Droplet Size Distribution of Oil-in-Milk Emulsions: Continuous Emulsification via a Vortex-Based Hydrodynamic Cavitation Device

Abstract

The continuous generation of oil-in-milk emulsions is gaining increasing interest in the food industry. In this work, flaxseed oil-in-milk emulsions were produced continuously for the first time using a vortex-based hydrodynamic cavitation device (VD). A loop configuration was used for operating the device in a continuous mode. The droplet size distribution (DSD) of oil-in-milk emulsions with a surfactant (sodium lauryl sulfate) was measured. The influence of the oil volume fraction (α_o = 0.05–0.45), effect of pressure drop (ΔP = 100, 150, and 200 kPa), and ratio of flow through VD, Q, and emulsion, $q\left(\frac{Q}{q}=1-100\right)$ , on DSD was investigated. DSD was found to be bimodal in nature. The Sauter mean diameter (d ₃₂) was found to increase with α_o. A new empirical correlation was developed to predict d ₃₂ as a function of the key operating parameters. The DSD and key characteristic diameters (d ₃₂, D ₁₀, D _50, and D ₉₀) of FO in milk emulsions were estimated for the first time using an at-line characterization methodology based on an inexpensive voltage sensor and an ANN model. The methodology was validated by comparing the predicted DSD with experimental data. This work demonstrates that the presented approach of using VD in a loop configuration leads to emulsions with a Sauter mean diameter of less than 5 μm and energy consumption per unit mass of emulsion of less than 10 kJ/kg. The results presented will be useful for developing and establishing continuous milk-based emulsions.

1. Introduction

Emulsions in the food industry are important for offering healthy food options, which has been a major trend in recent times. − Some chemicals, including bioactives or nutraceuticals, are poorly soluble in aqueous media. The oil in an aqueous phase emulsion offers an excellent way to deliver such components. , There is an increasing trend to provide tailored products via on-demand production in a distributed manner. The DSD of emulsions is one of the most important critical quality attributes (CQAs) since it determines stability, rheology, texture, appearance, and overall emulsion quality. Significant efforts are underway to develop emulsions with the targeted droplet size distribution (DSD) in a continuous production process, and new equipment and devices are being designed to support this goal.

Various techniques and equipment are available for emulsion production, such as high-pressure homogenizers, microfluidizers, rotor-stator systems, ultrasonication, membrane-based methods, and more. , Among these, hydrodynamic cavitation (HC) has emerged as a promising alternative to conventional emulsification techniques. These conventional emulsification techniques are often energy-intensive, costly, and not well-suited for continuous, on-demand food processing. Hydrodynamic cavitation (HC) is a process that involves the generation and collapse of vapor bubbles or cavities within a liquid. , Collapsing cavities generate intense, localized shear and turbulence energy dissipation rates, which may be harnessed to generate fine emulsions at lower energy costs. ,

Among the HC devices, the vortex diode (VD) is particularly attractive due to its simple design, absence of moving parts, robustness, and scalability for continuous operation. Previous studies have successfully demonstrated the application of VD for generating fine oil-in-water emulsions. , Its application to nutritionally relevant food matrices remains, however, largely unexplored. The flaxseed oil (FO) is a well-known nonpolar bioactive compound commonly found in the effective food category. FO is rich in omega-3 fatty acids and α-linolenic acid (ALA), and ALA is an essential fatty acid recognized for its role in supporting cellular health, nerve function, and cognitive development in children, as well as promoting cardiovascular health in human beings. ,− Milk offers a natural protein-stabilized medium that can enhance FO bioavailability. Milk proteins are amphiphilic molecules that adsorb naturally at the oil–water interface, where they form thick interfacial films that stabilize oil droplets through a combination of steric hindrance and electrostatic repulsion. These protein-rich interfacial layers reduce droplet coalescence and thereby maintain emulsion stability. − In the present work, we evaluate the application of VD for generating emulsions of FO in milk with an oil volume fraction up to 0.45. Though natural emulsifiers present in milk are useful to stabilize emulsions, additional external surfactants (sodium dodecyl sulfate, SDS) were used in the present work to ensure that coalescence was fully inhibited.

For any stable emulsion, DSD characterization is very crucial. A commonly used technique to measure DSD is laser diffraction. However, it is not suitable for in-line or at-line measurements of the DSD in continuous emulsification processes. At-line measurements are essential for the operation and control of the continuous emulsification processes. Ravi et al. developed an at-line characterization methodology for measuring the DSD of the rapeseed oil (RO) in water emulsions using an inexpensive voltage-based sensor that provides rapid and nonintrusive at-line measurements of DSD. They used the ANN model developed by Ranade and Ranade for estimating the DSD from the data acquired from the voltage sensor. In this work, we demonstrate the application of this previously developed method of at-line measurements of DSD for FO in milk emulsions for the first time. By integrating the nutritional relevance of FO, functional properties of milk, the emulsification capability of vortex-based devices, and the practicality of ANN-driven at-line characterization, this work advances the industrial application of hydrodynamic cavitation for continuous food emulsion production. The approach and insights presented here provide a foundation for researchers, engineers, and dairy scientists to further develop scalable and efficient emulsification processes.

2. Experimental Information

2.1. Experimental Setup and Procedure

In this study, the experimental setup developed previously by Ravi et al. was used for continuously generating emulsions of flaxseed oil (FO) in milk using VD. A schematic diagram of the setup is shown in Figure [a photo and details of the setup are shown in Figure S1 and Table S1 in section S1 of the Supporting Information (SI)]. The system is composed of two separate feed tanks: one containing milk (with or without surfactant) and the other containing flaxseed oil. Each fluid is pumped independently using dedicated peristaltic pumps (Longer Pump WT600-2J for milk and BT100-3J for oil), with flow rates represented by q _M for milk and q _o for oil. These two streams merge at a T-junction (PTFE, 8 mm inner diameter, supplied by RS Pro). The resulting mixture then enters a recirculating loop that includes the VD. A separate peristaltic pump (Longer Pump WT600-2J) drives the circulation within this loop. A gas disengagement arrangement is included to remove gases, if any, as illustrated in Figure . The emulsion is collected in a vessel for subsequent use or analysis.

1.

Schematic diagram of a continuous experimental setup with an integrated at-line characterization system.

