The drop breakage process

The first approaches to modeling the drop breakage process in liquid-liquid dispersions were based on the Weber number for the calculation of the mean drop diameter (see Table 5.2), as well as a maximum stable drop diameter for breakage to occur and a minimum drop diameter above which coalescence will take place (2, 27, 37). Both diameters depend on the intensity of agitation and on physical properties of the constituents. However, these calculations were limited to very low dispersed phase viscosities and holdup fractions. Doulah [25] proposed a correction to the derived correlations to account for high holdup dispersed fi actions, whereas Arai et al. [48 ] derived an expression for the maximum droplet diameter by incorporating the viscosity of the dispersed phase. Similar expressions were also proposed by Calabrese etal. [41]. 

To calculate the drop breakage rate in liquid-liquid dispersions, several models have been proposed [33, 38, 42, 49-52]. Some of these models have been applied to the suspension polymerization process with great success [ 8,36,49,53 ]. In these models, the drop breakage rate is expressed in terms of a breakage frequency, c% v), and a respective Maxwellian efficiency term  

Assume that a drop of volume u breaks up into Nja daughter drops and Nsa satellite drops. Furthermore, assume that the daughter and satellite drops are normally distributed about their respective mean values, vja and Vsa. Then, the following expression can be derived for 

It should be noted that the daughter drop number density function, v), should 

Accordingly, one can calculate the mean volumes of daughter and satellite drops, formed by the breakage of a drop of volume u in terms of and Nja and the ratio of their respective volumes, ry, = v a/vsa [6]  

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