Experimental and numerical analysis of the emulsification of oil droplets in water with high frequency focused ultrasound

Highlights

• •High frequency focused ultrasound emulsification of oil droplets in water was investigated through experiments and numerical modeling.
• •The effect of transducer power, frequency, oil viscosity, interfacial tension and initial droplet radius on the emulsification process was assessed.
• •The experiments showed that the acoustic pressure increased from 9.01 MPa to 26.24 MPa as the power was raised from 74 W to 400 W.
• •The main mechanisms of oil dispersion in water are oscillatory, bulb, sheet and catastrophic modes.
• •The numerical model gives reasonable prediction of the trend and magnitude of the experimental acoustic pressure data.

Abstract

Focused high frequency ultrasound emulsification provides significant benefits such as enhanced stability, finer droplets, elevated focal pressure, lowered power usage, minimal surfactant usage and improved dispersion. Hence, in this study, the high frequency focused ultrasound emulsification of oil droplets in water was investigated through experiments and numerical modeling. The effect of transducer power (74–400 W), frequency (1.1 and 3.3 MHz), oil viscosity (10.6–512 mPas), interfacial tension (25–250 mN/m) and initial droplet radius (10–750 µm) on the emulsification process was assessed. In addition, the mechanism of droplet break-up was examined. The experiments showed that the acoustic pressure increased from 9.01 MPa to 26.24 MPa as the power was raised from 74 W to 400 W. At 74 W, the Weber number (We) at the surface and focal zone are 0.5 and 939.8, respectively. However, at 400 W, the We at the transducer surface and focal region reached 2.7 and 6451.8, respectively. Thus, bulb-like and weak catastrophic break up dominates the emulsification at 74 W. The catastrophic break up at 400 W is more vigorous because the ultrasound disruptive stress and We are higher. The time for the catastrophic dispersion of a single droplet at We = 939.8 and We = 6451.8 are 1.01 ms and 0.45 ms, respectively. The numerical model gives reasonable prediction of the trend and magnitude of the experimental acoustic pressure data. The surface and focal pressure amplitudes were estimated with errors of ∼ 6.5% and ∼ 10%, respectively. The predicted Reynolds number (Re) between 74 and 400 W were 8442 and 21364, respectively. The acoustic pressure at the focal region were ∼ 26 MPa and ∼ 69 MPa at frequencies of 1.1 MHz and 3.3 MHz, respectively. Moreover, the acoustic velocities were ∼ 16 m/s and ∼ 42 m/s at 1.1 MHz and 3.3 MHz, respectively. Hence, smaller droplets could be attained at higher frequency excitation under intense catastrophic modes. The Ohnesorge number (Oh) increased from 0.062 to 3.12 with the viscosity between 10.6 mPas and 530 mPas. However, the We remained constant at 856.14 for the studied range. Generally, higher critical We is required for the different breakup stages as the viscosity ratio is elevated. Moreover, the We increased from 25.68 to 1284.22 as the droplet radius was elevated from 15 to 750 µm. Larger droplets allow for higher possibility and intensity of breakup due to diminished viscous and interfacial resistance.

1. Introduction

The formulation of oil-in-water and water-in-oil emulsions is essential to the operation of numerous industrial processes [1], [2], [3], [4], [5], [6], [7], [8], [9]. Emulsification is central to numerous commercial applications such as enhanced oil recovery [1], [2], crude oil transportation [3], petroleum processing [7], [8], pharmaceutical [4], food [6] industries etc. For instance, emulsified fuel in the form of water-in-oil has been widely deployed for improvements in internal combustion engines and industrial burner operations [5], [7], [8]. Emulsified fuels have been shown to provide enhanced combustion efficiency, lowered pollutants formation and reduced fuel usage [5], [7]. Likewise, emulsification of heavy crude oil (µ = 200–400 mPas at room temperature) decreases the flow viscosity and enhances the transportation of these high viscous fuels [3], [11]. Moreover, there are ample reports on the usage of emulsion flooding for enhanced oil recovery (EOR) [1], [2]. The application of emulsification in EOR allows for the increment of the displacement efficiency and boosting of the sweep volume [2]. Due to the tremendous advantages of emulsions in diverse applications, there is significant attention that has been focused on the study of the formation and mechanism of emulsions. There has been a two-fold increment from around 9000 to 20,000 reports on emulsification in the past decade (2012–2022).

