Breakup liquid filaments

Next we examine the breakup mechanism of immiscible droplets in a continuous phase and that of liquid filaments (30). 

This formula is crude, and it does not account for differences in shear rates between the droplet and the medium (which are large when the viscosity ratio differs greatly from unity). Nevertheless, because of the shear-rate-dependence of, Eq. (9-22) can predict a.minimum in droplet size as a function of shear rate that is observed in some cases (Sundararaj and Macosko 1995 Plochocki et al. 1990 Favis and Chalifoux 1987). Viscoelastic forces have indeed been shown to suppress the breakup of thin liquid filaments that would otherwise rapidly occur via Rayleigh s instability (Goldin et al. 1969 Hoyt and Taylor 1977 Bousfield et al. 1986). Elongated filaments, for example, are observed in polymer blends (Sondergaard... 

In practice, the steady shear and oscillatory tests are commonly conducted via rotational rheometers, and the extensional test is widely performed in liquid filament rheometers or capillary breakup extensional rheometers (CaBER). 

Figure 6.5 Elmendorp s [52] comparison of breakup of Newtonian liquid filaments with Tomotika s theory.

Mixing of Immiscible Liquids, and Filament and Droplet Breakup... 

Although the dominant mixing mechanism of an immiscible liquid polymeric system appears to be stretching the dispersed phase into filament and then form droplets by filament breakup, individual small droplet may also break up at Ca 3> Ca. A detailed review of this mechanism is given by Janssen (34). The deformation of a spherical liquid droplet in a homogeneous flow held of another liquid was studied in the classic work of G. I. Taylor (35), who showed that for simple shear flow, a case in which interfacial tension dominates, the drop would deform into a spheroid with its major axis at an angle of 45° to the how, whereas for the viscosity-dominated case, it would deform into a spheroid with its major axis approaching the direction of how (36). Taylor expressed the deformation D as follows... 

FIGURE 5.2 Jet breakup (a) Necking in a liquid stream withi > 1.5R. (b) Disturbances of the circumference of a liquid jet of diameter D. Breakup occurs [4] when the amplitude of the disturbance is equal to D/2, which occurs first at a wavelength of 4.51 x D. (c) 1-2 pm filament forms between two drops as liquid jet nears the breakup point. Drawn from a photo by Castleman [6]. 

The first serious investigations of the breakup of drops of polymer solutions were by Chin and Han [82], who were concerned with the influence of viscoelasticity. Subsequent studies of the breakup of droplets of polymer solutions in liquid fluid matrix were by Elmendorp [52]. Some discrepancies with Tomotika s theory were found and filaments seem generally more stable. Elmendorp also considered experiments with molten polymer filaments in a polymer matrix. Specifically, he looked at the systems (polyethylene)/(polystyrene), (polyethylene)/(polypropylene), and (polyethylene)/(polyamide-6). The filaments exhibited breakup characteristics in agreement with Tomotika s theory (Figure 6.6). 

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