Coalescence frequency

The evolution of emulsions through coalescence can be characterized by a kinetic parameter, , describing the number of coalescence events per unit time and per unit surface area of the drops. Following the mean field description of Arrhenius, 

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Drops coalesce because of coUisions and drainage of Hquid trapped between colliding drops. Therefore, coalescence frequency can be defined as the product of coUision frequency and efficiency per coUision. The coUision frequency depends on number of drops and flow parameters such as shear rate and fluid forces. The coUision efficiency is a function of Hquid drainage rate, surface forces, and attractive forces such as van der Waal s. Because dispersed phase drop size depends on physical properties which are sometimes difficult to measure, it becomes necessary to carry out laboratory experiments to define the process mixing requirements. A suitable mixing system can then be designed based on satisfying these requirements. 

In Eq. (5.6), co is defined as a coalescence frequency per unit surface area of the droplets. Considering Eqs. (5.5) and (5.6) and assuming that > is constant (independent of T>), it can be concluded that the mean size in the emulsion increases with time according the following law ... 

Measurements of the Coalescence Frequency 155 Table 5.1. Characteristic coalescence frequency for different aUcane-in-water emulsions... 

Figure 5.7. Evolution of the coalescence frequency with time deduced from Eq. (5.14) for an octane-in-water emulsion stabilized with SDS. (Adapted from [42].)...

In the experiments described by Pays et al. [44], the double globules were composed of dodecane and the surfactants used were sorbitan monooleate (SMO), which is oil soluble, and the water-soluble SDS. The concentrations of both surfactants were fixed and the initial internal droplet volume fraction was varied between 5% and 35%. The coalescence frequency was determined from a simple experiment in which the globule surface was totally saturated by the water droplets. For... 

Figure 5.14. Variation of the coalescence frequency

The experimental studies described in this chapter certainly led to a better understanding of the coalescence phenomena in concentrated emulsions. Despite the complexity and variety of the destruction scenarios, different methods for measuring the coalescence frequency, ty, have been proposed. It should be within the reach of future work to measure ty for a large variety of systems in order to establish a comparative stability scale. This is a necessary step to determine the microscopic parameters that control the activation energy Ea and the attempt frequency coo. 

V. Schmitt, C. Cattelet, and F. Leal-Calderon Measurement of the Coalescence Frequency in Concentrated Emulsions. Europhys. Lett. 67, 662 (2004). 

Assuming that the internal droplets experience a hard-sphere-like repulsion when surfactant layers come in contact, an estimation of the van der Waals interactions can be obtained from the average length of the surfactant tails (1 3 nm) [20]. The coalescence frequency is therefore the unique free pa-... 

Let the total number of drops be N and the average volume of each drop be v, so that the total volume of dispersed phase is Nv. Then the volume of dispersed phase involved in coalescence is UiNv and the number of coalescences per unit time is w,A. Here is the coalescing rate or coalescing frequency measured in sec.-1 and the chance of having more than two drops involved in a single coalescence is assumed negligible. 

Coalescence is a difficult phenomenon to measure directly usually it is dealt with as a rate or frequency. The coalescence rate (or coalescence frequency) is expressed as the number of coalescences of a bubble during the mean residence time of the gas. Few published results (Reith, 1970 Flassan and Robinson, 1980a, 1980b) show a sharp increase of the coalescence frequency as N increases. The frequency decreases notably when a saline solution is used in place of water. 

The range of volume fraction within which either of two immiscible liquids may be continuous is primarily a function of the viscosity ratio, but is only weakly dependent upon vessel characteristics or stirring speed. The coalescence frequency for the dispersed drops is, however, a strong function of impeller speed (i.e., frequency xN2,85). 

For liquid-liquid systems, drop-size distributions and coalescence frequencies can be measured by a flash photomicrographic method and a modified dye-light transmittance technique. Both of these methods are accurate... 

V Coalescence frequency, fraction of drops coalescing per time L/s L/h... 

Coulalglou CA and Tavlarides LL. Drop size distributions and coalescence frequencies of liquid-liquid dispersions in flow vessels. AIChE J 1976 22 289-297. 

Coalescence frequencies can have a pronounced effect on the rate of mass transfer or chemical reaction in a liquid-liquid dispersion. Various investigators have attempted to model and measure coalescence frequencies in agitated vessels. A review of the experimental techniques is given by Rietema (R12) and Shah et al. (S16). 

All coalescence frequency work reported in the literature with the exception of that of two groups of investigators has used indirect means of obtaining an average coalescence frequency for the entire mixing vessel. The indirect methods can be divided into two categories chemical and physical. 

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