Emulsification is usually achieved through low and high energy dispersion approaches [12]. Low energy approaches (typically 10³-10⁵ W/kg) include spontaneous, solvent displacement and phase inversion, membrane emulsification. These techniques allow for the production of small droplets via simple design and relatively less energy requirements. However, they encounter limitations due to significant usage of synthetic surfactants, difficult process scale-up, membrane fouling and low output [13], [14]. Low energy emulsification may require surfactant-to-oil ratio (SOR) of more than 0.5 in order to provide good dispersion. In one study, Yang et al [12] observed the consumption of surfactant during the emulsification of medium chain triglyceride oil in water. Spontaneous emulsification and micro-fluidization were compared for the utilization of Tween 80 and Tween 85 emulsifiers for the production of droplets lower than 100 nm. Spontaneous emulsification required enormous surfactant amount of over 50% of the oil emulsified to attain ultrafine droplet sizes. However, micro-fluidization produced droplet sizes less than 100 nm with the usage of less than 10% emulsifier-to-oil ratio. Several other studies have highlighted the huge surfactant consumption (50–200% of oil treated) [15], [16]. These surface-active agents can be non-biodegradable and thus persist in the environment for a long period. This could result in detrimental impacts on human health and the environment [17]. The challenge is further complicated due to the process scalability hindrance and low emulsion production rate. Hence, high energy approaches are widely utilized in the industry [18]. High energy methods (∼10⁸-10¹⁰ W/kg) include high shear stirring, high pressure homogenization, micro-fluidization and ultra-sonication. Although high energy emulsification provides different benefits over low energy techniques, they continue to face several challenges that impede further developments. For instance, it is very difficult to obtain droplets with sizes less than 200 nm with high shear homogenization [26], [27] and high-pressure homogenization [13]. Moreover, micro-fluidization and high-pressure homogenization often require tremendous operating pressure (up to 500 MPa) and significant number of cycles [13]. Thus, ultrasound emulsification has emerged as an alternative method with potential solutions to challenges encountered by other high energy techniques.

Ultrasound assisted emulsification is often utilized due to benefits such as smaller droplet size, narrow distribution, enhanced stability, lower surfactant and power requirement [9], [10], [21], [22], [23], [24], [25]. In one study, Zhou et al [9] assessed the performance of ultrasound transducer, high speed and high-pressure homogenizers for the emulsification of 20% v/v soybean oil in water. Coarse emulsion was prepared with homogenization at 10000 rpm for 60 s. Thereafter, the three methods were used for further break-up of the coarse emulsion. Acoustic emulsification (f = 20 kHz, P = 300 W) provided improved stability, lower droplet size and better emulsion quality than the two other methods. The emulsion prepared under ultrasound remained stable for seven days. However, emulsions formed with high speed (15000 rpm for 120 s) and high pressure (100 MPa) methods were separated after 2 h and 5 days, respectively. In addition, the Sauter mean diameter (d32) was 0.15 µm, 0.75 µm and 2.4 µm for ultrasound, high pressure and high-speed homogenization, respectively. Similar observation of stability improvement and smaller droplets formation was reported by Abismail et al [21]. In a different study, Kaci et al [22] demonstrated that ultrasound at 1.7 MHz has a potential of forming stable emulsions in the absence of surface-active agents. The emulsion was prepared with sunflower of 5–15% v/v in water with 12 2 cm transducers in a 6 L compartment. There was considerable reduction in the mean droplet size from 160 µm to 1 µm for 5 and 10% sunflower composition. Furthermore, the average droplets reduced from 400 µm to 29 µm for the 15% sunflower composition. Kaci et al [10] further examined the performance of low (f less than 100 kHz) and high (f greater than 100 kHz) frequency ultrasound with high pressure homogenization for the dispersion of pre-emulsion of sunflower oil in water. The coarse emulsion was formed with high-speed homogenization at 13500 rpm in 5 min without the usage of surfactants. High frequency (1.7 MHz) ultrasound exhibited enhanced stability and finer droplets as compared to the low frequency (40 kHz) transducer and high-pressure homogenizer (150 MPa). Although low frequency ultrasound and high-pressure homogenization emulsions degraded within 0–16 days, high frequency ultrasound provided stability for 30 days. Different other studies have established the improved emulsification performance of high frequency ultrasound as compared to low frequency ultrasound and other high energy approaches [13], [19], [20].

Although there are different studies that have highlighted the enhancements provided by ultrasound, further assessments are needed to allow for developments of their design and functionality at varying conditions. To our knowledge, the usage of focused ultrasound at high frequency has not been conducted for the emulsification of crude oil in water. Ultrasound at high frequency can form surfactant free emulsions that remain stable for several days. In addition, focused transducers have the potential to elevate the acoustic pressure at specific locations, decrease energy usage and boost emulsification process. In contrast to traditional transducers wherein the wave is propagated to the entire domain, focused ultrasound could achieve improved control by directing the acoustic wave towards specific regions of interest. Thus, the power consumption for emulsification could be lessened by concentrating the ultrasonic wave on particular regions. This approach is important for local fluid emulsification and non-uniformly distributed phases. Moreover, higher pressure at the focus, coupled with high frequency, makes smaller droplets attainable with focused transducers. Hence, in this study, the emulsification of oil droplets in water with high frequency focused ultrasound was investigated through experiments and numerical modeling. The effect of transducer power (74–400 W), frequency (1.1 and 3.3 MHz), oil viscosity (10.6–512 mPas), interfacial tension (25–250 mN/m) and initial droplet radius (10–750 µm) on the emulsification process was assessed. Moreover, the mechanism of droplet break-up was examined. This is essential as there is need for better understanding of the mechanism and optimal conditions for high frequency emulsification.

2. Experimental methods

2.1. Materials

Crude oil with density of 842.1 kg/m³ and dynamic viscosity of 5.304 mPas at 20C was utilized as the droplet phase. Desalinated water from water treatment plant in Abu Dhabi was used as the continuous phase. The focused transducer (H101), matching network (H101-173), RF wattmeter (20–200 W) and hydrophone (Y-104) were supplied by Sonic Concepts. The RF power amplifier, TG5011A 50 MHz function generator and Hi-Spec 4 high speed camera were manufactured by Tomco technologies, TTZ and Fastec Imaging, respectively. Moreover, the oil injection syringe was supplied by BD Micro-fine plus syringe and the high-power light emitting diode (LED CRI 95 + ) was produced by Andoer.

