For high Reynolds number flows, the fine structure turbulence is universal in the inertial subrange according to the Kolmogorov local isotropy theory; while for low-to-moderate Reynolds number flows, the turbulence tends to display a common structure for a particular type of shear flows from the Townsend structural similarity. The power laws for the turbulent flows reflect the similarity in the turbulence fine structure.
The paper discusses the relationship between drop breakup and turbulence fine structure. A predictive formula for drop breakup in the turbulent flow is suggested based on the energy balance between turbulence separating kinetic energy (i.e. turbulence structure function) and surface tension. The model has been validated on a number of empirical relations for drop breakup in different turbulent flows.
It is known that the drop size distribution in shear flows can be approximately expressed by a lognormal distribution. Using statistical approach, the paper provides a theoretical proof on this fact. The model describes that the drop breakup experiences a cascade splitting process and the drop size tends to be asymptotically lognormally distributed. A numerical example is given to illustrate details of the breakup process.