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

Memoryless drop breakup in turbulence

The breakup of drops and bubbles in turbulent fluids is a key mechanism in many environmental and engineering processes. Even in the well-studied dilute case, quantitative descriptions of drop fragmentation remain elusive, and empirical models continue to proliferate. We here investigate drop breakup by leveraging a novel computer code, which enables the generation of ensembles of experiments with thousands of independent, fully resolved simulations. We show that in homogeneous isotropic turbulence breakup is a memoryless process whose rate depends only on the Weber number. A simple model based on the computed breakup rates can accurately predict experimental measurements and demonstrates that dilute emulsions evolve through a continuous fragmentation process with exponentially increasing time scales. Our results suggest a nonvanishing breakup rate below the critical Kolmogorov-Hinze diameter, challenging the current paradigm of inertial drop fragmentation.

The Role of Stochastic Time-Variations in Turbulent Stresses When Predicting Drop Breakup—A Review of Modelling Approaches

Many industrially relevant emulsification devices are of the high-energy type, where drop deformation and subsequent breakup, take place due to intense turbulent fluid–drop interactions. This includes high-pressure homogenizers as well as rotor-stator mixers (also known as high-shear mixers) of various designs. The stress acting on a drop in a turbulent flow field varies over time, occasionally reaching values far exceeding its time-averaged value, but only during limited stretches of time, after which it decreases down to low values again. This it is one factor separating turbulent from laminar emulsification. This contribution reviews attempts to take this intermittently time-varying stress into account in models predicting the characteristic drop diameter resulting from emulsification experiments, focusing on industrially applicable emulsification devices. Two main frameworks are discussed: the Kolmogorov–Hinze framework and the oscillatory resonance framework. Modelling suggestions are critically discussed and compared, with the intention to answer how critical it is to correctly capture this time-varying stress in emulsification modelling. The review is concluded by a list of suggestions for future investigations.

Interfacial Dynamics and Rheology of a Crude-Oil Droplet Oscillating in Water at a High Frequency

We report investigations of a pendant diluted crude-oil droplet in water that is forced to oscillate at a frequency ω. The droplet interface contains a significant amount of surface-active agents and displays a marked viscoelastic rheology with elastic moduli larger than viscous ones. At a low frequency, fluid viscosity and inertia are negligible, which allows a direct determination of the dilatational interface rheology. At a large frequency, eigenmodes of inertial shape oscillations are excited. By decomposing the interface shape into spherical harmonics, the resonance curves of the inertial modes of the interface are determined, as well as the frequency and damping rate of each mode. These two parameters are of major importance for the prediction of the deformation and breakup of a droplet in any unsteady flow without any prior knowledge of either the chemical composition or the detailed rheological properties of the interface. Then, interfacial rheology is related to interface dynamics by solving the coupled dynamic equations for the two fluids and the interface. It turns out that the rheology of the interface is well described by an equivalent two-dimensional viscoelastic material, the elasticities and viscosities of which depend upon the frequency. A first significant result is that shear and dilatational elasticities are closely connected, as are shear and dilatational viscosities. This implies that intrinsic rheology plays a major role and that compositional rheology is either negligible or strongly coupled to the intrinsic one. A second major result is that, for moderately aged droplets (≤5000 s), the elasticity and viscosity at a high frequency (10-80 Hz) can be extrapolated from low-frequency measurements (≤1 Hz) by a simple power law of the frequency, ω^z. The exponent z is related to the loss angle θ_loss by a relation found in many previous low-frequency investigations of crude-oil interfaces: z = θ_loss/2π. The present work thus extends classic observations obtained at a low frequency to a higher frequency range corresponding to the natural frequency of the droplets, where the droplet shape results from the balance between dynamic pressure and surface stresses and the interface involves simultaneous shear and dilatation. These results bring about serious constraints regarding the modeling of physicochemical underlying mechanisms and provide some insights for the understanding of the structure of crude-oil interfaces.