2.2. Method

The oil droplets emulsification experiment was conducted in a compartment of length 5.0 cm, width 4.3 cm and height 3 cm (Fig. 1b). The H101 focused transducer was attached to the wall of the dispersion chamber. Absorbing materials were utilized at the opposite and side walls to avoid wave reflection. The transducer was operated at a frequency of 1.12 MHz. Furthermore, the geometric focus and aperture diameter of the focused transducer are 63.2 mm and 64 mm, respectively. The distance along the transducer focal line was calibrated based on the graduation of a measuring T square (Fig. 1d). The ultrasound propagation was actuated with a sinusoidal signal which was defined with a 50 MHz pulse generator (Fig. 1a). The signal is a sine wave with peak-peak voltage of 250–550 mV and 20% duty cycle. The pulse was amplified with an RF power amplifier and sent to the transducer through a matching network. The actuating power was measured with the RF wattmeter. Prior to the injection of the oil, the acoustic pressure distribution was determined along the transducer centerline with a hydrophone (Fig. 1c). The hydrophone was placed horizontally and connected to an oscilloscope to detect the voltage amplitude. The acoustic pressure was determined from the voltage amplitude via the calibration factor recommended by Sonic Concepts. Thereafter, droplets of oil of sizes 0.03–3 mm were injected from the bottom of the dispersion chamber towards the focal region of the transducer. The interaction of the droplets of varying sizes and number with the focused ultrasonic waves was evaluated based on captured images from the high-speed camera through shadowgraph technique (Fig. 1e). The shadowgraph method provides the capability to visualize fine details in multiphase flows.

Fig. 1.

Experimental set-up of the emulsification process a Signal configuration and amplification b compartment c hydrophone positioning for pressure measurement d calibration and focal image e schematics of the emulsificiation process.

3. Numerical model development

3.1. Model description

The numerical model was developed based on the geometry and transducer used in the experiments in this study (Fig. 2). The spherically focused transducer of 64 mm diameter was evaluated at 1.1 MHz and 3.3 MHz. Ultrasound power range between 74 W and 400 W were assessed for their effect on the acoustic pressure and velocity (Fig. 3). The curved transducer surface propagates the ultrasound wave towards the focal point at 63.2 mm. The non-linear acoustic and conservation equations were solved with an explicit time integration scheme and discontinuous Galerkin finite element method in COMSOL 6.0. The 2D axis-symmetry was used to represent the domain in the propagating zone and the concave lens was assumed to be rigid. Thereafter, the output of the acoustic wave propagation was used to determine the emulsification behavior under various ultrasound parameters and emulsion properties. The continuous phase is composed of water and the dispersed phase is oil. Moreover, the source signal was sinusoidal with 20% duty cycle. The impedance boundary condition was used to prevent the reflection of the ultrasound. In addition, the absorbing layer holds the ultrasound and restrain the reflection of the waves from the outer edges.

Fig. 2.

Description of the numerical model.

Fig. 3.

A Distribution of acoustic pressure along the transducer axis b The effect of the ultrasound power on the focus acoustic pressure.

3.2. Governing equations

The emulsification of the oil droplets in water requires adequate representation of the acoustic waves. Under the operating conditions of focused ultrasound, the waves tend to exhibit non-linearity [28], [29], [30]. Moreover, the non-linear effects become stronger with rising acoustic pressure and actuating power. Hence, the propagation of the ultrasonic waves was described based on the non-linear Westervelt equation [31]:

$$\frac{1}{\rho c^2}\frac{\partial p_t}{\partial t}+\mathrm{\nabla }\bullet \left[\left(1+\frac{\beta p_t}{\rho c^2}\right)u_t\right]=Q_m$$ (1)

$$p_t=p+p_b$$ (2)

where $\rho$ is the medium density, $c$ is the speed of sound in the medium, $t$ is the time, $\beta$ is the nonlinear coefficient, $Q_m$ is the monopole term, $p_t$ is the total acoustic pressure, $u_t$ is the acoustic velocity.

The non-linear Westervelt provides resolution of the limitations in Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation. This includes the consideration of the wave reflection and scattering as well as functionality at various aperture angles.

The expressions for the continuity and momentum conservation are given as follows [31]:

$$\frac{1}{\rho c^2}\frac{\partial p_t}{\partial t}+\mathrm{\nabla }\bullet u_t=Q_m$$ (3)

$$\rho \frac{\partial u_t}{\partial t}+\mathrm{\nabla }\bullet \left(p_{t}I\right)=q_d+\rho \delta \mathrm{\Delta }{u}_t$$ (4)

where $\delta$ is the ultrasound diffusivity, $q_d$ is the dipole term.

The ultrasound diffusivity ($\delta$) and nonlinear coefficient ($\beta$) are defined as [31]:

$$\delta =\frac{2\alpha c^3}{{\omega }^2}$$ (5)

$$\beta =1+\frac{B}{2A}$$ (6)

where $B/A$ is the parameter of non-linearity, $\alpha$ is the attenuation coefficient, $c$ is the speed of sound and $\omega =2\pi f$ is the angular frequency, and $f$ is the ultrasound frequency.

