Citation: Ruiken, J.-P.; Villwock, J.;
Kraume, M. Behaviour of
Acoustically Levitated Drops in
Mid-Water. Micromachines 2023,14,
1923. https://doi.org/10.3390/
mi14101923
Academic Editors: Pingan Zhu
and Ye Tian
Received: 13 September 2023
Revised: 6 October 2023
Accepted: 7 October 2023
Published: 10 October 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
micromachines
Article
Behaviour of Acoustically Levitated Drops in Mid-Water
Jan-Paul Ruiken , Jörn Villwock and Matthias Kraume *
Department of Chemical and Process Engineering, Technische Universität Berlin, Ackerstraße 76,
*Correspondence: [email protected]
Abstract:
A low-impact acoustic levitation system has been developed to study immobilised single
drops in liquid–liquid systems. The ability to observe liquid drops several millimetres in diameter
for days enables fundamental research into a wide range of mechanisms. Non-invasive optical
measurements with excellent optical accessibility are possible. This experimental work provides
the basis for mass transfer studies, emphasizing the precise volume determination, signal noise,
reproducibility, and the impact of the acoustic field on the drop and its surrounding environment.
The setup can be effectively controlled and proves beneficial for research objectives provided that all
liquid phases are entirely degassed, and there are no compressible voids present within the liquids.
In addition to the precise, uniform, and reliable measurement conditions, we observed no acoustic
streaming in the proximity of the drop and there was no significant vibration of the drop. Qualitative
observations using rainbow schlieren deflectometry indicate that the nodal or anti-nodal planes of
the standing waves can act as barriers to the dispersion of inhomogeneous dissolved substances in
the continuous phase.
Keywords:
acoustic levitation; acoustic streaming; single drop; mass transfer; liquid–liquid systems
1. Introduction
Acoustic levitation of matter in a gaseous phase is a versatile research tool that has
been continuously developed over recent decades. In the design and intended use of the
levitation systems, a distinction is made between one- and multi-dimensional approaches.
One-dimensional acoustic levitators in a gaseous environment, where matter is fixed
in a specific position, have mainly been used for stationary evaporation [
1
,
2
], as micro-
reactors [
3
,
4
], or for crystallisation experiments [
5
], to mention some recent ones.
The design
and construction of these one-dimensional systems is relatively straightforward. However,
depending on the application, there may be some obstacles.
Beginning with the availability of affordable ultrasonic transducers, the combination
of large numbers of these low-power transducers and their control by FPGAs (field pro-
grammable gate arrays) or other micro-controllers opened the door to the multi-dimensional
levitation technique. There are many groups using and developing multi-transducer setups
for complex matter handling [6–11].
With respect to liquids as the continuous phase, matter placement [
12
,
13
] and phase
separation [
14
,
15
] in liquids are areas of research today. Acoustic trapping can be used to
handle small particles or droplets without contact and to locate these samples at a specific
position. For phase separation, the droplets are a few hundred micrometres in diameter.
An overview of the application of ultrasound in phase separation is given in [
16
], focusing
mainly on the petrochemical industry. Most of the investigations are “Lab on a Chip”;
they are in the MHz range of acoustic stimulation, working with wavelengths smaller than
1.5 mm with water as the continuous phase. This results in the manipulation of bubbles,
droplets, and particles of about Ø 100 µm and smaller [17].
This work aims to highlight the advantages of this unfortunately neglected levitation
technique using liquids as the continuous phase with dispersed diameters up to several
Micromachines 2023,14, 1923. https://doi.org/10.3390/mi14101923 https://www.mdpi.com/journal/micromachines
Micromachines 2023,14, 1923 2 of 18
millimetres. Apfel [
18
] used acoustic levitation in liquids to measure the strength of liquids
in 1971, more than 50 years ago. His developed technique and research were the basis for
several publications. In the 1980s, Trinh et al. constructed a simple levitation device to
levitate silicone drops in water, with a maximum diameter of 14 mm [
19
]. The largest men-
tioned bubble known to us, levitated in water, was reported by Asaki et al., at Ø 12 mm [
20
].
Experimental conditions, which are important for mass transfer measurements, such as
occurring vibrations of motionless drops, the surrounding flow field, and the behaviour
of long-term measurements, were not reported or not the focus of these works. Their re-
search focused more on drop oscillation and vibration modes and in situ measurements of
interfacial tension and viscosities. This line of research was discontinued in the late 1990s.
We pick up this unique technique and present a system for low-impact liquid–liquid
levitation of solvents in water, coupled with exclusively non-invasive optical measurement
techniques for real-time investigations with high precision, such as integral mass transfer
measurements across the interface and qualitative concentration field visualisation with
rainbow schlieren deflectometry. This work describes the developed setup, characterises
the levitation environment, quantifies the accuracy, signal noise, reproducibility, and shows
the influence of standing waves on the dispersion of inhomogeneous dissolved substances
in the continuous phase.