A portion of the product stream was diverted as a side stream for the at-line characterization. This side stream, with a flow rate of q _E, was directed into a separate holding tank with a capacity of 150 mL. The contents of the tank were stirred using a 3 cm magnetic stirrer operating at 300 RPM, which was sourced from Fisher Scientific. To enable the at-line characterization using the turbidity sensor, a diluent stream comprising deionized (DI) water was introduced into the holding tank at a flow rate of q _D. A dedicated peristaltic pump was employed to maintain a constant volume in the tank by removing the diluted emulsion at a combined flow rate of q _D + q _E. A turbidity sensor (SKU SEN0189, DFROBOT Gravity) was mounted on this outflow line. The sensor was operated in analog mode, and its voltage output was acquired using an Arduino UNO R3 board with a data acquisition frequency of 2 Hz and streamed to a connected laptop. The raw voltage data obtained from the turbidity sensor was processed directly, without the use of any filters or amplifiers, as outlined by Ravi et al.

This study used VD with a throat diameter (d _T ) of 3 mm. Further details regarding the geometry of the device can be found in the work by Simpson and Ranade. The same VD device was used by Ravi et al. The characteristic Euler number ( $\mathrm{\Delta }P/\frac{1}{2}\rho V_T^2$ ) was 32, where ΔP is the pressure drop across VD, ρ is the density, and V _T is the throat velocity. The vortex-based cavitation device (VD) used in this work did not have any moving parts. The intensity of the shear and cavitation occurring in the device is therefore a function of the flow rate through the device. Therefore, if a once-through configuration of the device is used, the extent of shear/cavitation is dictated by the net flow rate of the emulsions. For decoupling the extent of shear/cavitation from the net flow emulsions, a loop configuration, as shown in Figure was used in this work. This loop configuration allows decoupling of the intensity of shear and cavitation in the emulsification device, which is determined by the flow through VD (Q) and net flow rate of the emulsion (q). For a desired net flow rate of the emulsion, the flow rate through the cavitation device can be selected in a way to achieve the desired shear and cavitation, that is, the desired DSD. The loop configuration, therefore, allows the system to be robust and scalable and provides the ability to achieve the desired DSD for the desired capacity.

FO (ρ_o = 930 kg/m³ and μ_o = 0.053 Pa·s; Irish Health Oils, Evergreen, Ireland) and skimmed milk with 3% fat (ρ_M = 1030 kg/m³ and μ_M= 0.002Pa·s; Golden Vale, Spar, Ireland) were used for producing oil-in-milk emulsions. Preliminary emulsification experiments were carried out without surfactants. However, FO in milk emulsions was found to be stable only for 2 h in the absence of a surfactant. Therefore, for all the subsequent experiments, sodium dodecyl sulfate (SDS) was used as the surfactant (Fisher Scientific, UK). The SDS was selected based on the a previous study by Patil and Gogate. Sodium dodecyl sulfate (SDS, also referred to as SLS) was chosen as the surfactant because it is considered a GRAS (Generally Recognized as Safe) ingredient for food-based applications according to the guidelines published in 21 CFR 172.822. As a small-molecule surfactant, SDS rapidly adsorbs to the oil–water interface. The binding of SDS to proteins can induce partial denaturation, exposing hydrophobic regions that enhance protein adsorption to the droplet surface. SDS also imparts a negative charge to the proteins and interfaces, increasing the electrostatic repulsion between droplets. The overall effect of SDS at the concentration used in this study led to enhanced interfacial coverage and robust stabilization due to the combined effects of rapid surfactant adsorption, protein unfolding, and increased electrostatic repulsion. The synergy between the surfactant and protein interactions at the interface was found to provide adequately stable emulsions. Initially, FO in milk emulsions was produced with different concentrations of surfactants: 0.2, 0.4, and 0.8% (w/v), and the surfactant was mixed in milk. It was observed that further increase in the surfactant concentration beyond 0.4% (w/v) led to less than a 5% change in the Sauter mean diameter (d ₃₂) and DSD (see the results shown in Figure S2 of Section S2 SI). Based on these results, for all subsequent experiments, 0.4% (w/v) SDS was used as the surfactant.

The oil flow rate (q _o) and milk flow rate (q _M) were selected to produce emulsions with desired oil volume fractions (α_o) of 0.05, 0.15, 0.30, and 0.45 by using $q_{\mathrm{o}}=\frac{{\alpha }_{\mathrm{o}}{q}_{\mathrm{M}}}{1-{\alpha }_{\mathrm{o}}}$ . In order to facilitate comparison with RO in water emulsions, emulsification experiments of FO in milk were conducted by setting the required pressure drop across VD (the corresponding circulation flow rate through the loop was set for the appropriate pressure drop). The net flow rate of the emulsions, q (q _o + q _M), was selected to achieve the Q/q values of 1, 5, 20, and 100. The FO in milk emulsions produced at these Q/q values was compared with that in previously published studies. The operating parameters used in the experiments are listed in Table .

1. Details of the Experiments Performed to Produce Emulsions (Flow Rates in mL/min).

		Q = 1390 mL/min ΔP = 100 kPa		Q = 1570 mL/min ΔP = 150 kPa		Q = 1690 mL/min ΔP = 200 kPa
αo	Q/q	q o	q M	q o	q M	q o	q M
0.05	1	69.50	1320.50	78.50	1491.50	84.50	1605.50
	5	13.90	264.10	15.70	298.30	16.90	321.10
	20	3.48	66.025	3.93	74.575	4.23	80.275
	100	0.70	13.21	0.79	14.92	0.85	16.06
0.15	1	208.50	1181.50	235.50	1334.50	253.50	1436.50
	5	41.70	236.30	47.10	266.90	50.70	287.30
	20	10.43	59.075	11.78	66.725	12.68	71.825
	100	2.09	11.82	2.36	13.35	2.54	14.37
0.30	1	417.00	973.00	471.00	1099.00	507.00	1183.00
	5	83.40	194.60	94.20	219.80	101.40	236.60
	20	20.85	48.65	23.55	54.95	25.35	59.15
	100	4.17	9.73	4.71	10.99	5.07	11.83
0.45	1	625.50	764.50	706.50	863.50	760.50	929.50
	5	125.10	152.90	141.30	172.70	152.10	185.90
	20	31.28	38.225	35.33	43.175	38.03	46.475
	100	6.26	7.65	7.07	8.64	7.61	9.30

The droplet size distribution (DSD) of the produced emulsions was analyzed using a Malvern Mastersizer 3000 (MS) (Malvern Panalytical Ltd., UK). In the MS, the refractive indices of flaxseed oil (FO) and milk were set to 1.4795 and 1.3455, respectively, for both the red (632.8 nm) and blue (470 nm) lasers. Water served as the dispersant medium at room temperature (20 °C). The emulsion samples were introduced into the dispersant tank, where they were mixed with water and circulated through the flow cell for DSD analysis using the lasers. During measurements, the obscuration level was maintained between 5–10%, and the stirring speed was kept at 2500 rpm, following the protocol established by Upadhyay et al.