4. Results and discussion

4.1. Experimental results

Prior to the injection of oil for the emulsification experiment, the acoustic behavior was characterized along the focused transducer axis. The acoustic wave propagation in water along the transducer axis was measured with a fiber optics hydrophone. This type of hydrophone could provide negligible interference by electromagnetic waves, high sensitivity and light weight. The Y-104 hydrophone has a diameter of 1.5 mm and length of 25 mm with operating range between 50 kHz and 1.9 MHz. In addition, the hydrophone was oriented horizontally in front of the transducer and the tip was moved along the axis for measurements. The wave transmission is consistent with the operation of the HiFU. The acoustic pressure was highest at 26.24 MPa at the focus region at 63 mm from the transducer surface. However, there was a steep reduction in the pressure value ahead and behind the focal point. Moreover, the effect of the focused transducer power (74–400 W) on the acoustic pressure was determined. This power range provides wave-medium interaction that drives the emulsification process. In order to achieve the power range, the transducer was driven by actuating voltages of 250–550 mV. The acoustic pressure increased from 9.01 MPa to 26.24 MPa as the power was raised from 74 W to 400 W. This is consistent with the behavior of ultrasound transducers. Elevating the ultrasound power provides higher electric potential, transducer displacement and strain. Thus, the resulting acoustic pressure increases at the transducer surface and the propagating medium. Moreover, the relationship between the power and acoustic pressure is non-linear. This is consistent because the ultrasound intensity is directly proportional to the square of the pressure amplitude.

The emulsification of oil droplets with initial size between 0.03 and 3 mm with water as the continuous phase was evaluated at 74 and 400 W. Different emulsification mechanisms, depending on We and Oh, were identified. The droplet undergoes acoustic streaming that mobilizes them towards the focus zone of the transducer. During the streaming, the droplets undergo deformation along their path to the focus. Thereafter, they interact with the acoustic wave at the focus leading to different types of break up. The stability and potential breakup of the droplets are determined by the balance between disruptive stress from the focused transducer and the internal restorative forces of the oil. The main internal forces are the Laplace pressure and viscous force. The Laplace pressure is defined as follows [13]:

$${\mathrm{\Delta }P}_{\mathit{Laplace}}=\frac{2\sigma }{R_d}$$ (7)

where $\sigma$ is the interfacial is tension and $R_d$ is the droplet radius.

Hence, the droplets become less stable as the interfacial tension reduces and the radius increases. Moreover, decreasing the viscosity of the dispersed phase provides destabilization of the droplets. Once the external stresses from the ultrasound propagation surpass the restorative stresses, droplets go through a series of deformation and relaxation stages which is then accompanied by rupture. Emulsification is significantly enhanced with the focused transducer due to acoustic streaming of the droplets from the curved surface to the high We focal region. Moreover, the We is substantial in zones behind and ahead of the focal point. Prior to the droplet dispersion, the droplets undergo stages of deformation and relaxation. However, when the critical Weber number was surpassed, the droplets proceed to break up in different modes. The main break up pathways observed are bulb, thread, sheet-like and catastrophic in nature. The viscosity ratio between the dispersed and continuous phase is 5.3. Based on this viscosity ratio, a critical weber number of 1.4–1.6 signifies the limits for the onset of emulsification [32]. At 74 W, the We at the surface and focal zone are 0.5 and 939.8, respectively. However, at 400 W, the We at the transducer surface and focal region reached 2.7 and 6451.8, respectively. Bulb-like and weak catastrophic break up dominates the emulsification at 74 W (Fig. 4). The bulb break-up occurs predominantly at locations farther from the transducer focus at We between 1.6 and 11. Bulb dispersion is characterized by droplet stretching, and gradual formation of thin neck. Eventually the neck reaches a fracture point where smaller droplets are formed from the parent droplet (Fig. 4 b-c). Beyond a We of 350, the droplets proceed with catastrophic break up. Catastrophic dispersion occurs at the focal region of the focused transducer (Fig. 4a). It provides fine droplets with immediate breakage of the starting oil on interacting with the acoustic wave.

Fig. 4.

The interaction of the ultrasonic wave with oil droplets in water at 74 W: a Single droplet dispersion at focal region b Droplet stretching and break-up c Multiple droplet dispersion.

As the ultrasound power was increased to 400 W, the disruptive force enlarges, and this leads to more intense emulsification. In addition to the bulb (Fig. 5d) and catastrophic (Fig. 5a) break up, sheet and multimode dispersion was observed (Fig. 5c). At We between 11 and 100, droplet goes through deformation stages and then sheets or burst begin to emerge. This sheet formation is associated with the occurrence of significant deformation in several directions. The catastrophic break up at 400 W is more vigorous because the ultrasound disruptive stress and We are higher (Fig. 5b). With a We of about seven times those at 74 W at the transducer focus, the dispersed phase was emulsified into much smaller sizes. The size of the daughter droplets resulting from the emulsification of the initial droplet interaction with the acoustic wave depends significantly on the We. The typical child radius of the fragmented droplet ($r_{\mathit{ch}}$) can be described based on the Kelvin-Helmholtz equation [33], [34], [35]:

