A model for drop and bubble breakup frequency based on turbulence spectra

Abstract

In this article, a new Eulerian model for breakup frequency of drops induced by inertial stress in homogeneous isotropic turbulence is developed for moderately viscous fluids, accounting for the finite response time of drops to deform. The dynamics of drop shape in a turbulent flow is described by a linear damped oscillator forced by the instantaneous turbulent fluctuations at the drop scale. The criterion for breakup is based on a maximum value of drop deformation, in contrast with the usual critical Weber criterion. The breakup frequency is then modeled as a function of the power spectrum of Weber number (or velocity square), based on the theory of oscillators forced by a random signal, which can be related to classical statistical quantities, such as dissipation rate and velocity variance. Moreover, the effect of viscosities of both phases is included in the breakup frequency model without resorting to any additional paramete