A criterion for when an emulsion drop undergoing turbulent deformation has reached a critically deformed state

Turbulent breakup in emulsification devices is a dynamic process. Small viscous drops undergo a sequence of oscillations before entering the monotonic deformation phase leading to breakup. The turbulence-interface interactions prior to reaching critical deformation are therefore essential for understanding and modeling breakup. This contribution uses numerical experiments to characterize the critically deformed state (defined as a state from which breakup will follow deterministically, even if no further external stresses would act on the drop). Critical deformation does not coincide with a threshold maximum surface area, as previously suggested. A drop is critically deformed when a neck has formed locally with a curvature such that the Laplace pressure exceeds that of the smallest of the bulbs connected by the neck. This corresponds to a destabilizing internal flow, further thinning the neck. Assuming that the deformation leads to two spherical bulbs linked by a cylindrical neck, the critical deformation is achieved when the neck diameter becomes smaller than the radius of the smallest bulb. The role of emulsifiers is also discussed.