$$r_{\mathit{ch}}=\left\{\begin{array}{c}{B}_o{\mathrm{\Lambda }}_{\mathit{KH}}for{B}_o{\mathrm{\Lambda }}_{\mathit{KH}}\le r_p\\ min\left({\left(\frac{3\pi r_p^{2}v}{2{\mathrm{\Omega }}_{\mathit{KH}}}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.},{\left(\frac{3r_p^2{\mathrm{\Lambda }}_{\mathit{KH}}}{4}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)\end{array}\right)for{B}_o{\mathrm{\Lambda }}_{\mathit{KH}}>r_p$$ (8)

where ${\mathrm{\Lambda }}_{\mathit{KH}}$ is the disturbing wavelength, $r_p$ is the radius of the parent droplet, $v$ is the acoustic velocity, and ${\mathrm{\Omega }}_{\mathit{KH}}$ is the growth rate.

Fig. 5.

The interaction of the ultrasonic wave with oil droplets in water at 400 W: a Single droplet dispersion at focal region b Catastrophic droplet break-up c Sheet formation d Droplet stretching and break-up.

The disturbing wavelength (${\mathrm{\Lambda }}_{\mathit{KH}}$) is (Fig. 6) represented as follows [35]:

$${\mathrm{\Lambda }}_{\mathit{KH}}=\frac{9.02r_p\left(1+0.45\sqrt{\mathit{Oh}}\right)\left(1+{0.4Ca}^{0.7}\right)}{{\left(1+{0.865We}^{1.67}\right)}^{0.6}}$$ (9)

Fig. 6.

Mesh sensitivity analysis.

Where $\mathit{Oh}$ is the Ohnesorge number and $\mathit{Ca}$ is the capillary number.

The capillary number (Ca) is as follows [35]:

$$\mathit{Ca}=\frac{\mu v}{\sigma }$$ (10)

where $\mu$ is the droplet viscosity and $\sigma$ is the interfacial tension.

The Ohnesorge number (Oh) is as follows [35]:

$$\mathit{Oh}=\frac{\sqrt{\mathit{We}}}{\mathit{Re}}$$ (11)

As observed above, the disturbing wavelength is proportional to the We, Oh, Ca and $r_p$. The wavelength of the disturbance is elongated through increment in the starting droplet size, Oh and Ca. However, higher We causes shortening of the disturbance wavelength. In addition, the Oh shows an indirect relationship with the We. This implies that the higher We drives reduction in the Oh. Hence, higher We significantly reduces the acoustic interaction wavelength which in turn results in child droplets of diminished sizes. At 74 W, the estimated disturbance wavelength and size reduction ratio are 1.43x10^-5 m and 4.35, respectively. Comparatively, the disturbance wavelength and droplet size fragmentation factor at 400 W are 2.81x10^-6 m and 22.2, respectively. Furthermore, the time of droplet break-up decreased at elevated We. On average, the time for the catastrophic dispersion of a single droplet at We = 939.8 and We = 6451.8 are 1.01 ms and 0.45 ms, respectively.

4.2. Model results

4.2.1. Mesh sensitivity study

The grid independence assessment was conducted with four mesh sizes (Table 1). The meshes were evaluated for their independence on the model accuracy. The acoustic pressure at three different propagation times (2.52, 5.04, 10.07 μs) were utilized. The coarse mesh contains peak mesh element size greater than the ultrasound wavelength by a factor of 1.5. The normal, fine and extra fine meshes are at least the wavelength of the acoustic propagation. Quartic order was used for the meshing to improve the accuracy of the predictions. In order to adequately capture the acoustic wave propagation, the maximum mesh element should be smaller than the wavelength of the ultrasound [31], [36]. Hence, the coarse mesh gives a poor estimation of the magnitude and trend of the acoustic pressure at the three times as the highest mesh size is more than the ultrasound wavelength. The normal mesh improved the trend, but the magnitudes of the pressure were significantly under-predicted by ∼ 18.3–27.5%. To maintain balance between the computational time and accuracy, the fine mesh was utilized for further study because it provides close prediction (95.8–98.1%) to the extra fine mesh.

Table 1.

Mesh elements utilized for grid independence test.

Mesh Type	Number of Elements
Coarse	22,010
Normal	38,693
Fine	86,516
Extra Fine	158,837

4.2.2. Model validation

The numerical model wave behavior and trend at five different ultrasound power conditions were validated with the experimental actuation of the HiFU. On the wave behavior, the propagation of the acoustic wave at 400 W is described in Fig. 7. The wave departs the curved surface of the focused transducer with a pressure of ∼ 550 kPa. The propagation then transitions towards the focal region in space and time. The acoustic pressure magnitude continued to rise during the wave movement, reaching 1.25 MPa at 28 mm and 20 µs. The pressure at the focal region attained 23.79 MPa at 44.39 µs and reduced shortly after leaving the zone. Similar observation of the trend was found at 74 – 400 W, with variations in the pressure magnitude and propagation time.

Fig. 7.

Contour plot of the acoustic pressure propagation from the transducer surface to the focal region.