In order to assess reproducibility, the FO in milk emulsion experiments were repeated three times, and error bars for both the DSD and Sauter mean diameter (d ₃₂) were included wherever applicable. Potential sources of experimental errors include inaccuracies in measuring the flow rates, pressure drops, and DSD values. Flow rates were recorded using a digital flow meter (Krohne, Model: AF-E400) with an accuracy of ±5%, while pressure drop readings were taken using a pressure gauge (Digitron, 2023P), with a measurement range of 0–300 kPa and an accuracy of ±5%. These instrumentation limitations contribute to the uncertainty in the DSD and d ₃₂ measurements. The observed variation in DSD and d ₃₂ in triplicate experiments was found to be within ±10%.

The measured DSDs were expressed as the sum of three droplet populations (j = 1, 2, and 3) represented by the sum of three log-normal distributions as

$$f(d_{\mathit{mi}})=\sum _{j=1}^3{w}_j{f}_j(d_{\mathit{mi}})\mathrm{w}\mathrm{here}{f}_j(d_{\mathit{mi}})=\frac{1}{d_{\mathit{mi}}{\sigma }_j\sqrt{2\pi }}{e}^{[-{(\ln d_{\mathit{mi}}-{\mu }_j)}^2/2{\sigma }_j^2]}$$ 1

where d _mi is the droplet diameter of the i ^th bin, w _j is the volume fractions of the j ^th log-normal function, μ _j is the mean of the j ^th log-normal function, f _j (d _mi )­Δd _mi is the volume fraction of oil droplets of the j ^th population with diameters between d _mi and d _mi + Δd _i , and σ _j is the variance of the j ^th log-normal function. σ _j is the standard deviation of the j ^th log-normal function. The sum of the volume fractions of the three droplet populations is one:

$$\sum _{j=1}^3{w}_j=1$$ 2

Using eq , the number of parameters in eq is eight. The measured droplet size distribution (DSD) was fitted to extract a set of eight parameters: the mean (μ₁, μ₂, μ₃) and standard deviation (σ₁, σ₂, σ₃) for each of the three component distributions, along with two volume fractions (w ₁, w ₂). These parameter values were determined using the nonlinear optimization tool available in MS Excel by minimizing the sum of the squared errors between the measured and fitted data. Sample 3 LNF fitting for the DSD is shown in Figure S3 of section S3 in SI.

2.2. Development of the Calibration Equation and the Application of At-Line Characterization

A previous published study by Ravi et al. on the at-line characterization of droplet size distributions of rapeseed oil (RO) in water emulsions was performed using a low-cost turbidity (voltage) sensor integrated with an ANN-based soft sensor. The turbidity sensor output was first calibrated against a commercial turbidimeter (VELP Scientifica) to establish a linear correlation between the voltage and oil volume fraction, as described in Section S4 of SI. The calibration equation was used to convert the voltage values to NTU values. A schematic diagram (Figure S4a), photograph (Figure S4b), and procedure to develop the calibration equation are provided in Section S4 in the Supporting Information. The experimental DSDs obtained from the Malvern Mastersizer 3000 were represented by using three log-normal functions, yielding eight fitting parameters per condition. These parameters were then expressed as a function of Q/q using the power law equation, enabling the generation of approximately 10⁵ synthetic data sets to ensure adequate ANN training coverage across the operating space. The ANN was trained using this synthetic data set and subsequently validated against the independent experimental Mastersizer DSD data. The validation included a comparison of the predicted and measured characteristic diameters (D ₁₀, D ₅₀, D ₉₀, and d ₃₂). This methodology therefore provides a reproducible, inexpensive, and rapid approach for the at-line estimation of full DSDs in continuous emulsification processes.

A similar procedure was followed in this work to relate the acquired voltage data from diluted FO in milk emulsions to NTU. This recalibration was required since, unlike the previous work with the RO–water system, in this work, milk was used as the continuous medium in which FO droplets were suspended. Milk is a complex fluid consisting of fat globules dispersed in water with casein proteins acting as emulsifiers. Since the soft sensor measurements were conducted after significant dilution (the range of diluted volume fraction of FO in milk was 10^–6 to 10^–4), major differences between the two systems were not expected. However, given the differences in the nature of the emulsions and refractive indices, recalibration was performed. It is important to note that the at-line turbidity shows the highest voltage when the oil fraction in the measurement sample is zero, and the voltage decreases as the oil volume fraction increases. The following relationship (eq ) was obtained between NTU and voltage for the FO–milk system (see Figure a):

$$NTU=S(V_{\max }-V),\mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}S=(520\pm 15)\mathrm{a}\mathrm{n}\mathrm{d}{V}_{\max }=3.8\pm 0.05$$ 3

2.

(a) Relationship between the voltage and turbidity (NTU) and fitted lines are given by eq . (b) Parity plot of the Sauter mean diameter obtained from eq and Mastersizer.

The parameters of eq obtained for the FO–milk system are within 10% of those reported by Ravi et al. for RO in water emulsions. S was changed from 475 to 520, and V _max = 3.75 to 3.8 for the oil–water system and FO–milk system.

