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

Автор: Adeyemib I. Meribouta M. Khezzarc L.

Теги: chemistry biology microbiology science molecular chemistry white matter microstructure

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Текст

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

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Idowu Adeyemib, Mahmoud Meribouta, Lyes Khezzarc, Nabil Kharouac, Khalid AlHammadia, Varun
Tiwaria
aDepartment

of Electrical Engineering and Computer Science, Khalifa University, P.O. Box 127788, Abu
Dhabi, United Arab Emirates
bDepartment

of Mechanical Engineering, Khalifa University, P.O. Box 127788, Abu Dhabi, United Arab

Emirates

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cEcole

Abstract

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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 (74-400W), 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.

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Nationale Polytechnique de Constantine, Constantine, Algeria

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Keywords: Ultrasound; Emulsification, Focused Transducer; High Frequency; Oil-in-Water,
Numerical Analysis

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4478460

1. Introduction

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The formulation of oil-in-water and water-in-oil emulsions is essential to the operation of
numerous industrial processes [1-9]. 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 waterin-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 20000 reports on
emulsification in the past decade (2012-2022).

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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 nonbiodegradable 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 [27-28]
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.

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This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4478460

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, 21-25]. In
one study, Zhou et al [9] assessed the performance of ultrasound transducer, high speed and highpressure 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 = 20kHz, P = 300W)
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 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 < 100kHz) and high (f > 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].

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In addition to the enhanced dispersion performance provided by high frequency ultrasound,
focused transducers have the potential to elevate the acoustic pressure, decrease power usage and
boost emulsification process. Focused transducers operate by utilizing cylindrically or spherically
concave surfaces to intensify acoustic pressure at a focal region. This could allow for better control
and lessened energy utilization. In contrast to traditional transducers wherein the wave is
propagated to the entire domain, focused ultrasound could achieve improved control by directing
the acoustic towards specific regions of interest. Consequently, there is optimization of the power
consumption for emulsification. Moreover, higher pressure at the focus and smaller droplets could
be attained with focused transducers. Despite the significant prospects of focused transducers for
emulsification, there is little to no reports on their utilization for oil-in-water or water-in-oil
dispersion. Many of the studies on focused transducers have been concentrated on tissue tumor
emulsification, ablation and necrosis [29-30]. Furthermore, there is need for better understanding
of the mechanism and optimal conditions for high frequency emulsification [13, 26]. 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 (74400W), frequency (1.1 and 3.3 MHz), oil viscosity (10.6-512 mPas), interfacial tension (25-250

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This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4478460

mN/m) and initial droplet radius (10-750 µm) on the emulsification process was assessed.
Moreover, the mechanism of droplet break-up was examined.

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2. Experimental methods

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2.1 Materials

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Crude oil with density of 842.1 kg/m3 and dynamic viscosity of 5.304 mPas at 20 C 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.

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2.2 Method

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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 64mm,
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 50MHz 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 0.03-3mm 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.

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This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4478460

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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.

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3. Numerical model development

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3.1 Model description

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The numerical model was developed based on the geometry and transducer used in the experiments
in this study. 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. 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 (Fig. 2). 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.

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Fig. 2 Description of the numerical model

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This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4478460

3.2 Governing equations

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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 nonlinearity [31-33]. 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 [34]:

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𝛽𝑝𝑡
1 ∂𝑝𝑡
+ ∇ ∙ 1 + 2 𝑢𝑡 = 𝑄𝑚
2 ∂𝑡
𝜌𝑐
𝜌𝑐

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𝑝𝑡 = 𝑝 + 𝑝𝑏

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Where 𝜌 is the medium density, 𝑐 is the speed of sound in the medium, 𝑡 is the time, 𝛽 is the
nonlinear coefficient, 𝑄𝑚 is the monopole term, 𝑝𝑡 is the total acoustic pressure, 𝑢𝑡 is the acoustic
velocity.

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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.

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The expressions for the continuity and momentum conservation are given as follows [34]:

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1 ∂𝑝𝑡
+ ∇ ∙ 𝑢𝑡 = 𝑄𝑚
𝜌𝑐2 ∂𝑡

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∂𝑢𝑡
+ ∇ ∙ (𝑝𝑡𝐼) = 𝑞𝑑 + 𝜌𝛿∆𝑢𝑡
∂𝑡

𝜌

Where 𝛿 is the ultrasound diffusivity, 𝑞𝑑 is the dipole term.

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The ultrasound diffusivity (𝛿) and nonlinear coefficient (𝛽) are defined as [34]:

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2𝛼𝑐3
𝜔2

𝛽=1+

𝐵
2𝐴

Where 𝐵/𝐴 is the parameter of non-linearity, 𝛼 is the attenuation coefficient, 𝑐 is the speed of
sound and 𝜔 = 2𝜋𝑓 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

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𝛿=

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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 wavemedium 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.

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Fig. 3 a Distribution of acoustic pressure along the transducer axis b The effect of the ultrasound
power on the focus acoustic pressure.
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

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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]:

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∆𝑃𝐿𝑎𝑝𝑙𝑎𝑐𝑒 =

2𝜎
𝑅𝑑

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Where 𝜎 is the interfacial is tension and 𝑅𝑑 is the droplet radius.