2. Experimental Setup
In this section, the developed system is described, limits are named, the measuring
procedure is explained, and the image analysis is briefly presented.
2.1. Acoustic Levitation System
To acoustically levitate a drop motionlessly and reproducibly for a period from sec-
onds to several days, the acoustic levitation system must be well-adjusted, finely tuned,
and controlled
in real time to set up a stationary field of standing waves for reliable results.
The schematic of the developed system is shown in Figure 1, consisting of the systems
for acoustic levitation, image acquisition, level control, injection, and aspiration.
Figure 1. Schematic of the developed acoustic levitation system for liquid–liquid systems.
The single-axis levitator consists mainly of a custom-made well-matched submerged
plate-tip Langevin transducer. The transducer body, the two PZT4 ceramics, and the plate-
tip are Ø 15 mm in size, and the total length is 125 mm. The horn is made of Ti-6Al-4V and
tapers from Ø 15 to 6 mm to amplify the horn motion. Levitation is achieved at the resonant
frequency
fr
of approximately 66.5 kHz when the horn is immersed in water to a depth
of approx. 13 mm. An optical 125 mL cubical cuvette (Series 704, Hellma GmbH & Co. KG,
Micromachines 2023,14, 1923 3 of 18
Mullheim, Germany) contains the ultrapure water. The transducer is driven by an ultrasonic
amplifier (PDUS210-V4, PiezoDrive, Shortland, Australia), with capabilities of real-time
phase tracking and impedance detection. The outer bottom of the cuvette acts as a reflector
to create the necessary standing wave for acoustic levitation. The distance from the tip of the
transducer to the bottom of the cuvette is controlled by a motorised linear stage (MTS50-Z8,
Thorlabs Inc., Newton, NJ, USA). A precise and constant water level is crucial for good lev-
itation results; it is set by two peristaltic pumps (T100-S301/WX10-14-H, Longer Precision
Pump Co., Ltd., Baoding, China) and controlled with the signal of an ultrasonic distance
sensor (pico+15, microsonic GmbH), resulting in a 0.1 mm level control accuracy. One peri-
staltic pump is used to fill and one to drain and flush the system between measurements.
The temperature of the continuous phase and the ambient temperature are monitored by
two Pt100 temperature sensors (Ø 2 mm, 4-wire, Class B, TC LTD., Uxbridge, UK).
The shape and location of the drop can be observed using a monochrome high-speed
camera (CamRecord CL600x2, Optronis GmbH, Kehl, Germany), coupled with a telecentric
lens (S5LPJ0422 Correctal TL/2.0, Sill Optics GmbH & Co. KG, Wendelstein, Germany),
a frame
grabber (microEnable IV AD4-CL, Silicon Software GmbH, Mannheim, Germany),
and an LED panel (TH-100x100RD, CSS Inc., Kyoto, Japan) for transmitted illumination.
The established field of view is 7.68 mm ×7.68 mm.
The automated drop injection and aspiration system is the main feature of this setup.
The solvent drop is injected just below the only pressure anti-node with a hook-shaped
glass capillary guided by a fast-moving linear actuator (L12-20PT-6, IR ROBOT CO., Ltd.,
Bucheon, Korea). After injecting a defined volume, the linear actor retracts the capillary.
The observation of the drop starts. After a chosen contact time, a micro glass funnel (custom
design, WJM Glas GmbH, Berlin, Germany) is positioned over the levitating drop by a slow-
moving linear actuator (L12-80PT-6, IR ROBOT CO., Ltd., Bucheon, Korea).
The ultrasonic
field forces the funnel into resonance and creates its own acoustic field; the drop is drawn
into the funnel. Both injection and aspiration tools are connected to syringe pumps
(PSD/3-mini, Hamilton Company, Bonaduz, Switzerland) for precise liquid handling.
To suppress external vibrations and to ensure vibration-free measurements, the com-
plete system is mounted on a portable optical breadboard and then placed on an air-damped
optical table (CleanTop series 783 with Micro-g pneumatic legs, TMC). For external shock
detection, an acceleration sensor (QG40N-KAXYZ-1.5, DIS Sensors, Witten, Germany) and
an inclination sensor (QG40N-KDXYh-030, DIS Sensors, Witten, Germany) are placed on
the optical breadboard. All components of the setup communicate via a modular data
acquisition system (cRIO 9074, National Instruments, Austin, TX, USA) equipped with
measuring cards and controlled and operated with LabVIEW (Version 2021, National
Instruments, Austin, TX, USA).
The second accessible optical axis is used for qualitative 2D concentration measure-
ments with a rainbow schlieren deflectometry system (RSD) developed by Schulz et al. [
21
]
and further improved by Junne et al. [22].
2.1.1. Specifications
The setup is designed and optimised for one operating point of levitation, to ensure
the best levitation results in terms of low vibrations, high reproducibility, and robustness.