Before proceeding with the use of the voltage sensor data for the estimation of DSD, the potential sensitivity of the acquired voltage data to potential disturbances was evaluated. For diluting the emulsions for voltage measurements, deionized water with a turbidity of ∼0.1 NTU was used to minimize background scattering. If the turbidity of the dilution water increased by 2 orders of magnitude (from 0.1 to 10 NTU), the sensor voltage changed by 0.06 V (from 3.80 to 3.74 V), leading to a difference of about 30 NTU in the measurements. Typically, the turbidity of DI water is less than 0.2 NTU, and therefore, such small variations in the turbidity of the DI water used for dilution are not expected to influence the results. To assess the effect of the fat content in milk, samples with up to 6% added fat were tested. The baseline voltage changed from 3.80 to 3.70 V (a 0.1 V shift with a corresponding change in measured turbidity of ∼50 NTU). This indicates that it is important to recalibrate the sensor for milk with significantly different fat content. Emulsion production was conducted at 20 ± 5 °C. Within this moderate range of temperature, no measurable effect on the voltage output was observed, indicating the robustness to moderate variations in the processing temperature. In this study, the data acquisition rate was 2 Hz. At this data acquisition frequency, the sensor-generated noise was found to be negligible. Therefore, the methodology presented here can be considered robust.

Following Ravi et al., the relationship between the Sauter mean diameter and voltage can be established as follows:

$$d_{32}=\frac{0.9\times 3}{520(-\frac{\mathit{dV}}{d{\epsilon }_o})}$$ 4

A comparison of the Sauter mean diameters estimated from the voltage data using eq and those measured using the Mastersizer is shown in Figure . It can be seen that the data acquired from the inexpensive voltage sensor can provide an excellent estimate of the Sauter mean diameter (d ₃₂) of FO in milk emulsions.

The at-line methodology of DSD characterization based on the dilution of the produced emulsion, as presented by Ravi et al., was used here for characterizing FO in the milk system. The same turbidity sensor was used, and a similar trend of decreasing voltage with an increase in the dilution oil fraction (ε _o) was observed. Since the continuous emulsions had much higher values of oil volume fractions (0.05–0.45), a side stream with continuous dilution (Figure ) was used. The oil fraction in the diluted stream (ε_o) was determined from the flow rates of side stream (q _E), dilution water stream (q _D), and oil volume fraction of the produced emulsion (α_o) as

$${\epsilon }_{\mathrm{o}}=\frac{q_{\mathrm{E}}{\alpha }_{\mathrm{o}}}{q_{\mathrm{D}}+q_{\mathrm{E}}}$$ 5

The dilution flow rates used in the present work were calculated using eq . The maximum and minimum dilution flow rates were found to be q _Dmax = 2250 mL/min and q _Dmin = 420 mL/min, corresponding to a dilution oil volume fraction from 0.0002 to 0.0007.

To perform the at-line characterization, the emulsion was diluted by adjusting the flow rate of the diluent, which was regulated by manually changing the RPM of a peristaltic pump. The resulting mixture was then thoroughly mixed in a continuously stirred tank reactor (CSTR) to ensure homogeneity. The well-mixed, diluted emulsion was passed through a turbidity sensor that recorded the voltage values corresponding to the oil volume fraction. During this process, the flow rate was varied stepwise from q _Dmax to q _Dmin, and the corresponding voltage data was recorded over time. An example of this voltage data is shown in Figure S5a for the sample data for Q/q = 100 and 30% flaxseed oil in milk. In Section S4 of SI, Figure S5b shows the dilution oil volume fraction (ε _o) in the sample passing through the at-line turbidity sensor (calculated using eq ). After the acquisition of the voltage data for a suitable range of oil volume fractions, eq was used to convert the voltage data to NTU data. The turbidity in NTU was then related to the DSD, following the methodology presented by Ranade and Ranade and Ravi et al.

3. Results and Discussion

3.1. Droplet Size Distribution (DSD) of FO in Milk Emulsions

The shear and hydrodynamic cavitation generated in the VD cause droplet breakage and generate a fine emulsion from the oil and aqueous streams fed to it. The DSD of the generated emulsion depends on (a) the physical properties of the considered oil–aqueous system (primarily density, viscosity, and interfacial tension of the oil and aqueous phases) and the extent of shear/cavitation generated in the device, (b) the shear/cavitation generated in the VD, and (c) the ratio of flow through the loop (Q) and net flow of emulsion (q). Preliminary experiments indicated that the presence of proteins in milk as natural emulsifiers was not adequate to prevent coalescence beyond ∼2 h. The addition of an external surfactant, SDS, lowered the interfacial tension from ∼52 to ∼32 dyne/cm, thereby facilitating droplet disruption and a much more stable emulsion by enabling rapid coverage of newly formed interfaces. Proteins subsequently reinforce this stabilization through viscoelastic interfacial layers. Beyond lowering the interfacial tension, SDS–protein interactions play a key role in determining emulsion stability. SDS adsorption imparts a strong negative charge at the interface, generating electrostatic repulsion between droplets. Simultaneously, the binding of SDS to milk proteins promotes partial unfolding, which exposes hydrophobic domains and enhances their ability to anchor at the oil–milk interface. The resulting mixed interfacial films, composed of both proteins and SDS, provide complementary stabilization mechanisms: SDS ensures short-time scale stabilization during droplet formation, while proteins reinforce long-term stability through viscoelastic interfacial layers. This synergy explains why no significant change in DSD was observed beyond 0.4% w/v SDS, as interfacial sites were already saturated with a stable protein–surfactant network. Therefore, this work was focused on investigating the emulsions of FO in milk with SDS as a surfactant. Therefore, the influence of the physical properties of the oil and aqueous phases was not investigated in this work.

3.1.1. Effect of Q/q

The influence of Q/q on the DSD of FO generated in milk emulsions is shown in Figure for the four values of oil volume fractions (α_o) of 0.05, 0.15, 0.30, and 0.45. These results are shown here only for the operating pressure drop across VD at ΔP = 200 kPa. The corresponding results for the other two operating conditions, ΔP = 100 and 150 kPa, are shown in Figures S6 and S7 of the SI, respectively. It can be seen from Figure that, as intuitively expected, as Q/q increases, the DSD shifts leftward toward smaller droplet sizes. The DSD exhibited a bimodal distribution, particularly at higher volume fractions of oil. The observed bimodality in the droplet size distribution (DSD) provides a mechanistic fingerprint of the breakage caused by two distinct mechanisms: shear and cavitation. The submicron (∼10 μm) peak arises from cavitation-induced breakage, where bubble collapse generates localized hotspots and microjets capable of fragmenting droplets into very fine sizes. The second peak at ∼10 μm originates from the intense shear and circulation in the vortex chamber, which fragments the larger droplets. The influence of (Q/q) on the intensity of cavitation is not significant, and therefore, the droplet sizes originating from cavitation events are not sensitive to (Q/q). Unlike this, the shear prevailing in the vortex chamber and experienced by oil droplets (because of the longer residence time) is a strong function of (Q/q), which leads to a significant change in the sizes of larger droplets with an increase in (Q/q). At low values of the oil volume fraction, as Q/q increases, the maximum droplet diameter decreases significantly. However, the peak at a lower size does not change much. At higher oil volume fractions, the influence of Q/q is more pronounced.