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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 [35]. 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.

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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.

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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 11-100, 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 (𝑟𝑐ℎ) can be described based on the KelvinHelmholtz equation [36-38]:

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((

2
𝑟𝑐ℎ = min 3𝜋𝑟𝑝 𝑣
2Ω𝐾𝐻

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3𝑟𝑝2Λ𝐾𝐻
,
4

) (

)

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{

𝐵𝑜Λ𝐾𝐻 𝑓𝑜𝑟 𝐵𝑜Λ𝐾𝐻 ≤ 𝑟𝑝

𝑓𝑜𝑟 𝐵𝑜Λ𝐾𝐻 > 𝑟𝑝

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Where Λ𝐾𝐻 is the disturbing wavelength, 𝑟𝑝 is the radius of the parent droplet, 𝑣 is the acoustic
velocity, and Ω𝐾𝐻 is the growth rate.

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The disturbing wavelength (Λ𝐾𝐻) is represented as follows [38]:
Λ𝐾𝐻 =

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9.02𝑟𝑝(1 + 0.45 𝑂ℎ)(1 + 0.4𝐶𝑎0.7)

(1 + 0.865𝑊𝑒1.67)0.6

Where 𝑂ℎ is the Ohnesorge number and 𝐶𝑎 is the capillary number

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The capillary number (Ca) is as follows [38]:

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𝐶𝑎 =

𝜇𝑣
𝜎

Where 𝜇 is the droplet viscosity and 𝜎 is the interfacial tension

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The Ohnesorge number (Oh) is as follows [38]:

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As observed above, the disturbing wavelength is proportional to the We, Oh, Ca and 𝑟𝑝. 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.

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𝑊𝑒
𝑅𝑒

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𝑂ℎ =

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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.

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4.2 Model results

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4.2.1 Mesh Sensitivity Study

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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

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the ultrasound [34, 39]. 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.

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Table 1: Mesh elements utilized for grid independence test
Number of Elements
22010
38693
86516
158837

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Mesh Type
Coarse
Normal
Fine
Extra Fine

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Fig. 6 Mesh sensitivity analysis

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4.2.2 Model Validation

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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.

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Fig. 7 Contour plot of the acoustic pressure propagation from the transducer surface to the focal
region.

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The numerical model acoustic pressure at the transducer surface and focus region were assessed
with the experimental measurements at five different ultrasound powers. 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 pressuremedium 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.

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Fig. 8 Numerical model validation at the: a transducer surface and b focal point

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4.2.3 Parametric Analysis

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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 allows for the optimization of the emulsification process as well
as gaining fundamental understanding of the dispersion mechanism.

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4.3.2.1 Effect of Ultrasound Power

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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.

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Fig. 9 Radial distribution of the acoustic pressure at the focal region at different ultrasound
power.

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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 potentiality for breakup between the surface and focus. This provides different possibilities
of breakup mechanism depending on the We and viscosity ratio (µd/µc). Generally, higher critical
We is required for the different breakup stages as the viscosity ratio is elevated (Table 2). In

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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.

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Fig. 10 Effect of ultrasound power on the Re and We.

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Table 2: Critical We required for different breakup modes at viscosity ratio greater than and less
than 100
Critical We (µd/µc > 100)
[40-43]
<2.7
2.7-12
12-50
50-100
80-350
>350

Breakup Mode

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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

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4.3.2.2 Effect of Ultrasound Frequency

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No breakup
Oscillatory or Vibrational
Bag or Thread
Bag-Stamen or Multimode
Shear
Catastrophic

Critical We (µd/µc < 100)
[35]
1.4-2.85
2.85-11
13-20
30-100
-

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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].

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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.

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4.3.2.3 Effect of Oil Viscosity

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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
[45]. 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 [44-49]. One of such estimations of the
viscosity influenced We can be described by Brodkey correlation [44]:

427

𝑊𝑒𝑐,

𝑛𝑒𝑤

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= 𝑊𝑒𝑐,𝑜(1 + 1.077𝑂ℎ1.6)

Where 𝑊𝑒𝑐, 𝑛𝑒𝑤 is the critical Weber number with strong viscous effect, 𝑊𝑒𝑐,𝑜 is the critical Weber
number with negligible viscosity influence and 𝑂ℎ is the Ohnesorge number.

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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.

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Fig. 12 Effect of oil viscosity on We and Oh.

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4.3.2.4 Effect of Initial Oil Droplet Size

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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.

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Fig. 13 Effect of droplet radius on We and Oh.

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4.3.2.5 Effect of Interfacial Tension

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Another fluid property that significantly affects the droplet dispersion and break-up is the
interfacial tension. Thus, interfacial tension between 20-250 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

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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.

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Fig. 14 Effect of interfacial tension on We and Oh.

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5. Conclusion

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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.

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Acknowledgement

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The authors acknowledge the support from Khalifa University through research grant number
CIRA-2020-086. The authors are grateful for the support provided by Dr. Afshin Goharzadeh in
the high speed image capturing.

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References

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This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4478460