Fibrils breakup

Similar to the breakup of droplets, both the critical breakup time and the critical breakup length should be exceeded in order for fibril breakup to occur. 

This model allows a more straightforward prediction of fibril breakup times during processing, for which the moment of initiation of interface disturbances can in general not be determined. 

Figure 11.17 The four snapshots show the evolution and breakup of a spiral wave pattern in 2-dimensional simulated cardiac tissue (300 x 300 cells). The chaotic regime shown in the final snapshot corresponds to fibrillation. Reprinted from [587] with permission from Lippincott, Williams and Wilkins.

The most efficient mechanism of drop breakup involves its deformation into a fiber followed by the thread disintegration under the influence of capillary forces. Fibrillation occurs in both steady state shear and uniaxial extension. In shear (= rotation + extension) the process is less efficient and limited to low-X region, e.g. X < 2. In irrotatlonal uniaxial extension (in absence of the interphase slip) the phases codeform into threadlike structures. 

Thus, tjj is an important parameter describing the breakup process for fibers subjected to lower stresses than those required for fibrillation, i.e., K < 2. In practice, one of the most serious obstacles for quantitative use of Timotika s theory is estimation of the initial distortion, a. ... 

Detailed analysis of microstructure development within the extruder showed that, in the process of microstructure formation of extmdates, the deformation, coalescence, breakup, and relaxation of the dispersed phase were all involved. The process of deformation ofLCP domains in the shear flow before the extmder die was controlled by the viscosity. The shear flow before the die could result in the deformation and fibrillation ofLCP droplets, if the viscosity ratio (0.01 or smaller) favored the fibrillation. The coalescence and further deformation of the LCP domains in the die entrance lead to the increase in volume and aspect ratio of the fibrils [20]. 

Thus, tb is an important parameter describing the breakup process for fibers subjected to lower stresses than those required for fibrillation, i.e., k < 2. The above indicates that breakup is less likely at low interfacial tension. Since the matrix viscosity appears in the left side of the equation (in the capUlary number), one may expect shorter breakup times with lower matrix viscosity, but it is noteworthy that this term also changes the Tomotika function on the right side of the equation. Figure 7.15 shows the distortion growth rate at the dominant wavelength as a function of viscosity ratio. To obtain a low value of 0(1, X), thread viscosity should be high and the matrix viscosity has to be low (Potschke and Paul 2003). 

Emulsion microrheology predicts that in a Newtonian system a drop will break when the deformabUity exceeds D > /2, that is, when the reduced capillarity number 1experimental data for viscoelastic systems indicate that the drop elasticity has a stabilizing effect thus, that Ko- and the minimum drop diameter for drop break increase with drop elasticity [284-286]. When conditions are identical for Newtonian and viscoelastic drops, the latter fibrillate easier and upon cessation of flow the filament breakup and formation of satellite drops are retarded by elasticity [287]. 

The application of chaotic flows leads to much smaller droplets than allowed by the equilibrium between the shear and interfacial forces [204-206] and than those obtained in some commercial mixers. The smaller size of droplets can be directly traced back to their precursor thinner flbrils as the droplets originate from the fibrils by capillary instability and breakup. The exponential stretching encountered in chaotic mixers subdues the growth of interfacial instabilities in both lamellas and fibrils and consequently smaller diameter fibrils are produced. In some cases, fibrils with an aspect ratio as high as 1000 are produced [204]. In addition, the chaotic mixing conditions have been shown to slow down the rate of coalescence of droplets [207]. Another study utilized the rapid intermaterial area generation in chaotic flows to promote chemical reactions in the synthesis of thermoplastic polyurethanes [140]. 

A series of articles was published by Utracki et al. [318-322] on the modeling of mixing of immiscible fluids in a twin screw extruder. The fourth paper in the series [321] incorporates several refinements of the earlier model, one of the most important refinements being the incorporation of the effect of coalescence. The model considers two breakup mechanisms, both based on the micro-rheology. One breakup mechanism is the drop fibrillation and disintegration into fine droplets when the Weber number is greater than four times the critical Weber number. The second mechanism is drop splitting that occurs when the Weber number is below four times the critical Weber number. 

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