3.

Influence of Q/q on the DSD of FO in milk emulsions: (a) α_o = 0.05, (b) α_o = 0.15, (c) α_o = 0.30, and (d) α_o = 0.45 at ΔP = 200 kPa. The symbols denote the experimental data. The dotted lines denote eq with the parameters listed in Table .

The DSDs of all 16 operating conditions were fitted with the sum of three log-normal function distributions (eq ) using Excel’s nonlinear solver. The quality of the fit was assessed by both R ² and residual analysis. Across all conditions, R ² values exceeded 0.98, while the residuals were consistently bound between −0.1 and +0.1, with no systematic trends observed. This indicates that the selected model adequately captures the experimental data. The values of the fitted parameters at ΔP = 200 kPa are listed in Table . The values of the fitted parameters for the other two pressure drops (ΔP = 100 and 150 kPa) are listed in Tables S2 and S3 in section S5 in the Supporting Information (SI).

2. Fitted Parameters of eq for Describing DSDs Obtained at ΔP = 200 kPa.

α o	Q/q net	W 1	W 2	μ 1	σ 1	μ 2	σ 2	μ 3	σ 3
0.05	1	0.12	0.15	–0.50	0.23	0.00	0.37	2.96	1.23
	5	0.15	0.20	–0.44	0.24	0.28	0.45	2.37	0.87
	20	0.15	0.30	–0.41	0.24	0.48	0.51	2.16	0.57
	100	0.14	0.24	–0.41	0.23	0.33	0.44	1.72	0.66
0.15	1	0.04	0.08	–0.37	0.24	0.38	0.48	3.33	0.72
	5	0.05	0.12	–0.35	0.24	0.49	0.52	2.92	0.54
	20	0.05	0.15	–0.34	0.24	0.53	0.52	2.62	0.45
	100	0.05	0.18	–0.37	0.22	0.50	0.49	2.37	0.42
0.30	1	0.07	0.26	–0.37	0.23	0.56	0.51	2.25	0.42
	5	0.07	0.14	–0.36	0.25	0.51	0.53	2.89	0.61
	20	0.11	0.20	–0.39	0.24	0.41	0.49	2.71	0.78
	100	0.11	0.29	–0.37	0.25	0.57	0.54	2.45	0.51
0.45	1	0.06	0.10	–0.39	0.24	0.33	0.46	3.22	0.85
	5	0.07	0.17	–0.35	0.24	0.53	0.53	2.77	0.60
	20	0.07	0.22	–0.35	0.24	0.59	0.54	2.50	0.48
	100	0.07	0.26	–0.37	0.23	0.56	0.51	2.25	0.43

3.1.2. Effect of Oil Volume Fraction (α _o)

To better understand the influence of the oil volume fraction α_o, the data shown in Figure is plotted in a different way in Figure . The corresponding results showing the influence of α_o on the DSD for emulsions produced at ΔP = 100 and 150 kPa graphs are shown in Figures S8 and S9 of the SI. The influence of α_o on the DSD is clearly seen in Figure . As α_o increases, the magnitude of the first peak, representing submicron-sized droplets, decreases, and the peak at around 10 μm increases.

4.

Influence of the FO volume fraction on the DSD of FO in milk emulsions: (a) Q/q = 1, (b) Q/q = 5, (c) Q/q = 20, and (d) Q/q = 100 at ΔP = 200 kPa. The symbols denote experimental data. The dotted lines denote eq with the parameters listed in Table .

It will also be instructive to examine the influence of the operating pressure drop across the device on the generated DSD, as discussed in the following.

3.1.3. Effect of Pressure Drop (ΔP)

The measured DSDs for Q/q = 20 at different pressure drops across VD are shown in Figure for four different values of the oil volume fraction. As the pressure drop increases, a general reduction in the droplet size is observed, attributed to the enhanced cavitation that promotes droplet breakup. At higher values of the pressure drop, the fraction of droplets with diameters in the range of 2 to 4 μm was found to increase, as indicated in the DSDs shown in Figure . The influence of the operating pressure drop on the DSD at other values of Q/q is shown in Figures S10–S12 of the SI. It can be seen that the trends for all values of Q/q are similar.

5.

Influence of pressure drop across VD on the DSD of FO in milk emulsions: (a) α_o = 0.05, (b) α_o = 0.15, (c) α_o = 0.30, and (d) α_o = 0.45 at Q/q = 20. The symbols denote experimental data. The dotted lines denote eq with the parameters listed in Tables , S2, and S3.

Though we have not investigated the influence of physical properties on the DSD in this work, it will be instructive to compare the DSD of FO in milk emulsions with more widely studied oil-in-water emulsions.

3.1.4. Comparison with Rapeseed Oil-in-Water (RO) Emulsions

For this purpose, we have selected previously published results on rapeseed oil (RO) in water emulsions generated using the same vortex-based cavitation device. The DSDs obtained for these two different oil and aqueous phase systems at the same ΔP are compared in Figure . The comparison is presented for three values of the oil volume fractions (0.15, 0.3, and 0.45) and two values of Q/q (1 and 100). It can be seen that at low values of the oil volume fraction, FO in milk emulsion is much finer than that in the RO in the water emulsion, despite the same device and operating conditions. As the oil volume fraction increases, the difference between the two narrows and is not as significant as that observed at lower values of the oil volume fraction. Several factors, such as different surfactants, the presence of natural emulsifiers, vapor pressure, and viscosity, may cause the observed differences in the droplet sizes obtained with RO–water and FO–milk emulsions.

6.

Comparison of DSDs of FO in milk emulsions with those of RO in water emulsions: (a) α_o = 0.15, (b) α_o = 0.30, and (c) α_o = 0.45 at ΔP = 200 kPa. The symbols denote experimental data. Data for RO in water emulsions is taken from Ravi et al. Columns L and R show the results for Q/q = 1 and 100, respectively.