Within an ambient temperature range of 21
◦
C
±
3 K and ultrapure water as the continuous
phase, the field of standing waves can be set up easily. The system is designed to levitate in
the only anti-node, which is located in the centre of the cuvette. A variety of solvents with
a negative acoustic contrast factor
φ<
0 can be levitated in this system as the dispersed
phase. The acoustic contrast factor φwas defined by Gor’kov [23] as follows:
φ=ρd+2
3(ρd−ρc)
2·ρd+ρc
−1
3·ρc·c2
c
ρd·c2
d
, (1)
with the densities
ρ
and the speed of sound
c
of the dispersed (
d
) and continuous phase (
c
).
Micromachines 2023,14, 1923 4 of 18
The minimal initial drop diameter is determined by the detachment behaviour of the
injection capillary. If a drop is levitating, there is no lower diameter limit. The largest in-
jected drop that can be levitated and gives good levitation results is Ø 5.5 mm. Larger drops
require a higher power input to stay in position, which leads to cavitation and resulting vi-
brations. The upper limit in this system is a deformed and slightly vibrating Ø 10 mm drop.
The dispersed and continuous phases must be completely degassed. Otherwise, the field
of standing waves would immediately cause cavitation, resulting in vibrations and acoustic
streaming. Table 1summarises the specifications of the developed system.
Table 1. Specifications of the developed acoustic levitation system.
Variation Range
contact time seconds to days
initial drop diameter (volume) Ø 2–5.5 mm (4.19–87.11 µL)
ambient temperature 18–24 ◦C
dispersed phase solvents (φ<0)
continuous phase ultrapure water
2.1.2. Measuring Procedure
The plate-tip of the Langevin transducer is positioned at a specific height and the
amplifier is enabled with activated phase tracking, resulting in a resonant frequency of
fr≈
66.5 kHz, a sinusoidal driving voltage of
Vpp =
30 V, a phase shift of
θ=−
10
°
,
and a
maximum power input to the transducer of
Pt≈
1 W. The bottom of the cuvette acts as a
reflector. The open cuvette is automatically filled with ultrapure water to a preset level.
To levitate a drop with
φ<
0, the power input of the transducer is between 0.7 and 1.0 W.
The impedance
|
Z
|
of the transducer, or rather the resonating system, is a good indicator
that the system is able to levitate and is set up correctly. To achieve a levitation result
with low vibrations, there should be no gas bubbles in the cuvette or gas dissolved in the
phases. Any compressible voids or materials immersed in the continuous phase will cause
vibrations and acoustic streaming. Therefore, only glass and titanium grade 5 are placed
inside the cuvette, and even PTFE should be avoided.
The injection system is flushed and filled, and then the injection capillary is attached
to the linear actuator. The first drops must be injected in the manual control environment,
before starting the automated measurements.
A measurement begins with the level control system adjusting the water level in the
cuvette. Before a drop of a certain volume is injected, the high-speed camera (HSC) is
activated and acquires images continuously at 10 Hz. The linear actuator moves into the
cuvette and injects the drop near the anti-node, and then exits the cuvette. The contact time
can be selected according to the type of experiment. At the end of a measurement, the drop
is aspirated by a glass funnel that moves above the drop. When the ultrasound is turned
off, the drop enters the funnel and is aspirated. This procedure can be repeated according
to the desired design of experiments.
2.2. Image Analysis
The images are evaluated with MATLAB (R2022b, MathWorks), and the main work-
flow for image processing is illustrated by a sample code in Appendix A.1.
The resting levitating drops are rotationally symmetric about the z-axis; therefore, 2D
images are used to calculate the drop volume. The images contain location and different
shape properties of interest. With an image resolution of (1024 px)
²
, a spatial image
resolution of 7.5 µm/pixel, and sharp drop outlines, precise calculations are possible.
The drop volume
Vdrop
is acquired by rotating every pixel line of the binarised 2D im-
age around the z-axis and summing up the volume of every disc of 1 px height (Figure 2a).
Micromachines 2023,14, 1923 5 of 18
Figure 2.
(
a
) Volumetric measurements, image to volume: (1) acquired image, (2) binarised image,
and (3) rotated pixel layers forming the disks. (b,c) Visualisation of the introduced measures.
The volume-equivalent diameter dsof a perfect sphere is defined as
ds=6·Vdrop
π1/3
, (2)
and will be further referred to as the diameter dof a drop.
A drop’s covered distance
lc
can be determined by calculating the cumulative sum of
each centroid shift from frame to frame, which gives a good overview of a measurement.
With changing system parameters, such as the drop’s volume, water level, tempera-
ture, etc., the resonant system is slowly affected, and the drop’s position changes accord-
ingly. These changes are rather slow compared to spontaneous vibrations of other nature.
