Experimental investigations of turbulent fragmenting stresses in a rotor-stator mixer. Part 2. Probability distributions of instantaneous stresses

Abstract

Drop fragmentation in high intensity turbulent emulsification processing equipment–such as rotor-stator mixers (RSMs)–has traditionally been described in terms of a stress balance; between the stabilizing stress of the drop and the time-averaged turbulent stress at the most intense position of the flow. As shown in part 1 of this series, this approach is often a fruitful first approximation. However, the instantaneous local stress experienced by drops differs from the time-averaged local stress due to hydrodynamics in general and the stochastic nature of a turbulent flow in particular.This study estimates the probability distribution of instantaneous turbulent stresses in an RSM from velocity fields obtained using particle image velocimetry. Results show that regions with low average stress still have a substantial probability of having instantaneously high stresses. This explains why low probability breakup is observed at these positions in visualization experiments.Results also show that the probability distribution of instantaneous stresses is approximately lognormal. The results are compared to two commonly used models for how to take the stochastic variations into account: the exponential decay model, and the multifractal emulsification model. It is concluded that both models predict reasonable distributions shapes but underestimate the width of the stress distribution.