Danckwert segregation

To compare the "state of unmixedness", Danckwerts introduced the intensity of segregation, which is calculated in terms of the mean square of the fluctuations, as... 

The concept of segregation and its meaning to chemical reactors was first described by Danckwerts (1953). The intensity or degree of segregation is given the symbol I, which varies between one and zero. Shown in Fig. 1 is a tank with two components, A and B, which are separated into volume fractions, qA and l-qA this condition represents complete initial segregation (1 = 1). Stirring or... 

Danckwerts (D8) discussed the case of a perfect mixer. For the completely segregated case, all molecules within a point have the same age, a, and so... 

At the same symposium, Danckwerts (D2) drew attention to the effect of incomplete mixing on homogeneous reactions. He introduced the concept of segregation, which indicates that in the same vessel there are clumps of fluid which have different concentrations, caused by incomplete mixing. The effect on the conversion of chemical reactors is again an increase in conversion for reactions of an order greater than 1 and a decrease in conversion when the order is less than 1. 

Danckwerts defined a degree of segregation J based on the fluctuations in concentration which occur. He studied a chemical reaction in a binary mixture of two components A and B, in which a is the volume fraction of A at a certain point and (1 — a) the volume fraction of B at this same... 

For the case of more or less parallel streams Danckwerts defined the degree of segregation by means of the age of a point. 

System Interaction rate State of segregation (here defined) Degree of segregation (Danckwerts) State of mixedness (Zwietering)... 

This latter formula, which is commonly used in the industrial practice, also holds for the case of an estimation of the mixture quality using random sampling. However, the main problem in this global analysis lays in the well-known (since the famous Danckwert s example in chemical reactors [23]) fact that two different structures can correspond to the same intensity of segregation criteria. Fig. 1 illustrates this idea, which has a very practical sense in the context of pharmaceutical blending. 

Danckwerts [1] gave a set of criteria to provide a measure of the level of mixing. The scale of segregation measures the size of the... 

The definitions of the degree of mixing presented above aim at a local characterization of the mixture homogeneity in the physical space. There also exist more indirect mixing indices. The segregation index J of Danckwerts (12) is one of the most famous ones. It applies to continuous reactors and relies upon the variance of age J = Var oip/Var a>where a is the age of a molecule,... 

Now consider a maximum segregation reactor (Danckwerts, 1958 Zwietering, 1959). Let C = pit) be the overall concentration in a batch reactor at time t. (This can be calculated for linear and for cooperative uniform kinetics.) Then the product overall concentration in a maximum segregation reactor is easily calculated as... 

The degree of segregation according to Danckwerts [91] represents the ratio of the local variance to the variance at the feed point into the mixer. If this feed consists of two streams, one with the concentration of ci = 0 and the other with a concentration of C2 = 1, the degree of segregation is as follows [see expression (3.8)] ... 

Danckwerts expresses the goodness of mixing by two statistically defined quantities, the scale and the intensity of segregation. He states that his treatment is suitable chiefly for mixtures where the smallest particles capable of independent movement are very small compared to the size of the portions which will normally be taken for use or analysis. For his analysis, he assumes that the mixture is uniform in texture that is, it cannot be divided into two parts of equal size in which the mean concentration or the scale or intensity of segregation differ significantly. He further states This is the most important limitation on the practical value of the definitions and tests which will be proposed. He emphasizes the fact that large scale segregation, caused for example by... 

Danckwerts mentions two measures of scale of segregation, (1) the linear scale, S, defined as the area under the correlogram ... 

A familiar experimental technique used in solids mixing is method 4, which involves analysis of a number of samples of size v. Danckwerts Computes the volume scale of segregation F, from this analysis as follows ... 

In addition to defining maximum mixedness discussed above, Zwietering also generalized a measure of micromixing proposed by Danckwerts and defined the degree of segregation, J. as... 

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