For analyzing
the movement, the centroid
cy/z
will further describe the position of the
drop. To detect and quantify these faster movements, the centred moving average
cy/z,∆t
(CMA) of the centroid
cy/z
over a time interval
∆t
[
−
k,k] is calculated regarding the y-axis
and z-axis:
cy,∆t=1
2k+1
k
∑
j=−k
cy,t(j)and cz,∆t=1
2k+1
k
∑
j=−k
cz,t(j). (3)
A schematic description of a drop and characteristic measures are visualised in Figure 2b.
The individual y- and z-deflection lengths
ld,y/z
between the current centroid
cy/z
and the
CMA centroid cy/z,∆tare calculated as follows:
ld,y=cy−cy,∆tand ld,z=cz−cz,∆t. (4)
The overall deflection length ld,yz is then acquired through Pythagoras:
ld,yz =q(ld,y)2+ (ld,z)2. (5)
The angle of deflection αdeg,y→can be calculated as follows:
αdeg,y→=180
π·arccos cy−cy,∆t
ld,yz !, (6)
and will only be defined when the corresponding deflection length
ld,yz
is at least four
pixels of the high-speed camera (HSC) image. Deflections under 30
µ
m in length are not
considered to be significant movements.
The idle velocity
vi
represents the drop’s 2D moving speed. It is obtained by dividing
the covered distance between every frame by the elapsed time of the time interval
∆
t[
t0
,t]:
vi=
m
∑
j=2q(cy,j−1−cy,j)2+ (cz,j−1−cz,j)2
∆t. (7)
The frame rate at which the images are captured greatly affects this measure.
Micromachines 2023,14, 1923 6 of 18
The almost spherical shape of the levitated drops is characterised by the parameters
ae,be,γeof a fitted ellipse (Figure 2c). The roundness is described by the circularity C:
C=4·π·Ap
p2, (8)
with the area Apand the perimeter pof the 2D image of the drop.
3. Materials and Experiments
Ultrapure water is always used as the continuous phase in this work. Toluene is
the main solvent. The acoustic contrast factor in water is
φ<
0 and, therefore, can be
levitated in the developed system. For rainbow schlieren deflectometry measurements
of the concentration streaks, three additional solvents are introduced. For visualisation
over the levitating drop, butyl acetate and 1-butanol (
ρd<ρc
,
φ<
0) with a solubility
of 6.8 and 84 g/L are used. To visualise the flow below the drop, propylene carbonate
(
ρd>ρc
,
φ>
0) with a solubility of 240 g/L was chosen, but cannot be levitated in the
only anti-node as a pure substance. By mixing 5vol% propylene carbonate with toluene,
the mixture
of solvents can be levitated (
φ<
0) and propylene carbonate will be visible as
the main transfer component (TC) by rainbow schlieren deflectometry. The properties of
the pure substances and the mixture are listed in Table 2.
Table 2. Physical properties of the used pure substances and the mixture at 20 ◦C.
Aqueous Speed Acoustic Contrast
Manufacturer Purity Solubility Density * of Sound * Factor φ* (Equation (1))
[wt%] [g/L] [g/mL] [m/s] [-]
dispersed phase toluene Supelco ≥99.9 0.5 +0.86691 1320.34 −0.199
butyl acetate Supelco ≥99.5 6.8 +0.88147 1148.77 −0.338
1-butanol ChemSolute ≥99.5 84 +0.80968 1256.41 −0.311
propylene carbonate Carl Roth ≥99.7 240 m1.20466 1461.75 0.110
5vol% propylene carbonate in toluene - - - 0.88462 1150.94 −0.332
continuous phase ultrapure water 0.99829 1482.46 0
* Own measurements with an Anton Paar Density and Sound Velocity Meter DSA 5000 M.
+
Data from [
24
],
if needed, are interpolated with a polynomial of the fourth degree to 20 ◦C. mGiven in manufacturer datasheet.
3.1. Evaluation of the Precision of Image Analysis
The absolute accuracy and signal noise of the measured volume and resulting volume-
equivalent diameter of a perfect sphere are determined by using optical calibration targets,
with precise chrome dots imprinted on glass. These dots represent drops of Ø 1.00 and
5.00 mm. The targets are captured for three minutes at a frame rate of 10 Hz.
3.2. Behaviour of Levitating Drops
In order to examine the behaviour of levitating drops from injection to long-term
investigations, three different time intervals are analysed:
• 0–20 s, representing the injection behaviour;
• 1–2 min, representing the short-term behaviour;
• 1 min–8 h, representing the long-term behaviour.
t
=
0 s is the moment of drop detachment, as the injection capillary gets pulled out.
The measurements
focus on motion, shape, injection accuracy, signal noise, and repro-
ducibility. The system toluene/water is used for these investigations, because of its low
aqueous solubility and, therefore, small volume change during a measurement. The initial
diameters for the experiments are in the range of Ø 3–5.5 mm.
