Drop breakup viscosity ratio

Some authors report the next guide principles that may be applied for blend morphology after processing, (i) Drops with viscosity ratios higher than 3.5 cannot be dispersed in shear but can be in extension flow instead, (ii) The larger the interfacial tension coefficient, the less the droplets will deform, (iii) The time necessary to break up a droplet (Tj,) and the critical capillary number (Ca ) are two important parameters describing the breakup process, (iv) The effect of coalescence must be considered even for relatively low concentrations of the dispersed phase. 

Taylor [64] found that in simple shear flow, a dispersed drop with viscosity ratio p = 1 breaks up when the Ca > 0.5. Breakup seems to occur when the shear stress and the interfacial stress are of the same order of magnitude. The critical Capillary number depends on the type of flow and on the viscosity ratio. In the mixing process two regimes can typically be distinguished ... 

The deformation and breakup of Boger-fluid drops in Newtonian liquids under simple shear flow were investigated by direct visualization using a specially designed Couette apparatus which enables visuahzation from two different directions (i.e. to get a 3-D image). Four types of breakup modes were observed. Boger-fluid drops ean break up in simple shear flows along the flow axis or the vorticity axis. The breakup mode was foimd to depend on drop size, viscosity ratio, interfacial tension, matrix viscosity and drop phase viscoelasticity. 

Illustration Satellite formation in capillary breakup. The distribution of drops produced upon disintegration of a thread at rest is a unique function of the viscosity ratio. Tjahjadi et al. (1992) showed through inspection of experiments and numerical simulations that up to 19 satellite drops between the two larger mother drops could be formed. The number of satellite drops decreased as the viscosity ratio was increased. In low-viscosity systems p < 0(0.1)] the breakup mechanism is self-repeating Every pinch-off results in the formation of a rounded surface and a conical one the conical surface then becomes bulbous and a neck forms near the end, which again pinches off and the process repeats (Fig. 21). There is excellent agreement between numerical simulations and the experimental results (Fig. 21). 

Upon breakup, the filament breaks into a set of primary or mother drops whose sizes are, to a first approximation, proportional to R. The size of drops produced when the filament breaks can then be obtained from the distribution of R. Each mother drop produced upon breakup carries a distribution of satellites of diminishing size for example, each mother drop of radius r has associated with it one large satellite of radius r, two smaller satellites of radius i 2 four satellites of radius r(3), and so on. For breakup at rest, the distribution of smaller drops is a unique function of the viscosity ratio. 

Fig. 22. Radius of drops produced by capillary breakup (solid lines) and binary breakup (dotted lines) in a hyperbolic extensional flow for different viscosity ratios (p) and scaled shear rate (p,cylo) (Janssen and Meijer, 1993). The initial amplitude of the surface disturbances is ao = 10 9 m. Note that significantly smaller drops are produced by capillary breakup for high viscosity ratios.

Fig. 25. Drop size distributions f(V,p)] based on drop volume (V) obtained by repeated stretching and breakup in a journal bearing flow for different viscosity ratios (p) (left). The curves for the different distributions overlap when the distribution is rescaled (right) (Muzzio, Tjahjadi, and Ottino, 1991).

Figure 14.2 Influence of viscosity ratio and continuous phase viscosity (/i) on drop breakup [15]. Reprinted with permission from H. J. Karam and J. C. Bellinger, Ind. Eng. Chem. Fundam., 7, 575 (1968). Copyright 1968 American Chemical Society...

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.

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. 

Also if t]c breakup is difficult. At t]D/t]c = 10 4, which is about the magnitude in most foams, Wecr would be as large as 30. At such a small viscosity ratio, the bubble or drop is deformed into a long thread before breaking. However, for some protein surfactants, the surface layer of the drop can be stagnant (Section 10.8.3) and then the drop can presumably break at a smaller Weber number. 

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] ... 

The mechanisms governing deformation and breakup of drops in Newtonian liquid systems are well understood. The viscosity ratio, X, critical capillary number, and the reduced time, t, are the controlling parameters. Within the entire range of X, it was found that elongational flow is more efficient than shear flow for breaking the drops. 

The microrheology makes it possible to expect that (i) The drop size is influenced by the following variables viscosity and elasticity ratios, dynamic interfacial tension coefficient, critical capillarity number, composition, flow field type, and flow field intensity (ii) In Newtonian liquid systems subjected to a simple shear field, the drop breaks the easiest when the viscosity ratio falls within the range 0.3 < A- < 1.5, while drops having A- > 3.8 can not be broken in shear (iii) The droplet breakup is easier in elongational flow fields than in shear flow fields the relative efficiency of the elongational field dramatically increases for large values of A, > 1 (iv) Drop deformation and breakup in viscoelastic systems seems to be more difficult than that observed for Newtonian systems (v) When the concentration of the minor phase exceeds a critical value, ( ) >( ) = 0.005, the effect of coalescence must be taken into account (vi) Even when the theoretical predictions of droplet deformation and breakup... 

The theoretical predictions of drop deformation and breakup are limited to infinitely diluted, monodispersed Newtonian systems. However, it is possible to obtain valid relationships between processing parameters and morphology. Thus it was found that in the system PS/HDPE the viscosity ratio, blend composition, screw configuration, temperature, and screw speed significantly influence the blend morphology [Bordereau et al., 1992]. For more detail on the topic see Chapter 9, Compounding Polymer Blends, in this Handbook. 

Unlike in NEMD models, the microstructures emerging due to competition between the breakup and coalescence processes can be studied by using DPD modeling. For example, in Figure 26.23, the four principal mechanisms, the same as those responsible for droplets breakup [ 118,119], can be observed in DPD simulation of the R-T instability. As shown in [116,119], moderately extended drops for capillary number close to a critical value, which is a function of dynamic viscosity ratio... 

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 microrheology discussed in Section 2.1.2.3 describes the breakup of isolated drops in a Newtonian system. The mechanisms leading to deformation and breakup take into account the three principal variables the viscosity ratio (X), critical capillary number (Kcni), and the reduced time (f ), defined in Eq. (2.19). For application of microrheology to polymer blends the theories developed for Newtonian emulsions need to be extended to viscoelastic systems in the fidl range of composition, that is, they must take into account coalescence. Since the microrheology evolution up to about the year 2000 has been summarized by Utradri and Kamal [3] the following text win focus on more recent developments. 

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. 

Dimensionless time for drop breakup versus viscosity ratio... 

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