The breakup of immiscible fluids in turbulent flows

Abstract

The breakup of immiscible fluid particles in a prototypical turbulent flow has been investigated. Dispersed fluids of varying density, viscosity and interfacial tension with water were injected continuously on the centreline 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. Particle breakup 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 breakup 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 r.m.s. value of turbulent velocity fluctuations and $L$ is the local integral length scale. High-speed video images corroborate this result. Prior to breakup, 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 owing to capillary effects resulting from differences in the radius of curvature along their length. The breakup time of these particles scales with the capillary time $t_d = \mu_dD/\sigma$, where $\mu_d$ is the dispersed fluid viscosity, $D$ is the undeformed particle diameter, and $\sigma$ is the interfacial tension between the dispersed fluid and water. These results are analogous to the breakup mechanisms observed by several investigators in low-Reynolds-number flows; however, they contradict the classical theory for turbulent particle breakup, which suggests that fragmentation results from isolated interactions with turbulent velocity fluctuations over distances comparable to or smaller than the undeformed dispersed particle diameter.