Droplet breakup modes

Indirectly related to the cell models of this section is the work of Davis and Brenner (1981) on the rheological and shear stability properties of three-phase systems, which consist of an emulsion formed from two immiscible liquid phases (one, a discrete phase wholly dispersed in the other continuous phase) together with a third, solid, particulate phase dispersed within the interior of the discontinuous liquid phase. An elementary analysis of droplet breakup modes that arise during the shear of such three-phase systems reveals that the destabilizing presence of the solid particles may allow the technological production of smaller size emulsion droplets than could otherwise be produced (at the same shear rate). 

From a liquid film such as a water film, the diameter of a drop formed under the action of gravity is calculated to be 9 mm with the above equation. Similarly to the liquid dripping mode, the liquid film breakup mode governed by the dripping mechanism is also typified by large droplets and low liquid flow rates. 

The mechanical breakup mode occurs around the rims of the sheet where the air-liquid relative velocity is low, forming relatively large droplets. At low relative velocities, aerodynamic forces are much smaller than surface tension and inertia forces. Thus, the breakup of the liquid rims is purely mechanical and follows the Rayleigh mechanism for liquid column/jet breakup. For the same air pressure, the droplets detached from the rims become smaller as the liquid flow rate is increased. 

Basic Breakup Modes. Starting from Lenard s investigation of large free-falling drops in still air,12671 drop/droplet breakup has been a subject of extensive theoretical and experimental studies[268] 12851 for a century. Various experimental methods have been developed and used to study droplet breakup, including free fall in towers and stairwells, suspension in vertical wind tunnels keeping droplets stationary, and in shock tubes with supersonic velocities, etc. These theoretical and experimental studies revealed that droplet breakup under the action of aerodynamic forces may occur in various modes, depending on the flow pattern around the droplet, and the physical properties of the gas and liquid involved, i.e., density, viscosity, and interfacial tension. 

According to Hinze,12701 droplet breakup may occur in three basic modes ... 

The first mode may occur when a droplet is subjected to aerodynamic pressures or viscous stresses in a parallel or rotating flow. A droplet may experience the second type of breakup when exposed to a plane hyperbolic or Couette flow. The third type of breakup may occur when a droplet is in irregular flow patterns. In addition, the actual breakup modes also depend on whether a droplet is subjected to steady acceleration, or suddenly exposed to a high-velocity gas stream.[2701[2751... 

Figure 3.10. Some modes of droplet breakup. Left bag breakup Right breakup.

Sleiched278 has indicated that this expression is not valid for pipe flows. In pipe flows, droplet breakup is governed by surface tension forces, velocity fluctuations, pressure fluctuations, and steep velocity gradients. Sevik and Park 279 modified the hypothesis of Kolmogorov, 280 and Hinze, 270 and suggested that resonance may cause droplet breakup in turbulent flows if the characteristic turbulence frequency equals to the lowest or natural frequency mode of an... 

Generally, the occurrence of a specific mode is determined by droplet impact properties (size, velocity, temperature), surface properties (temperature, roughness, wetting), and their thermophysical properties (thermal conductivity, thermal capacity, density, surface tension, droplet viscosity). It appeared that the surface temperature and the impact Weber number are the most critical factors governing both the droplet breakup behavior and ensuing heat transfer. I335 412 415]... 

Al-Roub et all421 identified three basic modes of liquid breakup during droplet impingement onto a liquid film (1) rim breakup, (2) cluster breakup, and (3) column breakup. The rim breakup mode involves the breakup and ejection of one or a few small droplets at the outer edge of the film, while the cluster breakup mode involves the breakup of liquid into clusters of many small droplets at the outer edge of the film. In the column breakup mode, liquid breaks up into one or a few droplets from a column of liquid at the center of the spreading droplet as a result of the surface waves reflecting back to their source. The diameter and number of the... 

The maj or limitation of the TAB model i s that it can only keep track of one oscillation mode, while in reality there are many oscillation modes. Thus, more accurately, the Taylor analogy should be between an oscillating droplet and a sequence of spring-mass systems, one for each mode of oscillations. The TAB model keeps track only of the fundamental mode corresponding to the lowest order spherical zonal harmonic 5541 whose axi s i s aligned with the relative velocity vector between the droplet and gas. Thi s is the longest-lived and therefore the most important mode of oscillations. Nevertheless, for large Weber numbers, other modes are certainly excited and contribute to droplet breakup. Despite this... 

A number of runs were carried out with the pump stopped but liquid flowing through the wide-open recycle valve w h an upstream pressure of 500 to 600 kPa [73 to 87 psi). This resulted in little change in performance over the pumping mode. This, combined with the Ap observation, suggests that most of the droplet breakup is taking place in the separator-level control valves. 

Ganan-Calvo showed that the breakup mode is axisymmetric and that the resulting droplets are monodispersed when the We number has a value below 40, with We defined as... 

FIGURE 20.5 The quasistatic model of droplet breakup for liquid-liquid systems (a) squeezing mode and (b) dripping mode. (Reproduced with permission from Anna, S.L. et al Formation of dispersions using flow focusing in microchannels, Carnegie Mellon University, Pittsburgh, PA, 2003.)... 

Fig. 18.8 Various breakup modes of a droplet exposed to acoustic disturbance at 2 = pg/pi 0.00123 and co = co. The Weber number is based on gas, WCg (Courtesy of Elsevier)...

Similar to the droplet breakup model in the previous section, many different vibration modes may be excited on the surface by the acceleration i (f), but the one represented by A in equation is assumed to dominate in the generation of droplets. This assumption is valid at powers just sufficient to cause the generation of droplets, but as the amplitude T is further increased, other modes may become large enough to form droplets, increasing the droplet size distribution and the complexity of analysis. 

FIGURE 1.4 Representation of droplet breaking modes, (a) Simple breaknp by waist thinning (b) asymmetric breakup by waist thinning (c) tip streaming and (d) capillary breakup. (Adapted from Hu Thomas et al. Phys. Fluid., 12, no 3, 484-489, 2000.)... 

The initial deformation of a droplet into a disc shape is similar for all breakup modes. The duration of this initial phase is estimated as fdef= l-6t by Hsiang and Faeth (1995) [15]. Thereafter, the droplet will fragment depending on the breakup modes. As proposed in Pilch and Erdmann [14], the correlations of ibreakup for different intervals of Weber numbers can be formulated as... 

Polymer melts are shear thinning, and the changing viscosities of polymer melts usually adds complexity in the study of drop deformation and breakup. To simplify the research, we investigated the deformation and breakup of model viscoelastic drops (Boger-fluid) in Newtonian liquids under simple shear flow. A specially designed Couette apparatus that can be used to visualize the drop in two dimensions was used to obtain a 3-D representation of the droplet. Different breakup modes are presented and the effect of drop size on drop breakup mode is discussed. 

Consider drops of different sizes in a mixture exposed to a 2D extensional flow. The mode of breakup depends on the drop sizes. Large drops (R > Caa,tal/xcy) are stretched into long threads by the flow and undergo capillary breakup, while smaller drops (R Cacri,oV/vy) experience breakup by necking. As a limit case, we consider necking to result in binary breakup, i.e., two daughter droplets and no satellite droplets are produced on breakup. The drop size of the daughter droplets is then... 

In the idealized mode, liquid jet breakup and droplet formation are fairly regular. The liquid jet running downwards collapses, forming droplets of uniform size at uniform spacing. After breakup, the liquid jet of length 4.51 d0 converts into a spherical droplet so that ... 

---