Injection behaviour (0–20 s)
: The dispersed phase is injected and placed close to the
pressure anti-node forming a motionless drop attached to the capillary. The capillary is
pulled out and the initial drop detaches and moves towards the pressure anti-node and
oscillates around its final position for a short period of time. The focus is on the covered
Micromachines 2023,14, 1923 7 of 18
distance, the decay of the movement, and the decay of shape oscillations. Starting with
the detachment from the capillary, the drop is observed over 20 s at a frame rate of 500 Hz.
This experiment represents a standard injection procedure.
Short-term behaviour (1–2 min)
: The injection movement has completely decayed
after one minute, representing the system at rest. These measurements are made to quantify
the occurring vibrations (deflection length
ld,yz
), the accuracy of the injected volume, in-
cluding the signal noise, idle velocity, and other shape measures. The short-term behaviour
of one minute is observed at a frame rate of 10 Hz.
Long-term behaviour (1 min–8 h)
: The injection movement has completely decayed
after one minute. The long-term behaviour of drops with varying initial diameters is
observed over 8 h at a frame rate of 10 Hz to quantify the occurring vibrations (deflection
length
ld,yz
) and the reproducibility of the measurements. Under ambient conditions in
the lab, the evaporation speed of water in the open cuvette is about 0.1 mm/h. The water
needs to be refilled to the initial level every four hours. The impact on the deflection length
by refilling the cuvette is shown below.
3.3. Flow Field in the Vicinity of the Drop
Particle image velocimetry and rainbow schlieren deflectometry measurements are
carried out to quantify acoustic streaming and the influence of standing waves on the
spread of inhomogeneous dissolved substances in the continuous phase.
Particle Image Velocimetry (PIV)
: For quantitative acoustic streaming measurements,
the continuous phase is initially homogeneously seeded with Rhodamine B particles
(Ø 20–50
µ
m). A Ø 4 mm toluene drop is then injected and PIV measurements are conducted.
Rainbow Schlieren Deflectometry (RSD)
: For non-invasive partial acoustic stream-
ing and flow field measurements in the continuous phase, RSD measurements for qualita-
tive visualisation are performed. The impact of the standing waves on the propagation of
solvents in the continuous phase is also qualitatively investigated with this method.
RSD visualises gradients in the refractive index (RI) of a system and, therefore, the con-
centration field in the system, if the RI values of the dispersed and continuous phases differ.
The systems with significant aqueous solubilities, butyl acetate/water, 1-butanol/water,
and toluene/water/propylene carbonate, are investigated. The drops are injected and the
resulting concentration field around the drop is visualised by the RSD system developed
by Schulz et al. [
21
] and further improved by Junne et al. [
22
]. A radial filter is used for the
measurements in this work. Two of the three solvents have a lower and one has a higher
density compared to the continuous phase, resulting in different vertical main directions of
mass transfer.
4. Results and Discussion
Firstly, the accuracy of the volume determination is analysed, which is crucial for the
application of this technique. Then the behaviour of the drops from injection to long-term
measurements is examined. The importance of liquid phase degassing in this technique is
discussed. Finally, the influence of the standing waves on the drop’s vicinity with different
dispersed substances is examined.
4.1. Evaluation of the Precision of Image Analysis
The absolute accuracy of the optically acquired volume by measuring the optical dot
calibration targets over three minutes is shown in Table 3, giving the acquired volume with
the calculated diameter (Equation (2)) and the resulting deviation. The spatial resolution of
7.5 µm/pixel has been previously calibrated and is independent of these measurements.
Micromachines 2023,14, 1923 8 of 18
Table 3. Determination of the optical accuracy with calibration targets over 180 s.
Calibration Target Optically Acquired Difference Idle Velocity
Diameter Volume Diameter Volume ∆Diameter ∆Volume vi,10Hz
[mm] [µL] [mm] [µL] [mm] [%] [µL] [%] [mm/min]
1.00 0.5236 0.9984 ±3.34 ×10−40.5211 ±5.23 ×10−4b=2.01‰ 0.0016 0.1581 0.0025 0.4735 0.0562
5.00 65.4499 4.9960 ±2.31 ×10−465.2921 ±90.61 ×10−4b=0.28‰ 0.0040 0.0804 0.1578 0.2411 0.0244
This results in a maximum error of the optical acquisition of 0.1581% in diameter and
0.4735% in volume, which occurs at the smallest diameter. Overall, the volume error can
be effectively approximated to
±
0.5% for diameters greater than 1 mm when the drop is
at rest and does not change its shape. The telecentric objective has low distortion, so the
acquired volume is independent of position. The signal noise of the volume over 180 s of a
fixed Ø 1.00 mm target is 2.01
‰
and decreases with size to 0.28
‰
for a Ø 5.00 mm target.
The noise in the image results in an idle velocity
vi
(Equation (7)) of less than 60
µ
m/min at
a frame rate of 10 Hz and is, therefore, negligible.