While DSDs provide detailed information on the generated emulsions, it will be useful to examine the influence of the oil volume fraction, Q/q, and ΔP, on the key characteristic diameters of the generated emulsions. This is examined in the following section.

3.2. Sauter Mean Diameter and Span of FO in Milk Emulsions

The measured DSDs were processed further to calculate the Sauter mean diameter, d ₃₂ (which is the ratio of the third moment and second moment of DSD), as well as percentile diameters, D ₁₀, D ₅₀, and D ₉₀ (corresponding diameters below which 10, 50 and 90% of the droplet volume falls). The influence of the pressure drop on the Sauter mean diameter for four different oil volume fractions is shown in Figure . It can be seen that as Q/q and ΔP increase, the Sauter mean diameter decreases. At a higher ΔP, the energy dissipation per unit mass in the cavitation device increases, which enhances cavitation: both the number density of collapsing cavities (significant increase) and the intensity of cavity collapse (moderate increase). At higher oil volume fractions, the shielding effect of the neighboring droplets is more pronounced than that at lower fractions. However, the increased number density of collapsing cavities generated at higher ΔP values reduces this shielding effect. As a result, the influence of enhanced cavitation on droplet breakage is stronger at higher oil volume fractions. Consequently, the reduction in d ₃₂ caused by increasing ΔP from 100 to 200 kPa is more pronounced (∼42%) at higher oil volume fractions than at lower fractions (∼14%).

7.

Influence of pressure drop across VD on the Sauter mean diameter: (a) α_o = 0.05, (b) α_o = 0.15, (c) α_o = 0.30, and (d) α_o = 0.45. The symbols denote experimental data. The lines denote the values estimated using eqs to .

For understanding the influence of the oil volume fraction on the Sauter mean diameter, the data shown in Figure are replotted in Figure . The left-hand side of Figure (L) shows the effect of the oil volume fraction on d ₃₂ for a given ΔP as a function of Q/q. The right side of Figure (R) shows the effect of Q/q on d ₃₂ for a given ΔP as a function of the oil volume fraction. The data indicates that the Sauter mean diameter is influenced by the oil volume fraction in a complex way. At low values of the oil volume fraction, there is almost no influence of the oil volume fraction on the Sauter mean diameter. This was also observed by Thaker and Ranade. As the oil volume fraction increases, there is a significant influence on the Sauter mean diameter. However, it appears that the influence of the oil volume fraction weakens again at even higher values of the oil volume fraction. The existence of these two regimes was also observed with RO in water emulsions, as presented in previous publications. , It should be noted that the VD used in this work was able to produce droplets of the order of 10 μm with an energy consumption of 10¹ kJ/kg. Compared to this, other competing devices capable of generating droplets of the order of 100 μm require at least an order of magnitude higher energy consumption (Shanmugam et al., Abismail et al., Patil et al.). A previous publication that compared the performance of VD with other devices is cited as well. The Sauter mean diameter is primarily controlled by cavitation phenomena. The intense shear and energy dissipation generated by cavity collapse lead to the generation of fine droplets (∼10 μm), which essentially determines the effective Sauter mean diameter. The experimental data indicates that at low α _o (<α_o,trans), the intensity of cavity collapse is not significantly influenced by the presence of neighboring oil droplets, and no significant shielding effects are observed. Consequently, the Sauter mean diameter remains nearly constant with respect to the oil volume fraction (d ₃₂ ≈ 3 μm). As α_o increases beyond the transition α_o,trans, the intensity of cavity collapse is likely to be reduced by the presence of neighboring droplets (see, for example, the results of numerical simulations for cavity collapse in the presence of two droplets presented by Pandey et al). At such higher values of the oil volume fraction, droplets may also get shielding from cavity collapse. The combined result of these two effects is a gradual increase in the Sauter mean diameter as the oil volume fraction increases. The dependence of d ₃₂ on the oil fraction implies that a higher oil volume fraction leads to a larger d ₃₂, and therefore, reduced emulsion stability and faster creaming are likely. The presented results provide useful guidance on the number of passes needed for achieving the desired d ₃₂, that is, the desired emulsion quality.

8.

Influence of the FO volume fraction (α_o) and Q/q on the Sauter mean diameter: (a) ΔP = 100 kPa, (b) ΔP = 150 kPa, and (c) ΔP = 200 kPa. The symbols denote experimental data. The lines denote the values estimated using eqs to .

Based on these observations, the following correlation (eq ) is proposed for estimating the Sauter mean diameter as

$$d_{32}=d_{321}{E}^{-(0.03+0.3{\alpha }_{\mathrm{o}})}$$ 6

where E is the energy consumption per unit volume of emulsion. E can be estimated from the operating pressure drop, ΔP (kPa), and the ratio of flow rate through the loop (Q, m³/s) and net flow of emulsion (q, m³/s) as

$$E=\frac{\mathrm{\Delta }\mathit{PQ}}{q}$$ 7

d ₃₂₁ is the Sauter mean diameter in microns at E = 1 kJ/m³. The d ₃₂₁ was found to exhibit two regimes and may be estimated (in microns) as

$$d_{321}=3\mathrm{for}{\alpha }_{\mathrm{o}}\le {\alpha }_{\mathrm{o},\mathrm{trans}}$$ 8

$$d_{321}=70{(\mathrm{\Delta }P-{\mathrm{\Delta }P}_{\mathrm{inc}})}^{-0.2}{\alpha }_{\mathrm{o}}\mathrm{for}{\alpha }_{\mathrm{o}}\ge {\alpha }_{\mathrm{o},\mathrm{trans}}$$ 9

where ΔP _inc is the inception pressure drop, which in this case was found to be 57 kPa (Thaker and Ranade). The transition oil volume fraction may be obtained by eq as

$${\alpha }_{\mathrm{o},\mathrm{trans}}=0.043{(\mathrm{\Delta }P-{\mathrm{\Delta }P}_{\mathrm{inc}})}^{0.2}$$ 10

The value of α_o,trans was ∼0.1. It can be seen from Figures and that the proposed correlation was able to capture the complex influence of the pressure drop, Q/q, and oil volume fraction.

