Treating an oil spill by application of a chemical dispersant is a useful means for dispersion of oil. Knowledge of the droplet size formed as a function of the energy dissipation rate is useful to scale the laboratory data to oceanic applications. A dimensional and scaling analysis was done by our group and published in a paper by Mukherjee et al. (2012). This paper presents a compelling case study of the methods discussed in this chapter.

Identify the important variables and perform a dimensionless analysis. Show that the Reynolds number, Weber number, and viscosity ratio of water to oil are the key parameters which affect the dispersed drop size.

The form for the correlation cannot be established from dimensionless analysis. Hence a scaling analysis where the order of magnitude of surface tension and the restoring viscous forces is compared with the inertial forces leading to drop break-up is needed. Perform such an analysis based on the discussion in the above paper and show that, depending on the relative values of the dimensionless groups, either the viscous or the surface-tension forces could be important as the restoring forces. Derive criteria to distinguish these effects and show practical implications.