4.2. Behaviour of Levitating Drops
The basis for accurate mass transfer measurements of immobilised drops is certainly
the stability in the position of the levitated drop and a uniform shape during the contact time
itself. Every movement in position or shape oscillations results in increased mass transfer.
We take a close look at several time periods to map a complete long-term measurement.
The focus
is on the shift of the centroid and its circularity in addition to the optically
acquired volume. Within this subsection, the toluene/water system is examined due to its
low aqueous solubility and, therefore, slow volume change within a measurement.
Injection behaviour (0–20 s)
: After the volume of the drop is injected, the drop is still
attached to the capillary. When the capillary is pulled back, the drop detaches and moves
towards the pressure anti-node and orbits around it for a short time. An injection of a
Ø 3.5 mm drop is shown in Video S1 of the Supplementary Material.
Figure 3a shows representative two-dimensional paths of three Ø 3 mm drops from
the point of detaching and the following two seconds approaching the resting position.
The first
movement upwards is caused by the buoyancy of the drop which then deflects
toward the pressure anti-node and orbits around it until the momentum decays. Drops of
different diameters behave similarly. This behaviour is analysed in more detail below.
Figure 3.
Movement of drops after injection. (
a
) Path of the centroid
c
in y- and z-direction for three
Ø 3 mm drops. (
b
) The covered distance in the yz-direction of drops with different initial diameters.
Figure 3b shows the trajectories of drops with differing initial diameters. The initial
covered distance does not correlate with the diameter and is in the range between 5 and
10 mm. Movement in the x-direction is not captured with this setup; the actual covered
Micromachines 2023,14, 1923 9 of 18
distance is certainly higher. A three-dimensional movement trajectory would lead to a
smaller variation in the initial range of the covered distance. After the decay of the initial
motion, the curves of the drops in Figure 3b are parallel and have a slope of ~27
µ
m/s or
~1.62 mm/min, respectively. This slope can be understood as the velocity of the centroid in
the yz-direction and is the idle velocity
vi
(Equation (7)). The idle velocity characterises the
measurement and how the standing waves affect the vibrations of the drop. It is a simple
and reliable indicator of a successful and usable measurement. After injection, a jump in the
average idle velocity can indicate a deviation in levitation (e.g., Figure 3b, Ø 5.5 mm drop
at 16.5 s). Considering the x-direction, we estimate that the three-dimensional movement is
below 40
µ
m/s and 2.4 mm/min, respectively. The injection behaviour measurements are
made at a frame rate of 500 Hz, so the signal noise of the centroid increases the idle velocity
compared to the 10 Hz measurements below.
A more detailed insight into the decaying behaviour is given in Figure 4. The trajecto-
ries of the distance between the actual centroid and the centroid at 20 s of the horizontal
and the vertical axis of all measurements with different diameters are shown.
Figure 4.
The absolute value of the deviation between the actual centroid and the centroid at 20 s for
all measurements (Ø 3–5.5 mm) differently coloured: (
a
) with respect to the horizontal axis y and
(b) with respect to the vertical axis z.
After four seconds, the horizontal deflection (Figure 4a) falls below the edge length of
one pixel of the HSC image (7.5
µ
m). For the vertical deflection, the initial motions decay
more slowly (Figure 4b). Most drops decay within the first three seconds below 7.5
µ
m.
A minority
of the drops need a longer decay time, some taking up to 16 s. The drops are,
in conclusion
, about to be almost stationary in position after 16 s at the latest. The drops
are more stable horizontally than in the vertical direction.
The acquired volume of these initially moving and deformed drops is shown in
Figure 5a, which illustrates one representative drop of each diameter. When the oscillation
in shape decays, the calculated volume is constant and results in the actual volume of the
drop. At this point, the drops show a circularity
C
of more than 0.98, and the drops can be
assumed to be rotationally symmetric about the z-axis. With increasing drop size,
the time
of oscillation lasts longer, and this behaviour can also be seen in Figure 3b by reaching
the constant slope more slowly. The variation of the dimensionless volume
v+
(recorded
volume/recorded end volume) is less than ±0.05% (Figure 5b) two seconds after injection.
In conclusion, the decay of the shape is faster than the decay of the position.
The acquired
drop volume is, therefore, reliable after two seconds. A total of 20 s after the detachment
from the capillary, the movement is stable. In addition, the transient circularity
C
of
an acquired drop can be used to verify whether the drop volume is reliable.
To acquire
volumes of asymmetrical shape caused by dynamic drop movements, at least one additional
optical axis is necessary. This additional axis would also allow the measurement of the
three-dimensional idle velocity of a drop.
Micromachines 2023,14, 1923 10 of 18
Figure 5.
Injection behaviour of the volume of different diameters: (
a
) the acquired volume within
the first three seconds after detachment and (b) dimensionless volume v+=vt/vt=20s.
Short-term behaviour (1–2 min)
: One minute after the drop is injected, the initial
movement of the drop has dissipated. For this time interval, about 600 images were anal-
ysed for drops of different initial diameters. The characteristic values for one representative
drop of every diameter are summarised in Table 4.
