Measurement and Prediction of the Mean Droplet Size in Water-in-Oil Emulsions

Droplet sizes were measured using a Particle Video Microscope (PVM) probe and a Focused Beam Reflectance Method (FBRM) probe for a variety of oils and shear rates. Two regimes in turbulent mixing flow were identified: i) the inertial sub-range where droplets are on the size scale of the smallest eddies in the turbulent mixing, and ii) the viscous sub-range in which droplets are smaller than the smallest eddies. A universal droplet size curve was generated using dimensionless numbers that included the Reynolds number, Weber number, and a non-dimensional droplet diameter. The curve showed good agreement with the PVM data and the transition from the inertial to viscous sub-range. The droplet size distribution for various oils matched a log-normal distribution using parameters (mean and standard deviation) predicted from correlations using the shear in the system, density, viscosity, and interfacial tension of the oil. The average difference between the surface area calculated from the PVM droplet size distribution and from the predicted log-normal distribution was 11.7%.