The break-up of immiscible fluids in turbulent flows

The break-up of immiscible fluid particles in a canonical turbulent flow has been investigated. Dispersed fluids of varying density, viscosity, and interfacial tension with water were injected continuously on the centerline in the fully-developed region of a turbulent water jet. Digital image processing techniques were used to track the particle size distributions as the initial globules of the dispersed fluid were broken into smaller particles and convected downstream in the jet. The measured size distributions were compared to the predictions of common phenomenological models for the break-up of fluid particles as a result of turbulent stresses. A representative particle-eddy collision model and a simpler model based solely on kinematic arguments were used. Both of these models underestimate the breakage of large particles and the corresponding formation of small particles.; Particle break-up frequencies were calculated from the evolution of the measured particle size distributions using a simplified version of the Boltzmann equation. The results of these calculations indicate that the break-up frequency of fluid particles at low Weber numbers scales with the passage frequency of the large-scale turbulent features of the flow, approximated as u′/L, where u ′ is the rms value of turbulent velocity fluctuations and L is the local integral length scale. High-speed video images corroborate this result. Prior to break-up, dispersed fluid particles with initial diameters within the inertial subrange of the background flow stretch to lengths comparable to the local integral scale. These elongated particles subsequently break due to capillary effects resulting from differences in the radius of curvature along their length. The breakup time of these particles scales with the time scale $td=mdDs$, where $md$ is the dispersed fluid viscosity, D is the undeformed particle diameter, and $s$ is the interfacial tension between the dispersed fluid and water. These results are analogous to the break-up mechanisms observed by several investigators in low Reynolds number flows; however, they contradict the classical theory for turbulent particle break-up, proposed independently by Kolmogorov and Hinze, which suggests that fragmentation results from isolated interactions with turbulent velocity fluctuations over distances comparable to or smaller than the undeformed dispersed particle diameter.