Table 4. Short-term characteristics over 60 s of representative toluene drops.
Target
Diameter Diameter Volume Deflection
Length Circularity Elliptical Shape Parameters as
in Figure 2c
Idle
Velocity
d dsVdrop ld,yz C aebeγevi,10Hz
[mm] [mm ±‰] [µL ±‰] [µm] [- ±‰] [mm ±µm] [mm ±µm] [°] [ mm
min ]
3.0 2.98 ±0.15 13.79 ±0.44 0.62 ±1.85 1.000 ±3.98 2.99 ±0.57 2.96 ±0.56 −1.23 ±0.77 0.49
3.5 3.47 ±0.12 21.82 ±0.35 0.40 ±0.69 0.997 ±5.89 3.49 ±0.66 3.43 ±0.84 −1.12 ±0.33 0.24
4.0 4.01 ±0.10 33.85 ±0.31 0.54 ±1.27 0.996 ±8.37 4.05 ±0.71 3.95 ±0.59 −1.10 ±0.20 0.24
4.5 4.48 ±0.13 47.04 ±0.39 0.76 ±1.99 0.995 ±7.24 4.54 ±0.80 4.37 ±1.24 −1.24 ±0.17 0.54
5.0 4.98 ±0.09 64.56 ±0.27 0.49 ±1.18 0.992 ±5.41 5.04 ±0.73 4.85 ±0.59 −0.51 ±0.10 0.34
5.5 5.49 ±0.11 86.62 ±0.34 0.46 ±0.67 0.990 ±5.76 5.58 ±0.79 5.31 ±0.60 −0.61 ±0.10 0.33
The units of the values are structured as follows: mean
±
(max
−
min)/2 [unit] or mean
±
(500
·
(max
−
min)/mean)
[unit ±‰].
The optical volume acquisition has a signal noise of less than 0.5
‰
in the range of
Ø 3–5.5 mm drops, almost independent of the diameter. The signal noise in the volume
of a Ø 5 mm drop is 0.27
‰
and the raw optical signal noise of a Ø 5.00 mm optical
target is 0.28
‰
(Table 3). The signal noise in volume is, therefore, due to the optical
acquisition and does not originate from any induced vibrations. The absolute deviation
in the injected volume of the drops is caused by the random uncertainty of the injection
system. By withdrawing the injection capillary, some of the dispersed phase may be left
on the capillary, lowering the injected volume. The interfacial tension also affects the
deviation of the injection of the target volume. Since this uncertainty is quantifiable, it
has no negative effect on the measurements. The acquired deflection length
ld,yz
is in
the sub-pixel range;
the drops
are overall not moving or vibrating significantly. For all
drops, the two-dimensional idle velocity at a frame rate of 10 Hz is less than 0.55 mm/min.
In addition, taking into account the undetected movement in the x-direction, the three-
dimensional idle velocity caused by the occurring vibrations can be estimated to be less
than 0.8 mm/min.
In terms of shape, the drops are of a spherical nature with a minimum circularity
C
of
0.99 (Table 4). The larger the diameter, the more it deviates from a perfect sphere. The cubic
cuvette and the transducer are not exactly concentric; therefore, there is a small negative
offset in the tilt γe.
Micromachines 2023,14, 1923 11 of 18
Long-term behaviour (1 min–8 h)
: Figure 6shows the deflection length
ld,yz
of a Ø 3,
4, and 5 mm drop. The irregular peaks at four-hour intervals are caused by the deliberate
slow relevelling of the water in the cuvette. A changing water level affects the position of
the drop mainly in the z-direction. Apart from these outliers, the deflections of the drops
are almost all below 7.5
µ
m and, therefore, extraordinarily stable in position, regardless of
the drop diameter. A time-lapse of a long-term measurement of a Ø 3 mm drop is shown in
Video S2 of the Supplementary Material. External vibrations cannot be completely ruled
out, as can be seen by three dots above 7.5 µm in Figure 6of the Ø 3 mm drop at 0.8 h.
Figure 6.
Deflection length
ld,yz
with
∆
t = 120 s of toluene drops, 8 h long-term behaviour. The spikes
occurring at 0.3, 4.0, 4.1, 4.3, and 8.0 h indicate a change in position caused by the need to relevel the
water every four hours.
The drops vibrate strongly when the dispersed and continuous phases are initially
saturated with air. This is shown in Figure 7for three example drops of different diame-
ters. The trajectories do not show a stable behaviour. Overall, the measurements are not
reproducible. The ultrasonic field degasses the phases, resulting in many small gas bubbles
on the walls of the cuvette. These compressible cavities absorb the ultrasonic waves and
strongly influence the resonant system. This can lead to a failure of the drop levitation,
as seen
for the Ø 4 mm drop leaving the anti-node at 5.1 h with no further signal acquired.
Figure 7.
