Breakup of drops

In the previous section, the problem of deformation of conducting drops and the possibility of their breakage was examined. Consider now the problem of breakage of non-conducting drops. 

Start with the estimation of the minimum radius of drops that are subject to breakage. For this purpose, it is necessary to estimate the forces acting on the drop in a turbulent flow that are capable of deforming it. 

A drop placed in a field of uniform and isotropic turbulence experiences the following forces from the external liquid dynamic pressure Q = kfp u /2 (where ky is a factor of the order 0.5 - density of the external liquid u - velocity of the 

Suppose the predominant influence is exerted by the dynamic pressure [19]. Then drop deformation is caused by the difference of dynamic pressures acting at the opposite sides of the drop  

consider the drops of size J /lo, where A is the inner scale of turbulence. Then large-scale pulsations (A A. 1), which don t vary too much on distances of the order of the drop size, do not exert a noticeable influence on these drops. Hence, the deformation and breakage of such drops can be caused only by small-scale pulsations. For such pulsations, the change of pulsation velocity Ui on the distance equal to the drop size 2R is 

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Link DR, Anna SL, Weitz DA, Stone, HA (2004) Geometrically mediated breakup of drops in micro fluidic devices. Phys Rev Lett 92 054503-1-4... 

R.A. De Bruijn Deformation and Breakup of Drops in Simple Shear Flows. Ph. D. Thesis Eindhoven University of Technology (1989). 

Figure 12-12 Sketches of possible flow patterns of bubbles rising through a liquid phase in a bubble column. Stirring of the continuous phase will cause the residence time distribution to be broadened, and coalescence and breakup of drops will cause mixing between bubbles. Both of these effects cause the residence time distribution in the bubble phase to approach that of a CSTR. For falling drops in a spray tower, the situation is similar but now the drops fall instead of rising in the reactor.

Link, D.R., Anna, S.L., Weitz, D.A., and Stone, HA. (2004). Geometrically mediated breakup of drops in microfluidic devices. Phys. Rev. Lett. 92,05403-05404. 

They lower the interfacial tension of liquid interfaces, thereby facilitating bending of the interface, hence deformation and breakup of drops and bubbles. 

To make an emulsion (foam), one needs oil (a gas), water, energy, and surfactant. The energy is needed because the interfacial area between the two phases is enlarged, hence the interfacial free energy of the system increases. The surfactant provides mechanisms to prevent the coalescence of the newly formed drops or bubbles. Moreover it lowers interfacial tension, and hence Laplace pressure [Eq. (10.7)], thereby facilitating breakup of drops or bubbles into smaller ones. 

FIGURE 11.7 Two types of laminar flow, and the effect on deformation and breakup of drops at increasing velocity gradient ( ). The flow is two-dimensional, i.e., it does not vary in the z-dircction. More precisely, the flow type in (b) is plane hyperbolic flow. ... 

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 mechanisms governing deformation and breakup of drops in Newtonian liquid systems are relatively well understood. However, within the range of compounding and processing conditions the molten polymers are viscoelastic liquids. In these systems the shape of a droplet is determined not only by the dissipative (viscous) forces, but also by the pressure distribution around the droplet that originates from the elastic part of the stress tensor. Therefore, the characteristics of drop deformation and breakup in viscoelastic systems may be quite different from those in Newtonian ones. Some of the pertinent papers on the topic are listed in Table 9.3. 

Some additional data about the breakup of drops can be found in [50-53]. 

The motion of formed ensemble of drops with gas flow is accompanied by continuous change of drops distribution over sizes this results from the concurrent processes of mass-exchange between the drops and the gas, coagulation and breakup of drops under action of intensive turbulent pulsations of various scales. 

Consider in succession the mass-exchange between drops and hydrocarbon gas, coagulation and breakup of drops, and their deposition at walls of the pipe, which will allow to determine dV/dt, h, /j, and I4. 

The rate of change of n that is due to the breakup of drops is expressed in terms of the breakup frequency /(V) of drops whose volume lies in the interval (V, V + dV) and the probability P(y,w) of drop with volume (V, V dV) being formed after the breakup of a drop of volume co,co-F dm). A model of drop... 

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