Thickness, striation

Macromixing The phenomenon whereby residence times of clumps are distributed about a mean value. Mixing on a scale greater than the minimum eddy size or minimum striation thickness, by laminar or turbulent motion. 

Striation thickness Average distance between adjacent interfaces of materials to be mixed by a laminar mechanism. 

Figure 7.27. Twisted-blade type of static mixer operating in the laminar flow regime (a) Distributive mixing mechanism showing, in principle, the reduction in striation thickness produced (f>) Radial mixing contribution...

If the length scales associated with changes in velocity are normalized by Vv (characteristic length scale for Stokes flow), length scales associated with changes in curvature are normalized by Ss (typical striation thickness) and velocities normalized by V (a characteristic velocity), then the normal stress condition becomes,... 

Despite the wide use of the striation thickness concept in the early commercial literature, the CoV is now the most widely used mixing index. The following correlations are valid for viscosity ratios 0.01 < nBlnA < 100, feeding into the center of the pipe and with CoV measured 2dp downstream for Sulzer mixers, 3dp downstream for Kenics mixer. 

Predicting the Striation Thickness in a Couette Flow System — Shear Thinning Model... 

Figure 6.48 Striation thickness reduction as a function of number of revolutions in a Couette device.

Figure 6.48 presents the reduction of the striation thickness as a function of number of revolutions, as well as ratio of inner to outer cylinder radius, k for a Newtonian fluid. If we were to plot the striation thickness for a shear thinning fluid, say a power law index n = 0.5, the naked eye would not be able to distinguish between the Newtonian and the shear thinning results. 

The average striation thickness r, defined in as total volume divided by one-half of the total interfacial area, can be written as... 

The foregoing clearly indicates that striation thickness is inversely proportional to total strain. We also note that the initial striation thickness is proportional to the size of the cube and inversely proportional to the volume fraction of the minor component. Hence, for any required final striation thickness, the larger the particles and the smaller the volume fraction of the minor component the more total strain is required. Therefore it is more difficult to mix a small amount of minor components into a major, than to make a 50-50 mixture, and the larger the individual particles of the minor, the more difficult it is to mix. By using Eq. E7.1-22, we can estimate the strain needed to reduce the striation thickness to a level where molecular diffusion or Brownian motion will randomize the mixture for a given strain rate and within the time (residence time) allotted for mixing. 

A good rule of thumb for an adequate mixing in processing equipment is a total strain of the order 10,000-25,000 shear units. This implies a four orders of magnitude reduction in striation thickness. 

The striation thickness is inversely proportional to total strain, and therefore the ratio of the striation thickness at the outer and inner radii is... 

Figure E7.10b shows the SDF and compares it to that of circular tube flow of a Newtonian fluid. The SDF is broad with about 75% of the flow rate experiencing a strain below the mean strain. A better insight into the meaning of the SDF is obtained by following simultaneously the reduction of the striation thickness and the flow rates contributed by the various locations between the plates (Fig. E7.10c). The distance between the plates is divided into 10 layers. We assume for the schematic representation of the SDF that the strain is uniform within each layer. Let us consider in each alternate layer two cubical minor particles separated by a certain distance, such that the initial striation thickness is Tq. By following the deformation of the particles with time, we note that although the shear rate is uniform, since the residence time is different, the total strain experienced by the particle is minimal at the moving plate and increases as we approach the stationary plate. But the quality of the product of such a mixer will not be completely determined by the range of strains or striations across the flow field the flow rate of the various layers also plays a role, as Fig. E7.10c indicates. A sample collected at the exit will consist, for example, of 17% of a poorly mixed layer B and only 1%...

Fig. E7.10c Schematic representation of the striation thickness at various locations in a parallel plate mixer with drag flow. The striation thickness at the entrance to the mixer is ro, somewhere at the middle r, and at the exit it is r2. Note that r2 is large for particles close to the moving upper plate (because of the short residence time) and small for particles close to the stationary lower plate. The fraction of flow rate at the exit of layers at different heights is shown at the right.

Another relatively simple measure for characterizing texture that is suggested in the polymer processing literature is the striation thickness, which is defined as the total volume divided by one-half the total interfacial surface (10)... 

Figure 7.43 shows the concentration distribution along 20 elements with alternately left and right twisting plates at 140° reducing the striation thickness to below... 

If the striation thickness, r, becomes smaller than (r)ent, which satisfies the relation below... 

First and foremost, the laminar mixing flow created in the reactive processing equipment, must reduce the striation thickness to a level where the diffusion characteristic time, tD = r2/ )AB, is small compared to the reaction characteristic time. Since the molecular diffusivities of low molecular weight components in polymeric melts (see Section 8.3) are very small and of the order of 10 6 cm2/s, the striation thickness must be reduced to the micron level in order to get a characteristic time t of the order of 1 s. Shear flow can accomplish this in reasonable mixing times because the striation thickness is inversely proportional to the total shear (see Section 7.3)... 

Comparing the preceding results with those of Fig. Ell.Id, where the striation thickness is constant, demonstrates the dramatic decrease of the reaction time, with a modest y = 1 s x shear flow. 

B. Jeong and C. G. Gogos, Reactive Extrusion of Initially Segregated Miscible Blends with a Time Reducing Striation Thickness, Submitted Adv. Polym. Technol. (2005). 

Effect of Compositional Nonuniformities on the Unifying Ability of Characteristic Time Ratios to Analyze the Dynamic State of Reactions Figure 11.10, plotting the dimensionless initial reactant concentration as a function of the Damkohler number, Da = ties/tr for both batch and continuous reactors. This analysis assumes a well-mixed reacting system, (a) What will the effects of poor mixing be and how will they influence this analysis (b) What is the maximum allowable striation thickness between the reacting species for the system to be considered well mixed ... 

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