Scale and Intensity of Segregation

The intensity of segregation refers to the difference in concentration of one component between areas of component A and B. The intensity is reduced as component A diffuses out of the circles into the area of component B or as the size of the clumps of A is reduced due to the diffusion of A. If the two components do not have any difference in color, the intensity of segregation can be pictured as the difference in the size of clumps A (Fig. 6.5). If there is a difference in color between A (black) and B (white), then the minimum intensity of segregation is achieved when the black has been 

Both reduction of scale and intensity produce uniformity, and so the quality of mixing, as far as texture is concerned, depends on both quantities. Note that the maximum reduction of the scale is achieved when the distance between interfaces approaches the length scale of the ultimate particles (or ultimately molecular scales), and the maximum reduction in intensity is obtained when the minor component is uniformly mixed throughout the major component. 

Scale and intensity have also statistical representations. The intensity can be defined mathematically as 

To define the scale of segregation we need to define first the correlation function, R (r). It is very similar to the variance in the sense that the variance measures the concentration difference of a point and the mean value, whereas the correlation function considers the concentration difference between two points r distance away. Thus, R (r) is given by 

The correlation coefficient is obtained by the normalization of the correlation function with the variance  

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FIGURE 5.3 Scale and intensity of segregation (from Brodkey, 1975). 

It was seen in an earlier chapter that the role of a mixer was to progressively reduce both the scale and intensity of segregation of the mixture ingredients. With free-flowing mixtures the scale of segregation within the mixture could be very large due to the preferential and segregating movement of individual... 

The nature and the strength of the interparticulate forces acting within the cohesive powder system will determine the ease, or dilTiculty, likely to be experienced in re-locating individual particles within a mixture and will also determine the llnal scale and intensity of segregation. 

Thus the quantities of scale and intensity of segregation are useful concepts in the understanding of high viscosity mixing. However, difficulties are encountered in the measurement of these parameters to give quantitative assessments of mixture quality. This is particularly true as one approaches a well-mixed state. 

Figure 5.3 Definition of the scale and intensity of segregation along with the scale of examination. (Reprinted from Ref. 4 with kind permission from John Wiley Sons. Inc., New York. USA.)...

The analysis of the image requires the knowledge of the correspondence between composition and color (if that is not linear, a calibration curve is required). Furthermore, if diffusion has not altered the composition at the various points, then each pixel is made dark (e.g., minor component) or light (e.g., major component) based on a threshold value. The power spectrum is now calculated from the composition data and an FFT algorithm. The correlation function is then calculated by using the inverse Fourier transform of the power spectrum and the scale and intensity of segregation are then... 

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... 

Quantitative characterization of the texture of extruded film was studied by Nadav and Tadmor [27, 28). The samples were characterized by measuring light transmission through a film sample. The results were analyzed using the concepts of scale of segregation and intensity of segregation. 

How the mechanics of this interaction develop separating processes, will then become apparent and the resulting regime of behaviour related to the scale and duration of the operation. From this evaluation, an assessment can be made as to the nature, degree and intensity of segregation that is likely to be produced. 

Commonly a minor component is to be dispersed within the bulk of the material and then mixture quality analysed at a very small scale of scrutiny. The cohesive mixture is usually of good quality when analysed at a large scale of scrutiny but at a small scale of scrutiny a high, and unacceptable, intensity of segregation can occur. To understand the nature of this problem the mixture and the structure of the mixture have to be examined on a micro as well as a macro scale. 

Dispersive mixing n. Any mixing process in which the principal action is reduction of the size of particles or interlayers. The progress of the process is judged by two criteria, intensity of segregation and scale of segregation. 

One can further distinguish between the scale and the intensity of segregation. The intensity of segregation is expressed as the maximum relative concentration difference in the vessel. The scale denotes the linear distance between the local maximum and the minimum concentrations. Any circulation flow reduces the scale of segregation by distributing the feed streams rapidly across the reactor The eddies combined with molecular diffusion reduce the intensity of segregation. 

Scale of segregation is a measure of the average separation between regimes comprising the same component and may be correlated to the average striation thickness, which is the average distance between like interfaces in a mixture [11]. On other hand, intensity of segregation is a measure of concentration [11]. 

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