Measures of Mixing

Two calculations are often used to evaluate the mixing in polymer processes. The first is the generation of surface area as simulated in two dimensions by the stretching of a line. The second is the standard deviation of the concentration of the minor component in a residence-time evaluation of the mixing process. This section will present both calculations. 

Stretching of a line of polymer is a commonly used measure of mixing that represents the generation of surface area [22, 23]. This increase in interfacial area between two materials is depicted in Fig. 8.2. 

A well-mixed system would have a standard deviation that would approach zero. If the mixture is poorly mixed, the standard deviation will be relatively high. 

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Bell, W. H., and B. W. LeTourneau, 1960, Experimental Measurements of Mixing in Parallel Flow Rod Bundles, WAPD-TH-381, Bettis Atomic Power Lab., Pittsburgh, PA. (App.)... 

Atlanta, Georgia measurement of mixing quality in chlorine dioxide pulp bleaching ... 

The concept of ion-dipole interaction between lecithin and cholesterol has been suggested by many workers for the packing of these lipids in myelin or in the cell membrane (18, 19, 52). This concept is not supported by the surface potential measurements of mixed monolayers of lecithin and cholesterol. In contrast to dicetyl phosphate-cholesterol... 

The uniformity of a multiphase mixture can be measured by sampling of several regions in the agitated mixture. The time to bring composition or some property within a specified range (say within 95 or 99% of uniformity) or spread in values—which is the blend time—may be taken as a measure of mixing performance. Various kinds of tracer techniques may be employed, for example ... 

The technique recently applied by Cutter and Oatts (14) and Krahforst and Cutter (IS) to preliminary measurements of mixed layer sulfide was developed... 

M 9] [P 8] Simulations predict the extent to which and by which pattern the interfaces are stretched, which is a qualitative measure of mixing efficiency (see Figure 1.24) [96], The evolution of the interface is given as a function of the dimensionless time. An initial bi-layered system forms a vortex-type structure with increasing spiral winding upon time. 

Entropy is a measure of mixed-up-ness of a system (J. W. Gibbs). 

Information concerning the stereoselectivity with ligands of type D is also very limited. The stability measurements of mixed ligand complexes of N-(2-pyridyl)-L-aspartic acid and different amino acids with Cu2+ and Ni2+ show quite a high stereo-... 

Alemanskin et al. (79) extended the use of the entropic measure of mixing to both dispersive and distributive mixing using essentially modified Shannon entropy for systems with multiple species. These authors have also employed entropy to asses color homogeneity in extruded samples by means of computer image analysis and using standard direct red-blue-red (RGB) correlations (80,81). 

This increase in stability, however, is accomplished at the sacrifice of mix flexibility. The data in Table IV indicate that the flexural strain at break of mixes No. 3 and 4 is reduced significantly below that of mixes No. 1 and 2 when the sulfur concentration in the binder is raised to 40 and 50 wt %, without increasing the total binder content. Flexibility is a measure of mix susceptibility to brittle fracture and is an important mix design consideration in rigid materials to prevent premature pavement cracking. 

Fig. 14 Illustration of the importance of rational data interpretation. The state (B) intuitively looks well mixed, but has the same number of black and white boxes as states (A) and (C). Evidently a larger box size is required to make meaningful mixing measurements. States (B) and (C) have very different structures, but produce similar measures of mixing using common statistics. For this reason, many customized mixing measures have evolved in the literature.

Traditionally reactor engineers analyze the mixing of fluids in terms of the degree of segregation (Levenspiel, 1972), a measure of mixing on the molecular scale. 

The Da is extremely useful for initial evaluation of reaction conditions under which mixing effects must be considered. The reaction rate constant of the undesired reaction, A r2, can vary over several orders of magnitude. When experimental data are not available but the class of reaction is known, the magnitude of kR2 can be estimated within two orders of magnitude or less. The mixing rate in vessels should not vary by more than two orders of magnitude. With these bracketed values, upper and lower limits on Da can be readily estimated and used as a first measure of mixing sensitivity as follows ... 

Unlike most other salts, measurement of mixing enthalpies of molten alkali metal carbonates, due to their corrosive nature, cannot be performed in fused silica containers and be mixed by the usual break-off technique. Andersen and Kleppa (1976) showed that the Au20Pd alloy was corroded only negligibly by alkali metal carbonate melts kept under a relatively high CO2 pressure. The experimental arrangement included plunger as well as a dipper crucible that could be manipulated from the outer side of the furnace. The mass loss of the most volatile carbonate, Rb2C03, was about 0.3%. However, in spite of the relatively small vaporization losses, the attack of vapors on the fused silica liner was considerable and the lower part of the device had to be discarded after 10-15 experiments. 

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