Dense Oil in Water Emulsions using Vortex-Based Hydrodynamic Cavitation: Effective Viscosity, Sauter Mean Diameter, and Droplet Size Distribution

Vortex-based hydrodynamic cavitation offers an effective platform for producing emulsions. In this work, we have investigated characteristics of dense oil in water emulsions with oil volume fractions up to 60% produced using a vortex-based cavitation device. Emulsions were prepared using rapeseed oil with oil volume fractions of 0.15, 0.3, 0.45, and 0.6. For each of these volume fractions, the pressure drop as a function of the flow rate of emulsions through the cavitation device was measured. These data were used for estimating the effective viscosity of the emulsions. The droplet size distribution of the emulsions was measured using the laser diffraction technique. The influence of the number of passes through the cavitation device on droplet size distributions and the Sauter mean diameter was quantified. It was found that the Sauter mean diameter (d32) decreases with an increase in the number of passes as n–0.2. The Sauter mean diameter was found to be almost independent of oil volume fraction (αo) up to a certain critical volume fraction (αoc). Beyond αoc, d32 was found to be linearly proportional to a further increase in oil volume fraction. As expected, the turbidity of the produced emulsions was found to be linearly proportional to the oil volume fraction. The slope of turbidity versus oil volume fraction can be used to estimate the Sauter mean diameter. A suitable correlation was developed to relate turbidity, volume fraction, and Sauter mean diameter. The droplet breakage efficiency of the vortex-based cavitation device for dense oil in water emulsions was quantified and reported. The breakage efficiency was found to increase linearly with an increase in oil volume fraction up to αoc and then plateau with a further increase in the oil volume fraction. The breakage efficiency was found to decrease with an increase in energy consumption per unit mass (E) as E–0.8. The presented results demonstrate the effectiveness of a vortex-based cavitation device for producing dense oil in water emulsions and will be useful for extending its applications to other dense emulsions.


Section S1: Identification of continuous phase
The continuous phase of the emulsion is not dictated by the volume fraction alone.It depends on variety of factors including the way emulsions are prepared.In the present case, the continuous phase of the emulsions was confirmed via microscopic images as well as via conductivity measurements.Emulsions with water as a continuous phase exhibit much higher conductivity than that with oil as a continuous  It can be seen from Figure S2 that for all the emulsions considered in this work (oil volume fraction up to 0.60), the measured conductivity values are very close to the conductivity values of surfactant containing water, indicating that the continuous phase is aqueous phase.For oil volume fraction of 0.95 emulsion (which is 0.05 water volume fraction dispersed in oil), the measured conductivity value is close to that of pure rapeseed oil, indicating that oil is the continuous phase.The exact point of phase inversion was not quantified in this work.
For establishing adequate surfactant quantify to be used in the emulsion experiments, the quantity of surfactant needed for mono-layer coverage was first estimated.For the highest oil volume fraction (0.60) considered in this study, even if the Sauter mean diameter is one micron, the quantity of Tween 20 surfactant required for forming a monolayer on all oil drops is less than 0.1% (wt).We used significantly excess surfactant (2 wt%) for all our experiments to ensure that there is no influence of surfactant quantity used on measured droplet size distributions (DSD).Preliminary experiments were carried out to examine influence of surfactant quantity on measured DSD.With the use of 2% Tween 20 surfactant, produced emulsions were found to be stable for a long time.The measured DSDs for oil volume fraction of 0.60 emulsion with the gap of 90 days are shown in Figure S3.For all the experimental results reported in this manuscript, the DSD measurements were carried out within a day after the emulsions were produced.The used quantity of surfactant can therefore be considered as adequate.

Section S2: Sensitivity of obscuration level in Laser diffraction measurements:
In Malvern Mastersizer 3000 utilize obscuration, the measure of light blocked or scatter by droplets, to gauge droplet concentration within the measurement cell.With increase in sample volume results in higher laser obscuration.Therefore, ensuring the appropriate range of obscuration is important for accurate measurements.The lower limit is set where the signal-to-noise ratio ensures reproducibility, while the upper limit is influenced by the occurrence of multiple scattering.To establish the upper limit to prevent the multiple scattering we conducted measurements of the same sample at various obscuration levels.Subsequently, we employed a three-log-normal function to fit the Probability Density Function (PDF) of the volume distribution.
The measured DSD and fitted parameters are shown in Figure S4:  It can be seen from Figure S4 that DSD obtained with obscuration level between 4% and 10% are similar.At higher than 10% obscuration levels, the DSDs become wider, as evidenced by the increased  values in the fitted log-normal distributions.To further illustrate the influence of obscuration levels, we present the standard deviation analysis for small droplets, at varying obscuration levels, as depicted in Figure S5.As outlined in Section 3.1, the acquired PDFs were fitted using three log-normal functions representing distinct droplet size ranges, namely PDF-1, PDF-2, and PDF-3, from smaller droplets to larger droplets.The standard deviation for PDF-1 is shown in Figure S5.It can be seen that standard deviation remained relatively constant until an obscuration level of approximately 10%.Beyond this level, a decline was observed, signifying the escalating influence of multiple scattering.Consequently, to ensure data accuracy and prevent artificial peak induced by multiple scattering, all measurements were conducted within the range of 5-10% laser obscuration.Section S3: Correlations for estimating pressure drop 1 The physical model to estimate the viscosity of emulsion is related to the pressure drop (in terms of

Section S4: Correlations between turbidity and absorbance
The relationship between turbidity (in NTU), and absorbance () for the same oil volume fractions is illustrated in Figure S6, where the absorbance (in m -1 ) is approximately 532 times less than the observed turbidity (in NTU).

Figure S3 :
Figure S3: Influence of time elapsed on measured DSD for 60% oil in water emulsion.

Figure S4 :
Figure S4: DSD obtained from Mastersizer for oil volume fraction (  ) of 0.15 at n =1 pass, with different obscuration values (%).The symbols represent the measured values, and the corresponding-coloured lines represent the fitted three log normal distribution obtained from Equation S-1.
Euler number, ) and Reynold number () based on Thaker et al.1 work for range of viscosity and device scale three different flow regimes was observed with  and .Laminar regime:  * =   * if  * <  12 * (S-2) Transient regime:  * =  ( * )  if  12 * ≤  * <  23 * (S-3) Turbulent regime:  * =  if  * ≥  23 * (S-4)The values of the Euler number and Reynolds number are scaled using the following: equation S-2, S-3 and S-4,  12 * and  23 * are boundaries between the laminar and transient, and turbulent regimes respectively.Equations for boundaries between regimes: regime parameter, , is not a constant but is a function of scale and viscosity.The data indicated following relationship for .

Figure S6 .
Figure S6.Correlation between turbidity (in NTU) versus absorbance () relationship for emulsions with different oil volume fractions and number of passes. 1)