Segregation scale intensity

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. 

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. 

From the theoretical viewpoint, much of the phase behaviour of blends containing block copolymers has been anticipated or accounted for. The primary approaches consist of theories based on polymer brushes (in this case block copolymer chains segregated to an interface), Flory-Huggins or random phase approximation mean field theories and the self-consistent mean field theory. The latter has an unsurpassed predictive capability but requires intensive numerical computations, and does not lead itself to intuitive relationships such as scaling laws. 

These measures of solute segregation are closely related to the spatial and temporal patterns of the flow in the melt. Most of the theories that will be discussed are appropriate for laminar convection of varying strength and spatial structure. Intense laminar convection is rarely seen in the low-Prandtl-number melts typical of semiconductor materials. Instead, nonlinear flow transitions usually lead to time-periodic and chaotic fluctuations in the velocity and temperature fields and induce melting and accelerated crystal growth on the typically short time scale (order of 1 s) of the fluctuations. 

First, the role of system design on the details of convection and solute segregation in industrial-scale crystal growth systems has not been adequately studied. This deficiency is mostly because numerical simulations of the three-dimensional, weakly turbulent convection present in these systems are at the very limit of what is computationally feasible today. New developments in computational power may lift this limitation. Also, the extensive use of applied magnetic fields to control the intensity of the convection actually makes the calculations much more feasible. 

Despite the utility of the physical methods described above, characterization of entities on the nanometer scale is still a problem. Well-mixed nanoparticles are not necessarily completely homogeneous, and one metal may preferentially segregate to the nanoparticle surface. Subtle differences in surface stoichiometries are presently extremely difficult to quantitatively evaluate with spectroscopy, even when the metal of interest has an intense surface plasmon. 

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

According to equation (1.6) the size of the material balls for a relatively intensive mixing operation of P/pV = 1 W/kg in an aqueous liquid (v = 10 m /s) is 32 pm and in a liquid with the viscosity of pure glycerine at room temperature (v = 10 m /s) is already 5.6 mm (see Table 1.1). This shows that viscous systems will always remain to a certain extent segregated, since the Kolmogorov micro-scale a can be comparatively little influenced by the mixing power 2 cc... 

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... 

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... 

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. 

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. 

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