Shear breakup

Suddenly exposed to a high-velocity gas stream, a droplet is deformed into a saucer shape with a convex surface to the gas flow. The edges of the saucer shape are drawn out into thin sheets and then fine filaments are sheared from the outer part of the sheets, which subsequently disintegrate into smaller droplets and are swept rapidly downstream by the high-velocity gas. Unstable growth of short wavelength surface waves appears to be involved in the breakup process. 21° This is known as shear breakup (Fig. 3.10)J246f... 

Table 3.3 Values of Weber Number for Transitions from No Deformation Regime up to Shear Breakup Regime at 0hd <0.1...

The conditions for bag and shear breakup are taken from experiments to be We > 6 and lUe/VReG>0.5, respectively, with the Weber and Reynolds numbers based on the drop radius. The rate of change of the radius of the parent drop. To, is given by an exponential law so that the parent drop approaches the stripping drop size asymptotically ... 

The DDB model is applicable to the shear breakup regime, assumed to start at... 

Figure 29.6 shows an example of one of the 2D droplet deformation studies carried out specifically for the purpose of modeling the LnCT by Sarchami et al. [9]. The flow conditions for this case are more extreme than can be handled by the theoretical methods for droplet deformation. As the figure shows, not only can these types of results be used to obtain information about jet deformation and trajectory, but they also provide an estimate for the size of the droplets and ligaments that form due to shear breakup at the tips of the elongated cross section. They also show the pattern of the flow field around the droplet. Of particular interest are the double vortices that form behind the droplet and help stretching it out and into a thin shape. The formation of these vortices can play an important role in the secondary atomization processes of the droplets formed in the lee-side of the jet (2D drop). 

F. 29.10 (a) Formation of drops from ligaments formed on the downstream side of the jet in the shear breakup regime (b) schematic top view of the cross section of a nonturbulent Jet at which a droplet (or ligament) is being formed similar to panel (a) (a From Herrmann [12]. Reprinted with permission. Copyright (2010) ASME)... 

Colloidal dispersions often display non-Newtonian behaviour, where the proportionality in equation (02.6.2) does not hold. This is particularly important for concentrated dispersions, which tend to be used in practice. Equation (02.6.2) can be used to define an apparent viscosity, happ, at a given shear rate. If q pp decreases witli increasing shear rate, tire dispersion is called shear tliinning (pseudoplastic) if it increases, tliis is known as shear tliickening (dilatant). The latter behaviour is typical of concentrated suspensions. If a finite shear stress has to be applied before tire suspension begins to flow, tliis is known as tire yield stress. The apparent viscosity may also change as a function of time, upon application of a fixed shear rate, related to tire fonnation or breakup of particle networks. Thixotropic dispersions show a decrease in q, pp with time, whereas an increase witli time is called rheopexy. 

Atomization. A gas or Hquid may be dispersed into another Hquid by the action of shearing or turbulent impact forces that are present in the flow field. The steady-state drop si2e represents a balance between the fluid forces tending to dismpt the drop and the forces of interfacial tension tending to oppose distortion and breakup. When the flow field is laminar the abiHty to disperse is strongly affected by the ratio of viscosities of the two phases. Dispersion, in the sense of droplet formation, does not occur when the viscosity of the dispersed phase significantly exceeds that of the dispersing medium (13). 

When an impeller is rotated in an agitated tank containing two immiscible Hquids, two processes take place. One consists of breakup of dispersed drops due to shearing near the impeller, and the other is coalescence of drops as they move to low shear zones. The drop size distribution (DSD) is decided when the two competing processes are in balance. During the transition, the DSD curve shifts to the left with time, as shown in Figure 18. Time required to reach the equiHbrium DSD depends on system properties and can sometimes be longer than the process time. 

Pipe Lines The principal interest here will be for flow in which one hquid is dispersed in another as they flow cocurrently through a pipe (stratified flow produces too little interfacial area for use in hquid extraction or chemical reaction between liquids). Drop size of dispersed phase, if initially very fine at high concentrations, increases as the distance downstream increases, owing to coalescence [see Holland, loc. cit. Ward and Knudsen, Am. In.st. Chem. Eng. J., 13, 356 (1967)] or if initially large, decreases by breakup in regions of high shear [Sleicher, ibid., 8, 471 (1962) Chem. Eng. ScL, 20, 57 (1965)]. The maximum drop size is given by (Sleicher, loc. cit.)... 

Some mycehal fermentations exhibit early sporulation, breakup of mycehum, and low yields if the shear is excessive. A tip speed or 250 to 500 cm/s (8 to 16 ft/s) is considered permissible. Mixing time has been proposed as a scale-up consideration, but httle can be done to improve it in a large fermenter because gigantic motors would be required to get rapid mixing. Culturing cells from plants or animals is beset by mixing problems because these cell are easily damaged by shear. 

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]. 

Figure 10 tt - 8 plot compeirison of effect of viscosity ratio 8 on reduced breakup time tt at critical Wc.ch limit for rotational and irrotational shear [18]. 

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... 

Breakup can occur if the shear stress is large enough to deform the particle, that is, when r > 2a j A. The surface area increases during breakup and sufficient energy must also be provided to compensate for the increase in surface energy. In turbulent flows, the available shear stress in the turbulent eddies of size A, can be estimated from [20]... 

Breakup will occur due to high turbulence and high shear rate. This will occur in the impeller region and close to the walls. In a stirred tank, almost all breakup of the bubbles occurs in the impeller region. According to Eq. (15.3), the energy required to break up a 5-mm bubble is on the order of 1W m 3, while 35 W m-3 is required to break up a 1-mm air bubble in water. A high rate of bubble breakup... 

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. 

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.

---