Global and local statistics in turbulent emulsions

TL;DR

This study investigates the statistical properties of turbulent emulsions in a Taylor-Couette flow, revealing how droplet size distribution, effective viscosity, and shear thinning behavior depend on flow conditions and oil volume fraction.

Contribution

The paper provides new insights into the relationship between turbulence, droplet fragmentation, and rheological properties in turbulent emulsions using a specialized shear flow system.

Findings

Droplet size follows a log-normal distribution, indicating fragmentation as a key process.

Effective viscosity increases with oil volume fraction and decreases with shear rate.

Flow behavior fits the Herschel-Bulkley model, with shear thinning intensifying at higher oil fractions.

Abstract

Turbulent emulsions are complex physical systems characterized by a strong and dynamical coupling between small-scale droplets and large-scale rheology. By using a specifically designed Taylor-Couette (TC) shear flow system, we are able to characterize the statistical properties of a turbulent emulsion made of oil droplets dispersed in an ethanol-water continuous solution, at the oil volume fraction up to 40%. We find that the dependence of the droplet size on the Reynolds number of the flow at the volume fraction of 1% can be well described by Hinze's criterion. The distribution of droplet sizes is found to follow a log-normal distribution, hinting at a fragmentation process as the possible mechanism dominating droplet formation. Additionally, the effective viscosity of the turbulent emulsion increases with the volume fraction of the dispersed oil phase, and decreases when the shear strength is increased. We find that the dependence of the effective viscosity on the shear rate can be described by the Herschel-Bulkley model, with a flow index monotonically decreasing with increasing the oil volume fraction. This finding indicates that the degree of shear thinning systematically increases with the volume fraction of the dispersed phase. The current findings have important implications for bridging the knowledge on turbulence and low-Reynolds-number emulsion flows to turbulent emulsion flows.