data for five types of impelleis in six tanks from 6 in. to 2 ft in diameter. The critical stirrer speed is given by the dimensionless equation... 

As already suggested, there are many empirical conelations, and also theoretical equations with supporting experimental data in the literature. In general, all are different. However, the correlation of Zwietering , who carried out a dimensional analysis of the important variables and covered experimentally a very wide range of impeller types, sizes and off-bottom clearances, vessel sizes and physical properties, is broadly similar to a large number of them. The equation is... 

In addition, the imparted turbulent energy theory also predicts a low exponent. For particles below about 200 fim, larger exponents have been leportetP. However, it has been suggested that since Njs falls away more rapidly than Zwietering s correlation would imply, its use therefore errs on the safe side. ... 

The values of obtained by various instrumental techniques were also compared and found to differ only by 11%. Nienow (2000) has also indicated that a single observer can get results that are reproducible within 5%. Therefore, despite its subjective nature, Zwietering s criterion and the results/correlations based on the same continue to be widely used for predicting the just-suspended condition. 

Values of S in Zwietering s (1958) correlation are given and compared with high density particles... 

Lima et al. (2009) investigated solid suspension in laboratory-scale Wemco and Denver cells and compared their results with those of van der Westhuizen and Deglon (2008). These investigators could also correlate using Zwietering-type correlation (Eq. 9.49). Expectedly, the parameters andp, which are dependent on the type and size of the impeller/cell design, were different for the three types of cells. 

Among the models for calculation of the shaft speed needed for suspension, the equation of Zwietering [12] is based on numerous experimental results. The shaft speed necessary to reach a state where the particles are just suspended (njs) can be correlated as follows ... 

Minimum speed for complete suspension It is necessary to ensure complete suspension of catalyst (see Joshi, 1982 Beenackers and Van Swaaij, 1993). The most important single parameter that influences complete suspension is the speed of agitation. This can be calculated from the early but still valid correlation of Zwietering (1958). In practice, the minimum agitation speed for uniform distribution of catalyst in the common loading range of 5 < w < 30 g/100 g liquid and particle size range of 10 < < 150 xm is 150-600 rpm. 

In mechanically agitated vessels, the minimum agitation speed for the just suspended state, Njs, has been the subject of many experimental and theoretical analyses (Nienow, 1985). The pioneering study by Zwietering (1958) covered by far the widest range variables. The resulting correlation is discussed below. 

Techniques for measuring the speed required for the condition for just suspension are discussed in Chapter 4 of this book and by Choudhury (1997). Also discussed are key aspects of the criteria, techniques, and precautions that one must take to obtain reliable data for solids suspension correlations. The Zwietering criterion of no particle remaining at the base of the vessel for more than 1 to 2 s is the basis for most of the published studies. 

There have been many experimental stndies and theoretical analyses, with the pioneering work of Zwietering (1958) as the earliest known. He derived the following correlation from dimensional analysis and estimated the exponents by fitting to data for jnst snspended impeller speed, Njgi... 

Choudhury (1997) and Choudhury et al. (1995) questioned the appropriateness of the use by Zwietering of the X parameter to correlate the effect of solid loading. They preferred the use of Ihe volume fraction as a percent, %V, because a designer can specify it directly. The following expressions are useful for converting between various measures of solid loading in a slurry. To convert from volume percent, vol %, use... 

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