Advanced ultrasound techniques for studying liquid–liquid dispersions in confined impinging jets

In impinging jets, two liquid streams collide at high velocities. Depending on whether the liquids are miscible or immiscible, impinging jets result in efficient mixing or the generation of dispersions and find applications in intensified reactions and processing of food, pharmaceuticals, and cosmetics.^1,2

Recently, impinging jets have been used to generate dispersions within the confinement of small channels (confined impinging jets, CIJ) in applications such as intensified solvent extraction and biofuel production.³ In these configurations, the flow patterns and drop size depend on various factors such as fluid flow rates, fluid properties, jets diameter, and impingement angle.⁴ For instance, higher impingement velocities can lead to the breakup of larger drops into smaller ones, thereby reducing the average drop size in the system.⁵ The liquid properties are also important, and liquids with high viscosity or surface tension may form larger drops that persist longer in the flow.⁶ The drop size distribution has significant effects on mass and heat transfer rates in multiphase processes.^7,8 Therefore, it is paramount to measure the drop size distribution and drop volume fractions in such systems using techniques that allow fast, cost-effective, and reliable measurements.^9,10 Drop size and drop volume fraction are important for process efficiency and optimization, performance evaluation, and product quality assurance.¹¹ Current approaches for studying liquid–liquid dispersed flows involve sensors based on conductivity,¹² capacitance,¹³ or local heat transfer,¹⁴ which can be intrusive and potentially disruptive to the flow field. Imaging methods have advanced alongside improvements in digital and fast cameras, image processing capacity, and in high-energy, high-frequency lasers. Optical techniques such as high-speed imaging¹⁵ and laser-based approaches, including planar laser induced fluorescence (PLIF)¹⁶ and particle image velocimetry (PIV),¹⁷ have also been utilized for measurements in liquid–liquid dispersed flows to investigate volume fractions, size distributions, and velocities of the dispersed phase. These optical methods are restricted to transparent test sections and fluids. Liquids with a matching refractive index can be used to increase the volume fractions that can be studied, but this restricts the range of suitable test liquids.¹⁸ Furthermore, common drawbacks in the application of electrical sensors include spatial resolution and the calibration procedure.¹⁹ Additionally, techniques based on magnetic resonance or x-ray imaging can be used in opaque systems but are based on radiation and have cost and safety limitations; they rely on density differences between the phases, which limit the fluid ranges that can be studied.^20,21 Tomographic techniques that have been used in liquid–liquid systems include electrical capacitance tomography (ECT) as demonstrated by Hasan and Azzopardi,²² and electromagnetic tomography (EMT) as shown by Wei and Soleimani.²³ While these techniques offer good accuracy, they are often associated with reduced spatial resolution and involve complex data processing methodologies.

Given these challenges, ultrasound techniques have risen as potential alternatives for measurements in liquid–liquid systems,²⁴ which can deliver rapid, cost-effective measurements that can be used in non-transparent systems and without harmful radiation. Moreover, they are suitable for use in highly concentrated dispersions and in opaque systems.²⁵ Ultrasound techniques have previously been used to study dense solid–liquid flows within fluidized beds.^26,27 Specifically, particle volume fractions ranging from 0.27 to 0.70 and particle size distributions between 500 and 1250 μm were measured. Ultrasound techniques have been applied to porosity and compressibility measurements in liquid suspended particles,²⁸ determining particle size distribution (PSD) as demonstrated by Wöckel et al.²⁹ and Nguyen et al.,³⁰ as well as for evaluating particle and bubble velocity profiles and porosity in porous materials as shown by Zhou et al.³¹ Other research areas that can potentially benefit from fast and noninvasive measurements enabled by ultrasound techniques, include drop coalescence,^32,33 thinning and rupture of liquid sheets,³⁴ and contact line motion.³⁵ The speed of ultrasound in a liquid can vary depending on the liquid type and temperature. In two-phase systems of immiscible liquids or of a solid and a liquid phase, the mixture volume fraction can be calculated from the speed of sound in each phase and in the two-phase mixture. From measurements of the ultrasound attenuation through a dispersion, the size distributions of the dispersed phase can be calculated.²⁶ Ultrasound speed measurements have been employed to calculate drop size distributions ranging from 0.25 to 2 mm and low dispersed phase volume fractions ranging from 0.0053 to 0.042 in liquid–liquid dispersions formed in a stirred vessel.²⁴ 

However, challenges may arise in signal post-processing, especially when the sound waves interact with multiple interfaces in multiphase mixtures. Furthermore, the sensitivity of sound waves to temperature and humidity can complicate technique development in environments where these factors are uncontrolled. Notwithstanding these challenges, ultrasound techniques can swiftly characterize various flow features, making them particularly valuable for online measurements and process control applications.

