Break-up of droplets

As an approximate rule, break-up of droplets occurs for a Weber number in excess of one, a rule of thumb that is actually valid for the range of viscosity ratios of the dispersed phase to the continuous phase of less than approximately five. Higher viscosities of the disperse phase lead to serious difficulties with emulsification because the shear energy is then dispersed in rotation of the droplets. 

The effect of coalescence and break-up of droplets on the yield of chemical reactions was studied by Villermaux (33). Micromixing effects may occur even in batch reactors if there is a drop size distribution and mass-transfer control. Although practical rules for the design and scale-up of liquid-liquid reactors are available as Oldshue showed in the case of alkylation (152), many problems remain unsolved (.5) mass transfer effects, high hold-up fractions (> 20 %), large density differences, high viscosities, influence of surfactants. 

The viscosity of the oil plays an important role in the break-up of droplets the higher the viscosity, the longer it will take to deform a drop. The deformation time is given by the ratio of oil viscosity to the external stress acting on the drop,... 

Apart from their effect on reducing y, surfactants play major roles in the deformation and break-up of droplets, and this is summarised as follows. Surfactants allow the existence of interfacial tension gradients which is cracial for the formation of stable droplets [8]. In the absence of surfactants (clean interface), the interface cannot withstand a tangential stress, and the liquid motion will be continuous (Figure 10.17a). 

The break-up of droplets in steady flow is generally approached through consideration of the hydrodynamic stability of liquid cylinders, which are assumed to be a precursor of break-up. The critical factor for the rate of break-up of a given cylinder is the rate at which instabilities grow, whereas for the ultimate drop size, it is the wavelength of the instability which dominates Figure 14.11). 

These are some of the factors upstream of the shearing device downstream one has to consider the flow conditions pertaining immediately after the stretching zone, and the relationship between pipe dimensions and flow rate and the coalescence or further break-up of droplets. 

The results are reported of a systematic study of the break up of droplets in concentrated emulsions at different viscosity ratios in simple shear flows. The system investigated consisted of silicon oil drops in an aqueons phase mixture of polyacrylic acid solution, hexylene glycol, distilled water and dobanol surfactant. The ratio between drop and matrix viscosity was varied from 0.1 to 22 and the volume fraction ranged from 0 to 70%. The results are discussed in terms of a simple mean field scaling model. 11 refs. 

Figure 3 Forces acting on dispersed fluids. (A) The balance of shearing force and interfacial force on a dripping ruptured droplet. The small arrows show the flow field around the droplet. (B) A jetting liquid in a coflowing microchannel. The interfacial force dominates the break-up of droplets under the Rayleigh-Plateau effect. Pane/fAj Tb/s figure is adapted from Wang et al (201 la) with permission of Wiley.

Figure 6.12 illustrates the various processes occurring during emulsification -break up of droplets, adsorption of surfactants and droplet collision (which may or may not lead to coalescence) [9, 10]. 

Figure 6.12 illustrates the various processes that occur during emulsification Break up of droplets, adsorption of surfactants and droplet collision (which may or may not lead to coalescence) [8]. Each of these processes occurs numerous times during emulsification and the time scale of each process is very short, typically a microsecond. This shows that the emulsification is a dynamic process and events that occur in a microsecond range could be very important. 

Break up of droplets will only occur at high s, which means that the energy dissipated at low levels is wasted. Batch processes are generally less eflBcient than continuous processes. This shows why with a stirrer in a large vessel, most of the energy applied at low intensity is dissipated as heat. In a homogenizer, p is simply equal to the homogenizer pressure. 

The reaction i4 —> F is carried out in a liquid/liquid dispersion in a CSTR. The reaction takes place in the dispersed phase. It is known that the reaction order is 0.5, and that the reaction is rate-determining. The degree of conversion is 0.8. It is suspected that the dispersed phase does not coalesce, so that the reactor is completely segregated. By increasing the impeller speed coalescence and break-up of droplets are promoted. How may this affect the conversion From figure 7.3 it follows that on complete mixing of the dispersed phase the conversion may go up to about 0.89. At a constant conversion of 0.8, the mean residence time could be reduced, and the reactor capacity increased, by a factor of 1.8. 

This also applies to the break-up of droplets. According to Taylor, the breaking up of a single drop requires the viscous forces acting on the droplet to exceed the interfacial forces for a sufficient amount of time. This also indicates that a limit may exist in single screw extruders whereby under certain conditions, laminar shear flow fails to achieve a critical level of stress needed to break up the droplet. 

To lower the interfacial tension, thereby promoting break up of droplets during processing... 

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