Breakup affine deformation

Cho and Kamal (2002) derived equations for the affine deformation of the dispersed phase, using a stratified, steady, simple shear flow model. It includes the effects of viscosity ratio and volume fraction. According to the equation, for viscosity ratio > 1, the deformation of the dispersed phase increases with the increase of the dispersed phase fraction. For compatibiUzed PE/PA-6 blends at high RPM (i.e., 100, 150, and 200 RPM) in the Haake mixer, the particle size decreases with concentration of the dispersed phase up to 20 wt%. This occurs because the total deformation of the dispersed phase before breakup increases as the volume fraction increases, and coalescence is suppressed. The increase of the particle sizes between 20 and 30 wt% results from the increase of coalescence due to the high dispersed phase fractions. The data for 1 wt% blends suggest that mixing in the Haake mixer follows the transient deformation and breakup mechanism, and that shear flow is dominant in the mixer. 

If the hydrodynamic stress is sufficiently high, Ca exceeds a certain value known as the critical capillary number, CacR. Under these conditions no stable shape can persist in the flow, and the droplet deforms continually until it breaks into daughter droplets. These can undergo consequent deformations and breakups until the droplets are so small that the interfadal stress overrules the hydro-dynamic stress. At Ca < Cocr the droplets are deformed into a shape which is stable in the flow and can be also predicted by the theory of Maffetone and Minale [76]. On the other hand, at very high values of Ca (Ca CacR), a quick affine deformation of the droplets occurs and long cylindrical threads are formed which are rather stable in the flow and decay only at very high deformations or even just after the cessation of flow [77,78]. 

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