Additional Considerations for Emulsions and Foams

Some equations have been developed specifically for emulsions. Some are variations 

For polydisperse, possibly non-Newtonian emulsions, Eilers [400] developed, 

For electrostatically or sterically interacting drops, emulsion viscosity will be higher when droplets are smaller. The viscosity will also be higher when the droplet sizes are relatively homogeneous, that is, when the drop size distribution is narrow rather than wide. The nature of the emulsifier can influence not just emulsion stability but also the size distribution, mean droplet size, and therefore the viscosity. To describe the effect of emulsifiers on emulsion viscosity Sherman [215] has suggested a modification of the Richardson Equation to the following form  

If the internal phase in an emulsion has a sufficiently high volume fraction (typically anywhere from 10 to 50%) the emulsion viscosity increases due to droplet crowding, or structural viscosity, and becomes non-Newtonian. The maximum volume fraction possible for an internal phase made up of uniform, incompressible spheres is 74%, although emulsions with an internal volume fraction of 99% have 

When solids are present in emulsions, the volume fractions of the particles and the droplets are usually not additive for the purpose of predicting overall dispersion viscosity. A number of different kinds of behaviours can result, depending on the sizes and shapes of the particles versus the droplets, and upon whether they exist as kinetically independent entities, whether the particles exist in adsorption layers surrounding the droplets, or dispersed within the droplets themselves, or a combination of all of the above. Pal et al. [382] and Nasr-El-Din [85] discuss the rheology of emulsions containing solids in some detail. 

Some equations have been developed specifically for emulsions. Some are variations on Einstein s equation, such as that developed by Taylor [74]  

Numerous adaptations of the Richardson and Broughton-Squires equations have been developed for specific application areas. For example, a variation of the Broughton-Squires equation for water-in-crude oil (North Sea crude oil) emulsion viscosity is [77] 

If the internal phase in an emulsion has a sufficiently high volume fraction (typically anywhere from 10 to 50%), then the emulsion viscosity increases due to 

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