Apart from the Sauter mean diameter, other characteristic diameters, like D ₁₀, D ₅₀, and D ₉₀, were estimated from the measured DSD. The overall trends exhibited by these characteristic diameters are similar to those seen for the Sauter mean diameter, which decreases with increasing Q/q and ΔP and increases with increases in α_o. For the sake of brevity, these results are included in Table S4 in Section S7 of the SI. Another characteristic parameter, Span of DSD [(D ₉₀–D ₁₀)/D ₅₀], is also considered one of the important parameters characterizing emulsions. In previous studies by Upadhyay et al. and Mugabi et al., it was shown that the effective viscosity of an emulsion increases with a reduction in the Span of DSD. Therefore, the influence of Q/q, α_o, and ΔP on the Span of the DSDs was examined using the characteristic diameters D ₁₀, D ₅₀, and D ₉₀ obtained from the measured DSDs of all of the produced emulsions. These results are shown in Figure . The ranges of characteristic diameters for all the operating conditions (ΔP, α_o, Q/q) are as follows. D ₁₀: 0.5–1 μm, D ₅₀: 6–25 μm, D ₉₀: 15–45 μm, and d ₃₂: 2–7 μm. It can be seen from this figure that Span reduces as Q/q increases. The DSD becomes narrower with an increase in Q/q. The influence is highest at lower values of Q/q (∼1). The Span also reduces with an increase in α_o. The increase in α_o increases the characteristic diameters, D ₁₀, D ₅₀, and D ₉₀. However, the increase in D ₁₀ and D ₅₀ is much larger than that in D ₉₀, thus causing a reduction in Span. An increase in ΔP reduces the Span. The span of the droplet size distribution, which reflects its polydispersity, was observed to decrease with increasing oil volume fraction (α_o) and flow ratio (Q/q). A lower span indicates a narrower and more uniform distribution of the droplets. For the FO–milk emulsions studied here, this narrowing has direct implications for product performance: emulsions with reduced span are expected to be more stable against creaming and coalescence, exhibit smoother texture and mouthfeel due to the absence of large outlier droplets, and display more predictable rheological behavior during processing. , Previous studies on model oil–water emulsions , linked narrower DSDs to lower effective viscosity; our results demonstrate that these relationships extend to milk systems as well. Thus, controlling the span through operating parameters, such as the pressure drop and flow ratio, provides a practical means of tailoring FO–milk emulsions for enhanced stability.

9.

Influence of Q/q and α_o on Span of the DSD: (a) ΔP = 100 kPa, (b) ΔP = 150 kPa, and (c) ΔP = 200 kPa.

3.3. DSD Prediction Using At-line Characterization Methodology

Previous studies by Ranade and Ranade and Ravi et al. provide a basic methodology for the development of a soft sensor based on an artificial neural network (ANN) for carrying out an at-line estimation of the DSD of the continuously produced oil-in-water emulsions using a turbidity sensor. In this work, we followed the same methodology with the appropriate recalibration and retraining of the ANN for estimating the DSDs of continuously produced FO in milk emulsions.

The methodology involved the representation of the measured DSDs of FO in milk emulsions using eqs and along with the corresponding eight parameters (listed in Tables , S2, and S3). These parameters were then empirically expressed as a function of Q/q (see Table S5) and were used to generate synthetic data of DSDs and the corresponding turbidity (in NTU) using the model presented by Ranade and Ranade. 10⁵ sets of data (DSD, oil volume fraction in the sample, and turbidity) were generated and used for training the ANN, and predictions were then validated with the experimental data. The turbidity and oil volume fraction in the diluted sample (ε _o) were used as inputs, and the eight parameters of eqs and for describing DSD were used as outputs. The DSD data was collected for 12 different emulsions produced continuously, each defined by a specific oil volume fraction and Q/q ratio. For each emulsion, at-line measurements were performed using four different diluent flow rates, resulting in oil volume percentages in the measurement samples of 0.037, 0.045, 0.052, and 0.06%. The corresponding measured voltage readings were converted to turbidity (NTU) using calibration eq , and these turbidity values, along with the oil volume fractions, were used as inputs to a trained ANN to estimate the DSDs. The sensitivity of the predicted DSDs to the S value used in eq is illustrated in Figure a, where the ANN-based DSD predictions are compared to those obtained from the Mastersizer. It can be seen that the results are quite robust with respect to the value of S. The influence of the volume fraction of the diluted sample on the predicted DSD is shown in Figure b. The results indicate that variations in the oil volume fraction had almost no impact on the estimated DSDs. This finding is encouraging, as it suggests that adjusting the diluent flow rate may not be necessary. A single diluent flow rate is sufficient for an accurate at-line DSD estimation. Consequently, all further DSD predictions were based on voltage measurements taken at a fixed dilution rate. The DSDs predicted from the at-line voltage measurements using S = 520 show very good agreement with the DSDs measured by the Mastersizer. The prediction accuracy for FO–milk (R ² = 0.967) was comparable to that of RO–water case published earlier (R ² = 0.988).

10.

Comparison between DSDs predicted by the ANN and those obtained from the Mastersizer for a representative emulsion with α_o = 0.3 and Q/q = 20: (a) impact of the slope parameter S in eq on the DSD for FO in milk emulsions. (b) Effect of oil volume fraction (ε _o) in the diluted stream passing through the turbidity sensor using S = 520.

The at-line methodology and ANN were used to estimate the DSDs from the voltage data obtained from the turbidity sensor. A comparison of the DSDs estimated using the soft sensor with the DSDs measured using the Mastersizer is shown in Figure a–d for the emulsions produced at ΔP = 200 kPa, for all volume fractions (α_o = 0.05, 0.15, 0.30, and 0.45). The comparison of the estimated and measured DSDs for the emulsions generated at ΔP = 100 and 150 kPa is shown in Figures S14 and S15 of the SI. Experimentally, the emulsions were produced in triplicate, and the droplet size distribution (DSD) and Sauter mean diameter (d ₃₂) were measured for each case. The experimental variability was found to be within ±5%, as reflected in the error bars in the revised figures. When comparing the predicted and experimental DSDs, the coefficient of determination (R ²) was consistently ≥0.95, indicating a strong agreement between the ANN predictions and Mastersizer measurements. Therefore, it can be seen from these figures that the ANN-based soft sensor is able to estimate DSDs quite well.