In this study, we applied ultrasound techniques for the first time to the characterization of dispersions formed in confined impinging jets in small channels. We developed signal post-processing methodologies to obtain from sound speed and attenuation measurements the volume fraction and the drop size distribution in a test channel of 2 mm inner diameter. To validate the ultrasound findings, a high-speed imaging method was employed to capture time-resolved images of the drops at the same time and location as the ultrasound transducers. In Secs. I–V, Sec. II elaborates on the experimental methodology, Sec. III describes the data post-processing for both ultrasound and imaging techniques, Sec. IV discusses the results, and Sec. V summarizes the conclusions.

Dispersions of kerosene oil and glycerol/water were generated in confined impinging jets (CIJ). One of the two phases is expected to be dispersed by the impact with the other phase depending on operating conditions. The two liquid phases have different refractive indexes so they can be imaged, and their properties can be found in Table I. The experimental setup of the CIJ is shown in Fig. 1(a). The impinging jets have an inner diameter of 0.5 mm and consist of two channels drilled perpendicular to each other, in the central plane of an acrylic block with dimensions 51 × 25 × 75 mm³. The formed mixture enters two opposite transparent FEP tubes, each with 2 mm inner diameter. The two fluids are introduced to the jets via two Ecom pumps (ECP2300).

The setup for the high-speed imaging experiments can be seen in Fig. 1(a). Imaging was carried out in one of the FEP tubings, 15 cm downstream of the impinging jets outlet. At the measurement point the tubing was enclosed within a visualization box filled with a 0.10 glycerol/water mixture that has a refractive index (1.344) close to that of the FEP tubing (refractive index of 1.346) to reduce the optical distortions caused by the curved tubing wall, and improve the quality of the high-speed images; for the ultrasound measurements a box is not required. The test section was back illuminated with an LED light. Images were captured with a high-speed camera (Phantom V1212) that had a ×12 monozoom lens (Navitar) and a ×2 add-on lens, at 3000 fps. The camera has 640 × 480 pixels giving a spatial resolution of the images equal to 4.64 μm/pixel. The lens was chosen for its good edge flatness and clarity. Images were processed using an in-house code developed with MIPAR, a commercial software developed within MATLAB's matrix processing algorithms and a recipe-based work flow.³⁶ For each case, 300 images were processed with an error of ± 4.64 μm on estimating the droplet diameter.

In impinging jets, the dispersed phase size distribution is related to the properties of both phases, the design of the jets, and the flow rate of the two phases. To investigate this, we carried out experiments for two different cases, namely cases 1 and 2. In case 1, kerosene oil was the dispersed phase, while in case 2, the aqueous phase (glycerol/water mixture) was the dispersed phase. For each case, we measured both the volume fractions and the drop size distributions under various experimental conditions using both ultrasound and high-speed imaging techniques. For the volume fraction studies, total flow rates of 60 ml/s were used for three volume fractions of the dispersed phase, namely 0.02, 0.05, and 0.10. The same conditions were used for the drop size distribution measurements with ultrasound. However, drop sizes from imaging were only obtained at 0.02 and 0.05 dispersed phase volume fractions for both cases 1 and 2. This is because it is challenging to obtain drop sizes from imaging at high fractions of the dispersed phase because of multiple reflections and overlapping of neighboring droplets.

A schematic diagram of the ultrasound equipment setup is shown in Fig. 1(b). The ultrasound transducers, which are 3/4″ in diameter, were positioned just after the visualization box. To measure drop sizes, two transducers were used: one as a transmitter and the other as a receiver. Both transducers were the RTD2250, which has a diameter of 3/4″ resonating 20 MHz, within a range of 1–40 MHz. Additionally, for measuring the drop volume fraction, two more transducers were employed, serving as both the receiver and emitter. These were the RTD2550, also 3/4″ in diameter, resonating at 2 MHz, with a frequency range of 1–5 MHz. These transducers were both manufactured by Sonatest. The ultrasound signal was generated using a function generator (33500B, Keysight), then amplified by 35 dB using an RF amplifier (TS500-C, Accel Instruments). This signal was transmitted through the test section via transducer T₁. Ultrasound gel is used between the transducers and the tube wall to eliminate any trapped air and reduce sound wave reflections from the wall. The ultrasound signal was then propagated through the dispersion, received by transducer T₂, and collected via the ultrasound pulser/receiver [see Fig. 1(b)], where it was amplified up to 50 dB. Finally, the digitized signal was captured by an oscilloscope (Keysight-DSOX3014T) and transferred to a computer for further signal post-processing.

