Catastrophic Phase Inversion in High-Reynolds-Number Turbulent Taylor-Couette Flow

Emulsions are omnipresent in the food industry, health care, and chemical synthesis. In this Letter the dynamics of metastable oil-water emulsions in highly turbulent (${10}^{11}\le \mathrm{Ta}\le 3\times {10}^{13}$) Taylor-Couette flow, far from equilibrium, is investigated. By varying the oil-in-water void fraction, catastrophic phase inversion between oil-in-water and water-in-oil emulsions can be triggered, changing the morphology, including droplet sizes, and rheological properties of the mixture, dramatically. The manifestation of these different states is exemplified by combining global torque measurements and local in situ laser induced fluorescence microscopy imaging. Despite the turbulent state of the flow and the dynamic equilibrium of the oil-water mixture, the global torque response of the system is found to be as if the fluid were Newtonian, and the effective viscosity of the mixture was found to be several times bigger or smaller than either of its constituents.

Figure 1

(a) Schematic of the ${\mathrm{T}}^3\mathrm{C}$ setup. Initially, the water (bottom) and oil (top) are separated. (b) In situ high-speed microscopy using LIF lighting, a half-mirror, and a $20\times$ magnification lens, through a $200\mu \mathrm{m}$ thick window at the top of the setup shown in (a).

Figure 2

${\mathrm{Nu}}_{\omega }$ as a function of Ta for a total of 32 experiments. By exploiting the relation between ${\mathrm{Nu}}_{\omega }=f(\mathrm{Ta})$, an effective viscosity ${\nu }_{\mathrm{eff}}$ was found for each experiment such that all the datasets collapse on a single curve, by minimizing $\sigma ({\mathrm{Nu}}_{\omega })$ for the collective data, binned in Ta. The inset shows the compensated datasets, revealing the overlap within a couple of percent. The colors of the lines indicate the oil fraction.

Figure 3

Effective viscosity normalized by the viscosity of water as function of oil volume fraction. The measurements with fixed $\alpha$ are shown by the circles. The continuous measurements, for which $\alpha$ is changed during the experiments (${\omega }_{\mathrm{IC}}/(2\pi )$ is fixed at 17.5 Hz), are shown as solid lines, while the dotted line is an experiment with ${\omega }_{\mathrm{IC}}/(2\pi )=8\mathrm{Hz}$. The shaded area between the dashed vertical lines shows the ambivalence region, bounded by two catastrophic phase inversion, $\overline{)\mathrm{J}1}$: w-o $\to$ o-w and $\overline{)\mathrm{J}2}$: o-w $\to$ w-o. When water is the continuous phase, increasing $\alpha$ ($\overline{)\mathrm{a}}$) leads to an increase in ${\nu }_{\mathrm{eff}}$, while when oil is the continuous phase decreasing $\alpha$ ($\overline{)\mathrm{b}}$), decreases ${\nu }_{\mathrm{eff}}$.

Figure 4

Droplet diameter of the dispersed phase obtained using in situ microscopy for decreasing $\alpha$ for a rotational speed of ${\omega }_{\mathrm{IC}}/(2\pi )=8\mathrm{Hz}$. A sharp jump in average diameter is found at the inversion point $\alpha \approx 50\%$, as is also visible in the measured torque (and from that ${\nu }_{\mathrm{eff}}$) as the dotted line in Fig. 3. The arrow indicates the direction of the $\alpha$ modification. Two example images are given in the Supplemental Material [60].