The numerical model acoustic pressure at the transducer surface and focus region were assessed with the experimental measurements at five different ultrasound powers (Fig. 8). The power studied are 74, 132.5, 205, 305 and 400 W. The pressure at the surface and focus are essential to the emulsification process as they give an indication of the minimum and maximum wave pressure-medium interactions. A well-controlled HiFU across the pressure ranges could provide a broad range of droplet sizes and specific focus on region of interest in static and continuous emulsification processes. The numerical model gives reasonable prediction of the experimental data. The trend shows that the surface and focal pressures increased with rising ultrasound power. The surface and focal pressure amplitudes were estimated with errors of ∼ 6.5% and ∼ 10%, respectively. Hence, the model was used further for the sensitivity analysis, optimization and characterization of the focused transducer behavior.

Fig. 8.

Numerical model validation at the transducer focal point.

4.2.3. Parametric analysis

The emulsification performance is significantly influenced by various process variables. Hence, different ultrasound and emulsion properties that impact the emulsification of oil droplets in water were examined. Ultrasound properties such as propagating frequency and power were assessed. Moreover, emulsion properties such as oil viscosity, droplet size and interfacial tension were evaluated. The sensitivity studies allow for the optimization of the emulsification process as well as gaining fundamental understanding of the dispersion mechanism.

4.2.3.1. Effect of ultrasound power

The effect of ultrasound power on the acoustic pressure distribution at the focal region along the radial direction is depicted in Fig. 9. Increasing the ultrasound power resulted in rising acoustic pressure and acoustic velocity. This is important in determining the droplet breakup mode, intensity and size. The 74 and 400 W actuation provided acoustic pressure of 9.50 and 23.79 MPa at the focus, respectively. Constitutively, increment in transducer power facilitates higher electric field and surface displacement which generates waves with enlarged pressure. However, the focal width remained the same at 3.14 mm since the excitation was at 1.1 MHz for studied conditions.

Fig. 9.

Radial distribution of the acoustic pressure at the focal region at different ultrasound power.

Furthermore, the influence of the ultrasound power on the Re and We was evaluated (Fig. 10). The radius of the droplet evaluated is 500 µm. The Re gives an indication of the flow pattern as regards the tendencies to be turbulent. Moreover, the We is a major parameter for identifying droplet fragmentation potential and mode. The predicted Re between 74 and 400 W were 8442 and 21364, respectively. Considering that these values are well above 4000, the interaction of the wave with the emulsion could be described as fully turbulent. The We increased from 856.14 to 5483.03 within the ultrasound power range at the focal point studied. This range of values would tend to favor the catastrophic mode of breakup. Because the transducer surface We can reach up to 2.7, there is potential for breakup between the surface and focus. This provides different possibilities of breakup mechanism depending on the We and viscosity ratio (µ_d/µ_c). Generally, higher critical We is required for the different breakup stages as the viscosity ratio is elevated (Table 2). In addition, focused ultrasound drives the droplets away from the surface towards the focal region through acoustic streaming. This tends to favor high We breakup mode such as shear and catastrophic pathways. This enhances emulsification by allowing for smaller droplet formation and faster breakup time (Fig. 11, Fig. 12, Fig. 13, Fig. 14).

Fig. 10.

Effect of ultrasound power on the Re and We.

Table 2.

Critical We required for different breakup modes at viscosity ratio greater than and less than 100.

Breakup Mode	Critical We (µd/µc > 100) [37], [38], [39], [40]	Critical We (µd/µc <1 0 0) [32]
No breakup	<2.7	1.4–2.85
Oscillatory or Vibrational	2.7–12	2.85–11
Bag or Thread	12–50	13–20
Bag-Stamen or Multimode	50–100	30–100
Shear	80–350	–
Catastrophic	>350	–

Fig. 11.

A Axial acoustic pressure distribution at the focal region at 1.1 MHz b Radial acoustic pressure distribution at the focal region at 1.1 MHz c Acoustic velocity at 1.1 MHz d Axial acoustic pressure distribution at the focal region at 3.3 MHz e Radial acoustic pressure distribution at the focal region at 3.3 MHz f Acoustic velocity at 3.3 MHz.

Fig. 12.

Effect of oil viscosity on We and Oh.

Fig. 13.

Effect of droplet radius on We and Oh.

Fig. 14.

Effect of interfacial tension on We and Oh.

4.2.3.2. Effect of ultrasound frequency

The effect of the focused transducer frequency (1.1 and 3.3 MHz) on the ultrasound characteristics was assessed with power of 400 W. The acoustic pressure at the focal region were ∼ 26 MPa and ∼ 69 MPa at frequencies of 1.1 MHz and 3.3 MHz, respectively. Moreover, the acoustic velocities were ∼ 16 m/s and ∼ 42 m/s at 1.1 MHz and 3.3 MHz, respectively. Although the acoustic pressure and velocity amplitude was higher at 3.3 MHz, the focal width was lower in comparison to that of 1.1 MHz. The focal width at 1.1 MHz and 3.3 MHz are 3.14 mm and 1.04 mm, respectively. The increased acoustic pressure and velocity achieved at higher frequency harmonics could produce improved emulsification capabilities. The emulsification at 3.3 MHz gives three times higher We compared to 1.1 MHz. Hence, smaller droplets could be attained at higher frequency excitation under intense catastrophic modes. Formation of fine droplets in the nanoscale could aid the stability of the emulsion for several months and lower the requirements for chemical surfactants [13]. Another factor that could support the stability of emulsions at higher frequency is the formation of hydrophilicity at the surface of the droplets [13], [22].