Figure 2 illustrates the propagation of the ultrasound signal through the tube filled with kerosene oil. It depicts the emission of the signal from transducer T₁ (first pulse), its reflection from the tube wall (second pulse, with multiple reflections visible due to the ultrasound gel application between the transducer and the tube wall and the inner and outer tube walls), and the transmission of the signal through the oil to the opposite side of the wall where it is received by transducer T₂ (last pulse, with multiple reflections, similar to those of transducer T₁). The time of flight (TOF) (the time that the sound wave takes to propagate through the tube inner diameter (2 mm) from T₁ to T₂ was found to be equal to $1.505×10−6 s$ for kerosene oil and $1.335×10−6 s$ for glycerol/water.

The attenuation of ultrasound in a dispersion is influenced by the thermophysical characteristics of the component phases, the drop size, the drop volume fraction, and the emitted ultrasound wave frequency. Mainly, the thermophysical properties encompass the density, thermal expansion coefficient, heat capacity, thermal conductivity, and viscosity of both phases.^39–41 Regarding dispersions, scattering becomes a primary cause of attenuation, linked to the drop size and density.^42,43 Moreover, multiple scattering occurs in the presence of many drops.

The identification of drops in the images is based on the algorithm developed in MIPAR. To avoid counting the same drops, one image was selected for every 20 recorded images. An adaptive threshold was then applied to compare the grayscale value of each pixel in the image against the average of 30 neighboring values. Dark pixels were selected as initial estimation of drop edges. Appropriate dilation and erosion operations were applied to each group of 300 images to adapt the strength of illumination, while the Hough transform was used to search for circles with dark outlines. For example, for images of kerosene oil dispersed in the aqueous phase [Fig. 3(a)], three brackets of the Hough transform were included to cover the necessary range of drop sizes, which are marked in Fig. 3(b) with different colors. When the aqueous phase was dispersed in kerosene oil, where larger drops were present, up to seven brackets were used in the Hough transform to include all possible diameters.

To obtain the drop volume fraction, the speed of sound was measured at an overall mixture flow rate of 60 ml/s, and input volume fractions of 0.02, 0.05, and 0.10 and the results can be seen in Table II. The experimental measurements were repeated three times, and standard deviations smaller than 0.135% were found.

The dispersed phase volume fractions were calculated using Eq. (3) and are also shown in Table II. As can be seen, the sound speed decreases with increasing dispersed input oil volume fraction. This is because the sound speed in oil is less than in the glycerol/water phase. The opposite happens when the dispersed glycerol/water input volume fraction increases.

In Figs. 4 and 5, the measured in situ volume fractions are compared against the input ones for cases 1 (oil dispersed) and 2 (aqueous phase dispersed), respectively. The close agreement between measured and input volume fractions up to 0.10 suggests that there is very little slip between the two phases and that the dispersion resembles that of well-mixed homogeneous flow.⁴⁶ 

To measure the drop size distribution using ultrasound, the ultrasound wave amplitudes were recorded separately for the two single phases, for excitation frequencies ranging from 5 to 18 MHz at intervals of 1 MHz (see Fig. 6, blue color for pure oil phase and pink color for pure aqueous phase).

Figure 6 shows that the ultrasound signal amplitude decreases with increasing emitted frequency. As the emitted frequency increases, the fluids absorb more energy from the sound waves, resulting in a decrease in the amplitude. The amount of sound attenuation in each fluid would depend on various factors, such as the density of the two phases, as well as the frequency of the sound wave. In general, sound waves are less attenuated in kerosene oil compared to glycerol/water due to the lower density of the oil.

The amplitudes were then measured during dispersed flows for the same frequencies, and the attenuation coefficients were calculated from Eq. (2) and are shown in Fig. 7.

Subsequently, an inversion method was applied to compute the droplet size distribution from the measured ultrasound attenuation coefficients (see Sec. III).

The frequency of the emitted ultrasound waves is related to the minimum and maximum drop sizes that can be detected. Higher frequencies generally result in better resolution and the ability to detect smaller drops. This is because high-frequency ultrasound waves have shorter wavelengths, allowing them to interact with and detect small drops more effectively. However, high-frequency waves also experience large attenuation and low penetration depth. Thus, for the selection of the ultrasound frequency, both resolution and penetration depth should be considered. Additionally, the inversion algorithm used in processing the attenuation data plays a significant role in determining the minimum drop size. Advanced inversion algorithms enhance resolution and measurement accuracy by improving data processing and interpretation, which can aid the measurement of small drops.

