Shear drop breakup

Concerning a liquid droplet deformation and drop breakup in a two-phase model flow, in particular the Newtonian drop development in Newtonian median, results of most investigations [16,21,22] may be generalized in a plot of the Weber number W,. against the vi.scos-ity ratio 8 (Fig. 9). For a simple shear flow (rotational shear flow), a U-shaped curve with a minimum corresponding to 6 = 1 is found, and for an uniaxial exten-tional flow (irrotational shear flow), a slightly decreased curve below the U-shaped curve appears. In the following text, the U-shaped curve will be called the Taylor-limit [16]. 

Bubble and drop breakup is mainly due to shearing in turbulent eddies or in velocity gradients close to the walls. Figure 15.11 shows the breakup of a bubble, and Figure 15.12 shows the breakup of a drop in turbulent flow. The mechanism for breakup in these small surface-tension-dominated fluid particles is initially very similar. They are deformed until the aspect ratio is about 3. The turbulent fluctuations in the flow affect the particles, and at some point one end becomes... 

S. Velankar, P. Van Puyvelde, J. Mewis, P. Moldenaers 2001, (Effect of compati-bilization on the breakup of polymeric drops in shear flow), /. Rheol. 45, 1007. 

Stroeve, P., and Varanasi, P. P., An experimental study of double emulsion drop breakup in uniform shear flow. J. Coll. Int. ScL 99,360-373 (1984). 

Most correlations show that di2 is proportional to the Weber number raised to the power of -0.6, which is consistent with the theory of drop breakup by turbulent shear forces. Strictly, these correlations should be applied only where the drop size is in the inertial subrange of turbulence, i.e.,... 

In drop-breakup experiments with polymers, the shear viscosity is typically shear-rate-dependent. So in plots such as Fig. 9-11, the viscosities are taken to be those of the melts at a nominal shear rate in the mixer. In the experiments of Sundararaj and Macosko, for example, the nominal shear rate y at a given motor speed is estimated from the linear drag flow that is assumed to exist in the narrowest gap of the mixer. 

Drop breakup occurs as impeller pumping brings the drops through the high shear zones surrounding the impeller blade... 

Where W is the Weber number and a.- is the shear stress, the same on both sides of the Interface. The critical condition for drop breakup in Newtonian liquid mixtures is given by ... 

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. 

Figure 6. Schematic representation of drop breakup in shear field at two different values of the viscosity ratio X (a) 0.1 < X < 1, (b) X < 0.01.

RDC Column. The rotating disc contactor (Fig. 19) provides for redispersion by a series of discs along the shaft, combined with a series of fixed stators. Vortices are formed in each compartment, and the shear of the fluid against the rotor or stator causes the drop breakup. In many instances. 

FIGURE 11.8 The effect of the viscosity ratio, drop over continuous phase inn/tlc), on the critical Weber number for drop breakup in various types of laminar flow. The parameter a is a measure of the amount of elongation occurring in the flow for a — 0, the flow is simple shear for a — 1, it is purely (plane) hyperbolic. 

When values of the capillarity number and the reduced time are within the region of drop breakup, the mechanism of breakup depends on the viscosity ratio, X. In shear, four regions have been identified [Goldsmith and Mason, 1967] ... 

Flow-induced coalescence is accelerated by the same factors that favor drop breakup, e.g., higher shear rates, reduced dispersed-phase viscosity, etc. Most theories start with calculation of probabilities for the drops to collide, for the liquid separating them to be squeezed out, and for the new enlarged drop to survive the parallel process of drop breakup. As a result, at dynamic equilibrium, the relations between drop diameter and independent variables can be derived. 

A more recent theory for the dynamic equilibrium drop diameter also started from separate calculations of the drop breakup and coalescence during the steady state shearing. The rate of particle generation was taken to be determined by microrheology, viz. Eq 7.52, [Huneault et al, 1995] ... 

Figure 9.7. Critical capillarity number for drop breakup in shear and extensional flow.

Fig. 9.1 Schematic illustration of a drop breakup caused by Kelvin-Helmholtz (KH) or Rayleigh-Taylor (R-T) instabilities. The breakup mechanisms are ciassified with respect to the (increasing) Weber number as bag, stripping (shear) and catastrophic breakup...

For K > 2 the drops deform into stable filaments, which only upon reduction of k disintegrate by the capillarity forces into mini-droplets. The deformation and breakup processes require time - in shear flows the reduced time to break is tb > 100- When values of the capillarity number and the reduced time are within the region of drop breakup, the mechanism of breakup depends on the viscosity ratio, A, - in shear flow, when X > 3.8, the drops may deform, but they cannot break. Dispersing in extensional flow field is not subjected to this limitation. Furthermore, for this deformation mode Kcr (being proportional to drop diameter) is significantly smaller than that in shear (Grace 1982). 

The use of extensional flow field for mixing is relatively unexplored, while a growing number of reports show that mixing in extensional flow field is more efficient than in shear, especially for blends with higher viscosity ratio, A > 3.8, where the shear field is unable to cause drop breakup (Grace et al. 1971). 

The critical time for drop breakup also varies with = / cr Furthermore, when k and % are within the drop breakup regions, according to Goldsmith and Mason [70] four mechanisms of drop breakup in shear lead to different blend morphologies ... 

Flumerfelt, R.W. (1972) Drop breakup in simple shear fields of viscoelastic fltuds. Ind. Eng. Chem, Pundam., 11 (3), 312-318. 

In practice, in a mixture much larger drops can be found than predicted by the critical capillary number because Grace s observations were based on single drops. In actual systems, where many drops exist, coalescence will occur. Because material elements also undergo varying levels of shear forces in time, the mixing process in polymer systems can be considered as a complex interaction between deformation, drop breakup, coalescence, and retraction. 

The previous discussion focused on the breakup of liquid thread suspended in a quiescent Newtonian fluid. In real mixing operations quiescent conditions will usually not occur, except perhaps for short periods of time. The more important issue, therefore, is how the breakup occurs when the system is subjected to flow. Good reviews on the breakup of liquid threads are available from Acrivos [304], Rallison [305], and Stone [306]. Probably the most extensive experimental study on drop breakup was performed by Grace [286] data was obtained over an enormous range of viscosity ratios 10- to 10 Grace determined the critical Weber (Capillary) number for breakup both in simple shear and in 2-D elongation the results are represented in Fig. 7.152. 

---