Axial segregation

Figure 9 (A) Relative standard deviation measured for axially segregated blends of different cohesion in a 1-quart V-blender. As cohesion increases, blending becomes slower. (B) Relative standard deviation measured for axially segregated blends of different cohesion in a 28-quart V-blender. In a large vessel, the effects of cohesion become unimportant.

However, for axially segregated (left/right) loading, the scale-up factors depended on cohesion, indicating that scale-up is a mixture-dependent problem. As shown in Figure 9A, the most cohesive system mixed much more slowly in the smaller (IQ) blender. However, all three systems mixed at nearly the same rate in the larger (28Q) vessel (Fig. 9B). 

A continuous bulk polymerization process with three reaction zones in series has been developed. The degree of polymerization increases from the first reactor to the third reactor. Examples of suitable reactors include continuous stirred tank reactors, stirred tower reactors, axially segregated horizontal reactors, and pipe reactors with static mixers. The continuous stirred tank reactor type is advantageous, because it allows for precise independent control of the residence time in a given reactor by adjusting the level in a given reactor. Thus, the residence time of the polymer mixtures can be independently adjusted and optimized in each of the reactors in series (8). 

Equation 21, the most often used relation for fitting axial segregation data from experiment, is amazingly successful for this purpose. For a finite-length ampoule, equation 21 is rewritten in terms of the fraction (/) of the sample solidified to give the normal freezing expression for the composition of the crystal (cs = kcm) grown from a melt with initial composition c0 ... 

Figure 12. Axial segregation data for the growth of gallium-doped germanium in a vertical Bridgman furnace. The figure is taken from Wang (6).

Analysis of solute transport in the presence of a magnetic field has received considerable attention. Hurle and Series (85) and Cartwright and Hurle (180) used the self-similar form of the velocity field near a rotating crystal as a framework for examining the role of an axial magnetic field in modifying axial segregation in the crystal. 

Fig. 11 Axial segregation in top views of double-cone blender from (A) experiment and (B) particle-d5mamic simulation using large (light) and small (dark) spherical grains. Similar patterns are seen in other tumbler designs, for example in the V-blender in (C) experiment and (D) simulation.

Trajectory segregation has been identified (Bridgwater et al., 1985) as the main cause of axial segregation or "banding" whereby particles of different sizes are selectively collected into bands occurring over the kiln length. This axial segregation is not considered in the present work and therefore not critically reviewed rather, attention... 

K.M. Hill and J. Kakalios. Reversible axial segregation of binary mixtures of granular materials. Physical Review E, 49 R3610-R3613, May 1994. 

K.M. Hill, A. Caprihan, and J. Kakalios. Axial segregation of granular media rotated in a drum mixer Pattern evolution. Physical Review E, 56 4386-4393, October 1997. 

Figure 10.17 Pictures of experiments of axially rotated containers with mixtures of different-sized particles illustrating relatively simple systems where effects of gravity and shear-rate gradients combined may give rise to complicated segregation patterns, (a) Axially segregation of different-sized particles in a cylindrical partially filled drum. (From Hill, K.M. et al., Phys. Rev. E, 56, 4386, 1997.) (b) Segregation of different-sized particles in a thin rotated box of a solid fraction of 0.65. (From Rietz and Stannarius, Phys. Rev. Lett. 100, 078002, 2008). (c) Pattern from experiments in (b) with velocities superposed, (d) Analogous results from those shown in (b and c), obtained for a fill level of 0.58 (less than the critical amount required for the complex circulation and segregation patterns of (b and c)).

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