The drop size distributions obtained from both the ultrasound and imaging techniques are presented in Fig. 8 for case 1 and in Fig. 9 for case 2. Our ultrasound experimental configuration successfully detected drops as small as 32 μm, as shown in Fig. 8. The highest frequency used of 18 MHz corresponded to a short wavelength of 73 μm. This shorter wavelength inherently improves the resolution of ultrasound measurements, allowing for the detection of drops as small as 32 μm. The smallest drop size measured from high-speed imaging was about 16 μm. To compare the two techniques, only drop sizes above 32 μm were used from the imaging data.

As can be seen in Figs. 8(a) and 8(b) for glycerol/water continuous dispersions, the drop sizes measured with both techniques shifted to larger sizes as the dispersed phase fraction increased from 0.02 to 0.05. In addition, the imaging technique captured a higher percentage of smaller drops compared to the ultrasound technique, which gave a higher percentage of larger drops. This discrepancy can be attributed to the limitations of our current function generator, which restricts the emission of high ultrasound frequencies. However, this limitation could be addressed by utilizing instruments that allow high-frequency ultrasound waves (frequencies > 18 MHz). Both techniques gave similar maximum drop sizes. For the 0.02 oil dispersion [Fig. 8(a)], the ultrasound technique measured drop sizes up to 240 μm, while imaging provided drop sizes up to 229 μm; for the case of 0.05 oil dispersion [Fig. 8(b)], ultrasound measured drop sizes up to 325 μm, while imaging gave drop sizes up to 321 μm.

Similarly, for aqueous dispersions (Fig. 9), imaging gave a higher percentage of smaller drops compared to ultrasound. For the 0.02 volume fraction [Fig. 9(a)], ultrasound measured drops up to 374 μm, whereas imaging measured drops up to 380 μm. For the 0.05 oil continuous dispersions [Fig. 9(b)], the largest drop sizes found were 695 μm from the ultrasound and 700 μm from imaging.

Based on the findings, it appears that while both ultrasound and imaging techniques yield similar measurements in terms of drop size ranges, there seems to be a discrepancy in the distribution of drops, with imaging showing a higher percentage of smaller drop sizes compared to ultrasound. This could potentially be attributed to assumptions during data processing for the two techniques. Moving forward, enhancing the measurement accuracy by expanding the frequency range in the ultrasound experiments could help address these differences.

The trends suggest that as the dispersed phase fraction increases, the Sauter mean diameter also increases for both oil and aqueous phases dispersed. This could imply that at higher concentrations, droplets are more likely to coalesce into larger droplets or that the corresponding flow conditions at the impingement area of the jets favor the formation of larger droplets. Moreover, ultrasound measurements are capable of measuring at larger volume fractions compared to imaging, extending the measurements to dispersed phase fraction of 0.10. This is useful in systems where optical methods are challenged by multiple refractions/reflections or crowding, which occur at high dispersed phase fractions.

We applied ultrasound techniques to liquid–liquid dispersions formed by confined impinging jets in small channels (with 2 mm internal diameter) to measure for the first time the phase volume fractions and the drop size distributions. The drop volume fractions were obtained by measuring the speed of sound in the dispersions, while the drop size distributions were obtained from the inversion of the ultrasound wave attenuation coefficient spectra. We further compared the results on drop size distribution with data obtained from high-speed imaging of the dispersions. Experiments were conducted in CIJ for both kerosene oil dispersed (case 1) and glycerol/water dispersed (case 2) systems. Our findings revealed that the speed of sound is directly proportional to the aqueous phase volume fraction and is inversely proportional to the kerosene oil volume fraction. This is because the sound speed in the aqueous phase (1498 m/s) is higher than in kerosene oil (1329 m/s). It was found that volume fractions of the dispersed phase measured with ultrasound were close to the input ones, indicating insignificant slip in the confined impinging jets. Additionally, the drop size distributions obtained from ultrasound and from imaging showed reasonable agreement. The findings show that ultrasound measurement techniques can provide a range of properties in liquid–liquid dispersed flows, even at high dispersed phase fractions, where imaging is limited.

The authors acknowledge the support from Engineering and Physical Sciences Research Council, UK, through the PREMIERE Programme Grant No. EP/T000414/1. C. Duan acknowledges the financial support from UCL and the China Scholarship Council.

The authors have no conflicts to disclose.

Fria Hossein: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Methodology (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Cong Duan: Data curation (equal); Methodology (equal); Writing – review & editing (equal). Panagiota Angeli: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.