4.2.3.3. Effect of oil viscosity

The impact of oil viscosity on the emulsification was determined at 10.6 mPas to 530 mPas. This range covers broad types of oil that can be emulsified. While the Oh increased with rising viscosity, the We remains constant. The Oh increased from 0.062 to 3.12 with the viscosity range assessed. However, the We remained constant at 856.14 for the studied range. It is expected that oil droplets will more likely proceed in chaotic breakup considering that the critical We of ∼ 350 is required for catastrophic events. Although the We number provides important information on the droplet breakup, viscous effects on emulsification are not directly embedded in it. In this case, Oh emerges as the determinant of the droplet breakup for viscous fluids. At oil viscosity of around 10.6 mPa, the Oh is quite lower than 1. Under this condition, the impacts of the viscosity can be neglected [42]. However, as the viscosity and Oh continue to increase beyond 200 mPa and 1, respectively, the viscous effect becomes more important. At Oh near and above 1, the critical We elevates for the different breakup modes with viscosity increment. There are reports that the critical We can increase to ∼ 25 and ∼ 50 at Oh of 1 and 3, respectively [41], [42], [43], [44], [45], [46]. One of such estimations of the viscosity influenced We can be described by Brodkey correlation [41]:

$${\mathit{We}}_{c,new}={\mathit{We}}_{c,o}\left(1+1.077{\mathit{Oh}}^{1.6}\right)$$ (12)

where ${\mathit{We}}_{c,new}$ is the critical Weber number with strong viscous effect, ${\mathit{We}}_{c,o}$ is the critical Weber number with negligible viscosity influence and $\mathit{Oh}$ is the Ohnesorge number.

As observed, the critical We at different modes is dependent on the Oh. The We of 856.14 at high viscosity would still allow for emulsification at this increased critical We at Oh of ∼ 3. However, the breakup would tend to produce relatively larger child droplets with less intensified mechanisms such as vibration, bag or shear dominating the process.

Furthermore, the viscosity has a significant impact on the acoustic interaction with the droplets and their subsequent break-up. It acts as a restorative force that inhibit the disruptive force that emanates from the ultrasonic transducer. For example, there are several reports that have demonstrated the ultrasound attenuation effect with changing viscosity. In the experiment of Majumdar et al [47], it was reported that the attenuation coefficient increases with rising medium viscosity. The empirical correlation is defined as:

$$\alpha =\frac{8{\pi }^2\mu f^2}{3\rho c^3}$$ (13)

Similar observation can be observed in the theoretical findings of Stokes [48] and the work of Shutilov and Alferieff [49]. The correlation based on the study of Shutilov and Alferieff [49] is described as:

$$\alpha =\frac{f^2}{8{\pi }^2\rho c^3}\left(\frac{4}{3}{\mu }_d+{\mu }_b\right)$$ (14)

where $\mu$ is the medium viscosity, b denotes bulk quantity, d denotes dynamic quantity, $c$ is the speed of sound, $\alpha$ is the attenuation coefficient, $\rho$ is the medium density and $f$ is the ultrasound frequency.

Considering that the viscosity influences the attenuation coefficient, this impacts the acoustic modelling. For instance, the attenuation coefficient is embedded in the ultrasound diffusivity which is present in the momentum conservation of the acoustic propagation in equation (4).

Moreover, the weakening of the ultrasound with viscosity was highlighted in the experiment of Luo et al [50].

4.2.3.4. Effect of initial oil droplet size

The droplet size is an important parameter that impacts the emulsification process. Hence, the effect of the droplet radius on the We and Oh was determined at 74 W, interfacial tension of 35 mN/m and oil viscosity of 5.3 mPa. Oil with starting radius between 15 µm and 750 µm were examined. The We increased from 25.68 to 1284.22 as the droplet radius was elevated from 15 to 750 µm. Consequently, the emulsification can proceed by oscillatory through catastrophic modes within the droplet radius assessed. The interfacial tension becomes more dominant with smaller droplets. This makes the fragmentation of the droplets proceed more with vibrational and bag modes in this state. But with larger droplets, shearing and catastrophic means begin to emerge and intensify. The Oh reduced from 0.18 to 0.025 within the same droplet size range. At droplet radius lower than ∼ 50 µm, where Oh is less than 0.1, the viscous effect can be neglected. However, viscosity becomes dominant as initial droplets with higher radius were used. Overall, larger droplets allow for higher possibility and intensity of breakup due to diminished viscous and interfacial resistance.

4.2.3.5. Effect of interfacial tension

Another fluid property that significantly affects the droplet dispersion and break-up is the interfacial tension. Thus, interfacial tension between 20 and 250 mN/m were examined for their impact on the We and Oh. The assessments were determined at ultrasound power of 74 W, oil viscosity of 5.3 mPa and initial droplet size of 1 mm. The results showed that both the We and Oh showed an inverse relationship with the interfacial tension. The inverse proportionality is consistent because the We is the ratio of the inertia force and the surface tension. The kinetic energy is the same whilst the interfacial tension increased. Likewise, the Oh is the ratio between the viscous force and the product of the inertia force and surface tension. The reduction in the We and Oh progressed in two stages. In the first stage, the lowering of the dimensionless numbers has a sharp gradient between 20 and 60 mN/m. Subsequently, the rate of reduction was less from 60 mN/m to 250 mN/m. This implies that as the interfacial tension increased, the emulsification of the droplet slowed down and became more challenging. Overall, the We decreased from 1498.25 to 119.86 as the interfacial tension was raised. Moreover, the Oh increased from 0.041 to 0.012 within the same interfacial tension range. Since the Oh is lower than 0.1, the viscous effect is insignificant. Hence, the predominant methods of break-up are through shear and catastrophic modes.