11.

DSD comparison of experimental data (symbols) and predicted data using ANN (continuous lines) for emulsions produced at ΔP = 200 kPa for Q/q = 1, 5, 20, and 100: (a) α_o = 0.05, (b) α_o = 0.15, (c) α_o = 0.30, and (d) α_o = 0.45.

The complete DSDs obtained from the measurements were utilized to calculate the key characteristic droplet sizes, including d ₃₂, D ₁₀, D ₅₀, and D ₉₀. These characteristic diameters were also calculated from the DSDs estimated using a soft sensor. A comparison of the characteristic diameters estimated from the Mastersizer and ANN-based soft sensor is shown in Figure a–d for all tested pressure drops (ΔP = 100, 150, and 200 kPa).

12.

Parity plots of the characteristic diameters (a) d ₁₀, (b) d ₅₀, (c) d ₉₀, and (d) Sauter mean diameter (d ₃₂) at different pressure drops.

It can be seen from Figure that the characteristic diameters from the soft sensor are in good agreement with those obtained from the Mastersizer measurements. Across all operating conditions, R ² values were ≥0.96 for D ₁₀ and d ₃₂ with relative RMSE < 5%. For D ₅₀, the R ² was 0.90–0.93 with a relative RMSE of 6–10%. For D ₉₀, the R ² was 0.96–0.98 with a relative RMSE of 10–15%. The RMSE for D90 was found to be higher than that for other characteristic diameters since D ₉₀ is very sensitive to the shape of the upper tail of the distribution. Overall, the ANN-based soft sensor exhibits robust predictive capability for different characteristic diameters, effectively representing both the fine and coarse ends of the particle size distribution.

The presented results on FO in milk emulsions and the demonstrated applicability of the at-line characterization of these emulsions using a simple voltage-based turbidity sensor and ANN will provide a platform for further work on achieving the desired oil-in-milk emulsions with tailored DSDs.

4. Conclusions

In the present study, for the first time, FO in milk emulsions was produced in continuous mode using a vortex-based hydrodynamic cavitation device. The influence of the key operating parameters, pressure drop across the device (ΔP = 100, 150, and 200 kPa), oil volume fractions (α_o = 0.05, 0.15, 0.30, and 0.45), and flow rate ratio (Q/q = 1, 5, 20, and 100) on the DSDs of FO in milk emulsions was investigated. The key characteristic diameters, namely, the Sauter mean diameter (d ₃₂) and other characteristic diameters (D ₁₀, D ₅₀, and D ₉₀) were calculated. An appropriate correlation for capturing the complex influence of the operating parameters on d ₃₂ was developed. For the first time, the ability to estimate the full DSD and key characteristic diameters using at-line measurements of turbidity sensors with the help of ANN-based soft sensors was demonstrated for FO in milk emulsions. The key conclusions from this study are

• The FO in milk emulsions produced using vortex-based hydrodynamic cavitation in continuous mode exhibited bimodal DSDs (similar to those observed in RO in water emulsions).

• The DSD moves leftward (toward smaller sizes), and the characteristic diameters (d ₃₂) decrease with an increase in Q/q and ΔP. The oil volume fraction (α_o) exhibited an opposite effect. The characteristic diameters increase with an increase in α_o.

• The influence of the key operating parameters on d ₃₂ can be estimated using eq . The results obtained from eq are in good agreement with the experimental data.

• The potential of using an inexpensive turbidity (voltage) sensor and an ANN-based soft sensor for carrying out at-line measurements and estimations of DSD and characteristic diameters for FO in milk emulsions over a broad range of oil volume fractions (at least up to 0.45) was demonstrated.

• The DSDs as well as characteristic diameters (d ₃₂, D ₁₀, D _50, and D ₉₀) estimated using the at-line sensor and ANN-based soft sensor showed good agreement (within ±12%) with the results obtained from the Mastersizer.

The demonstrated use of vortex-based hydrodynamic cavitation in a loop configuration for continuous emulsification and the at-line ANN–turbidity approach for droplet size measurement offer broader potential for application to diverse emulsions across the food sector and related industries.

Glossary

Nomenclature

d ₃₂

Sauter mean diameter (μm)

d _i

diameter of the i ^th droplet (μm)

D ₉₀

droplet diameter at 90 vol % in the DSD curve (μm)

D ₁₀

droplet diameter at 10 vol % in the DSD curve (μm)

D ₅₀

median of volume distribution; 50 vol % in the DSD curve (μm)

d _T

throat diameter (mm)

Eu

Euler number (−)

ΔP

inlet pressure drop (kPa)

Q

volumetric flow rate in the recirculation loop (m³/s)

q _oil

volumetric flow rate of oil (m³/s)

q _water

volumetric flow rate of water (m³/s)

q _E

volumetric flow rate of the emulsion (m³/s)

q _D

volumetric flow rate of the dilution stream (m³/s)

Re

Reynolds number, (−)

S

Slope, (−)

T

temperature (°C)

t

time (s)

V

voltage

V _T

throat velocity (m/s)

Glossary

Greek Letters

α_o

oil volume fraction, (−)

ρ_o

density of flaxseed oil (kg/m³)

ρ_M

density of milk (kg/m³)

μ_o

viscosity of flaxseed oil (mPa·s)

μ_w

viscosity of water (mPa·s)

σ

interfacial tension (N/m)

η

energy efficiency for droplet breakage (%)

τ

turbidity (1/m)

ε_o

oil volume fraction in the dilution stream (−)

Glossary

Acronyms

ANN

artificial neural network

CSTR

continuously stirred tank reactor

DSD

droplet size distribution

HC

hydrodynamic cavitation

NTU

nephelometric turbidity unit

FO

flaxseed oil

VD

vortex diode

PDF

probability density function

SI

Supporting Information

SDS

Sodium dodecyl sulfate

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.5c08173.

• Photograph of the emulsion production with at-line characterization; effect of the surfactant; fitting log-normal plot and parameter sample plots; experimental setup and procedure for calibrating the turbidity sensor; effect of Q/q and oil volume fraction (α_o) on the DSDs; Sauter mean diameter (d ₃₂) and emulsification efficiency (η); characteristic diameter information, and DSD prediction using the at-line methodology (PDF)

The authors declare no competing financial interest.