End-pinching

Immediately above the pinch, the number of rich streams is equal to the number of the MSAs, thus the feasibility criterion given by Eq. (5.8a) is satisfied. The second feasibility criterion (Eq. 5.12a) can be checked through Fig. 5.7. By comparing the values of with G, for each potential pinch match, one can readily deduce that it is feasible to match Si with either R or R2 immediately above the pinch. Nonetheless, while it is possible to match S2 with R2, it is infeasible to pair S2 with R] immediately above the pinch. Therefore, one can match Si with Ri and S2 with R2 as rich-end pinch exchangers. 

Breakup by end-pinching occurs when a drop is deformed at Ca close to Cacrit, and the flow is stopped abruptly. 

Breakup by end-pinching is most difficult for very viscous or inviscid drops. 

FIGURE 6-22 Induced fit in hexokinase. (a) Hexokinase has a U-shaped structure (PDB ID 2YHX). (b) The ends pinch toward each other in a conformational change induced by binding of o-glucose (red) (derived from PDB ID 1HKG and PDB ID 1GLK). 

Figure 2-17. A series of photographs of the time-dependent breakup of a drop hy the capillary-driven flow mechanism that is known as end-pinching. The drop is initially stretched in a flow, and then the flow is stopped, allowing the drop shape to evolve toward breakup. The viscosity of the drop relative to the suspending fluid is 1.2.

End-to-End Length of String vs. Time During Multiple End-Pinching Sequence... 

Figure 4, Time dependence of contour length of an end-pinching string in a 10%PDMS/PIB emulsion.

Twin-screw extruder In the melting section of CORI extruders, virtually all the degradation mechanisms that can essentially be distinguished, such as quasi-steady drop breakup, folding, end pinching, and decomposition through capillary instabilities, take place in parallel Polente et al. 2001... 

The affine deformation of the drops causes the drops to extend into long thin threads, which is referred to as fibrillation. This process continues until the local radii become so small that the Weber (Capillary) number starts to approach the critical Weber number. At this point the threads become unstable and disintegrate as a result of interfacial tension-driven processes the interfaces are now active. The most important mechanisms are the growth of Rayleigh disturbances in the midpart of the thread, end-pinching, retraction, and necking in the case of relatively short dumbbell-shaped threads. 

FIGURE 6.23 Evolution of end-pinching and capillary waves during the relaxation and breakup of an initially highly extended droplet suspended in a quiescent fluid. The time scale is r =... 

Figure 6.22a-e show breakup by shedding off small droplets from the bulbous ends ( end-pinching mechanism Stone and Leal, 1989) for 0.05

combined action of instabilities and end-pinching for /i = 1 and L/R = 14. Apparently, the time scale of the end-pinching mechanism is less than the time scale of the instability mechanism in cases where end-pinching prevails. 

Figure 6.23 can be used to compare the dimensionless times for end-pinching and instability growth. It is seen from this figure that the dimensionless time for end-pinching is about 64, whereas the dimensionless time for instability growth is 160 as calculated in Example 6.12. Figure 6.23 shows also that the dimensionless time for complete breakup is about 240. 

So, the total length of the thread will be 160 o.m and its radius 1.25 o.m. This thread will be subjected to end-pinching and capillary instability. The burst time due to the capillary instability is calculated as in Example 6.12. It is equal to 4 s, while the mean residence time in the extruder is 138 s. Thus, the final morphology will include finer droplets of the dispersed phase. ... 

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