Likewise, the interfacial tension influences the acoustic and break-up dynamics. For instance, in the report of Hinze [43], the maximum droplet diameter can be restricted based on the correlation below:

$$d_{\mathit{max}}={\left(\frac{\sigma }{\rho }\right)}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}W{e}_{\mathit{cr}}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}{\epsilon }^{-\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}$$ (15)

where ${\mathit{We}}_{\mathit{cr}}$ is the critical Weber number, $\sigma$ is the interfacial tension, $\rho$ is the density of the crude oil and $\epsilon$ is the mean rate of energy dissipation.

Thus, the maximum droplet size is dependent on the interfacial tension and critical Weber number.

5. Conclusion

Focused high frequency ultrasound emulsification provides significant benefits such as enhanced stability, finer droplets, elevated focal pressure, lowered power usage, minimal surfactant usage and improved dispersion. Hence, in this study, the high frequency focused ultrasound emulsification of oil droplets in water was investigated through experiments and numerical modeling. The effect of transducer power (74–400 W), frequency (1.1 and 3.3 MHz), oil viscosity (10.6–512 mPas), interfacial tension (25–250 mN/m) and initial droplet radius (10–750 µm) on the emulsification process was assessed. In addition, the mechanism of droplet break-up was examined. In order to achieve the power range, the transducer was driven with actuating voltages of 250–550 mV. The experiments showed that the acoustic pressure increased from 9.01 MPa to 26.24 MPa as the power was raised from 74 W to 400 W. At 74 W, the Weber number (We) at the surface and focal zone are 0.5 and 939.8, respectively. However, at 400 W, the We at the transducer surface and focal region reached 2.7 and 6451.8, respectively. Thus, bulb-like and weak catastrophic break up dominates the emulsification at 74 W. As the ultrasound power was increased to 400 W, the disruptive force enlarges, and this leads to more intense emulsification. In addition to the bulb and catastrophic break up, sheet and multimode dispersion was observed. The catastrophic break up at 400 W is more vigorous because the ultrasound disruptive stress and We are higher. At 74 W, the estimated disturbance wavelength and size reduction ratio are 1.43x10^-5 m and 4.35, respectively. Comparatively, the disturbance wavelength and droplet size fragmentation factor at 400 W are 2.81x10^-6 m and 22.2, respectively. Furthermore, the time of droplet break-up decreased at elevated We. On average, the time for the catastrophic dispersion of a single droplet at We = 939.8 and We = 6451.8 are 1.01 ms and 0.45 ms, respectively. The numerical model gives reasonable prediction of the trend and magnitude of the experimental acoustic pressure data. The surface and focal pressure amplitudes were estimated with errors of ∼ 6.5% and ∼ 10%, respectively. The predicted Re between 74 and 400 W were 8442 and 21364, respectively. Considering that these values are well above 4000, the interaction of the wave with the emulsion could be described as fully turbulent. The acoustic pressure at the focal region were ∼ 26 MPa and ∼ 69 MPa at frequencies of 1.1 MHz and 3.3 MHz, respectively. Moreover, the acoustic velocities were ∼ 16 m/s and ∼ 42 m/s at 1.1 MHz and 3.3 MHz, respectively. The emulsification at 3.3 MHz gives three times higher We compared to 1.1 MHz. Hence, smaller droplets could be attained at higher frequency excitation under intense catastrophic modes. The Oh increased from 0.062 to 3.12 with the viscosity between 10.6 mPas and 530 mPas. However, the We remained constant at 856.14 for the studied range. Generally, higher critical We is required for the different breakup stages as the viscosity ratio is elevated. Moreover, the We increased from 25.68 to 1284.22 as the droplet radius was elevated from 15 to 750 µm. Consequently, the emulsification can proceed by oscillatory through catastrophic modes within the droplet radius assessed. The interfacial tension becomes more dominant with smaller droplets. Larger droplets allow for higher possibility and intensity of breakup due to diminished viscous and interfacial resistance. Overall, the We decreased from 1498.25 to 119.86 as the interfacial tension was raised. Furthermore, the Oh increased from 0.041 to 0.012 within the same interfacial tension range. Since the Oh is lower than 0.1, the viscous effect is insignificant. Hence, the predominant methods of break-up are through shear and catastrophic modes.

CRediT authorship contribution statement

Idowu Adeyemi: Formal analysis, Methodology, Software, Writing – original draft, Writing – review & editing. Mahmoud Meribout: Conceptualization, Methodology, Writing – review & editing. Lyes Khezzar: Conceptualization, Methodology. Nabil Kharoua: Methodology. Khalid AlHammadi: Conceptualization, Methodology. Varun Tiwari: .

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.