Physical mechanisms for droplet size and effective viscosity asymmetries in turbulent emulsions

TL;DR

This study investigates the asymmetric behaviors of oil-in-water and water-in-oil emulsions in turbulent shear flow, revealing the roles of surface contaminants and flow dynamics in droplet size and viscosity, and demonstrating how surfactants restore symmetry.

Contribution

It uncovers the micro- and macro-scale mechanisms behind emulsion asymmetries and introduces a scaling law for droplet size based on flow Reynolds number and boundary layer dynamics.

Findings

Oil-in-water and water-in-oil emulsions exhibit distinct hydrodynamic behaviors.

Surface-active contaminants cause asymmetries in droplet size and viscosity.

Adding surfactants restores symmetry between emulsions.

Abstract

By varying the oil volume fraction, the microscopic droplet size and the macroscopic rheology of emulsions are investigated in a Taylor-Couette (TC) turbulent shear flow. Although here oil and water in the emulsions have almost the same physical properties (density and viscosity), unexpectedly, we find that oil-in-water (O/W) and water-in-oil (W/O) emulsions have very distinct hydrodynamic behaviors, i.e., the system is clearly asymmetric. By looking at the micro-scales, the average droplet diameter hardly changes with the oil volume fraction neither for O/W nor for W/O. However, for W/O it is about 50% larger than that of O/W. At the macro-scales, the effective viscosity of O/W is higher when compared to that of W/O. These asymmetric behaviors can be traced back to the presence of surface-active contaminants in the system. By introducing an oil-soluble surfactant at high concentration, remarkably, we recover the symmetry (droplet size and effective viscosity) between O/W and W/O emulsions. Based on this, we suggest a possible mechanism responsible for the initial asymmetry. Next, we discuss what sets the droplet size in turbulent emulsions. We uncover a -6/5 scaling dependence of the droplet size on the Reynolds number of the flow. Combining the scaling dependence and the droplet Weber number, we conclude that the droplet fragmentation, which determines the droplet size, occurs within the boundary layer and is controlled by the dynamic pressure caused by the gradient of the mean flow, as proposed by Levich (1962), instead of the dynamic pressure due to turbulent fluctuations, as proposed by Kolmogorov (1949). The present findings provide an understanding of both the microscopic droplet formation and the macroscopic rheological behaviors in dynamic emulsification, and connects them.