Deflection length
ld,yz
with
∆
t = 120 s of toluene drops of non-degassed systems, 8 h
long-term behaviour. At 5.1 h, the Ø 4 mm drop left the anti-node; gas bubbles formed and caused
the levitation to fail.
Micromachines 2023,14, 1923 12 of 18
The idle velocities from 1 minute to 8 h, including the deflections caused by relevel-
ling the water, are given in Table 5for the previously shown measurements of degassed
(Figure 6) and non-degassed (Figure 7) systems.
Table 5.
Idle velocity of toluene drops in degassed (Figure 6) and non-degassed (Figure 7) systems,
8 h long-term behaviour.
Diameter Idle Velocity
d vi,10Hz,degassed vi,10Hz,non−degassed
[mm] [mm/min] [mm/min]
3 0.2415 1.509
4 0.1855 16.544
5 0.2255 8.4570
The measurements show that the standing waves do not induce significant drop vibra-
tions in systems that have been degassed. It can be estimated that up to 10% of the idle
velocity of the degassed systems is caused by the signal noise of the optical acquisition sys-
tem (cf. Table 3, Ø 5 mm). The idle velocities of the long-term measurements are generally
lower than the short-term measurements. We believe that the continuous exposure to the
acoustic field degasses the system even more. This results in fewer vibrations over time and
also prevents the dissolution of ambient air components into the continuous phase in the
open cuvette. To achieve a high level of vibrations and idle velocity,
the dispersed
and con-
tinuous phase should not be degassed or can be additionally gassed beforehand. The idle
velocities of non-degassed systems are highly variable and, therefore, not reproducible.
In this case, long-term measurements are difficult. Bubbles are the result of degassing
and have a very strong negative effect on the resonance system and thus on the acoustic
trapping of the drops.
Drops of small diameter show lower reproducibility of mass transfer rates, making
them the preferred choice for further investigations. Figure 8shows the reproducibility of
the dissolution of five Ø 3 mm drops in degassed ultrapure water.
Figure 8.
Volume of dissolving Ø 3 mm toluene drops over 8 h, with a maximum volume error
of ±0.5%.
The initial volume has a maximum offset of 3.5% compared to a perfect Ø 3 mm
sphere, due to the random injection behaviour mentioned above. The mass transfer rates,
here measured
as the volume transfer rate, given as the slope of the volume trajectory,
range from 0.249 to 0.293
µ
L/h, as shown in Table 6. The idle velocity of the measurement
can be an indicator of enhanced mass transfer. Measurement M2031 has by far the smallest
Micromachines 2023,14, 1923 13 of 18
mass transfer rate and a small corresponding idle velocity. In addition, the temperature
and, therefore, the aqueous solubility of toluene in water is reduced.
Table 6. Characteristic measures of the measurements shown in Figure 8.
M2031 M2036 M2137 M2143 M2144
mass transfer rate ˙
Vd[µL/h] 0.249 0.272 0.293 0.290 0.293
idle velocity vi,10Hz [mm/min] 0.15 0.24 0.22 0.20 0.24
temperature Tc[◦C] 18.0 19.3 22.9 23.0 23.1
The measurements show good reproducibility if only measurements M2137, M2143,
and M2144 are considered. In this case, the temperatures and the idle velocities are within a
narrow range. The effect of temperature on the solubilities and, therefore, on mass transfer
cannot be eliminated by tempering the system presented. An isolated tempering chamber
would be required. However, the temperature is known and the effect can be quantified.
4.3. Flow Field in the Vicinity of the Drop
Particle Image Velocimetry (PIV)
: The principle of PIV is to seed a fluid with sufficient
small tracer particles to visualise flow fields by tracking their paths. The main idea is that
the particles have negligible sedimentation velocities and, therefore, fully follow an induced
flow field. The experiments were conducted with non-degassed water accompanied by
acoustic streaming, with the result shown in Figure 9.
Figure 9.
Image of the setup during PIV measurements of a toluene drop after 10 min, with Rho-
damine B particles and a bubble trapped in the nodes. The ultrapure water was not initially degassed,
resulting in a gas bubble.
The acoustic field collects and levitates the particles in the node, forming a circular
plane. In a second node, a gas bubble was formed by releasing gas from the continuous
phase caused by the ultrasonic field. Both Rhodamine B particles and gas bubbles have
a positive acoustic contrast factor
φ>
0 and are attracted to the nodes in the system.
The pressure field created a symmetrical particle formation at the bottom of the cuvette.
The seeded particles are not only affected by acoustic streaming but also by the
standing waves themselves. Therefore, PIV cannot be used to measure the flow field in
the continuous phase in this levitation system and the rainbow schlieren deflectometry
technique will be used to partly visualise flow patterns in the continuous phase.
Rainbow Schlieren Deflectometry (RSD)
: The occurring concentration gradients in
the continuous phase caused by mass transfer are visualised by RSD measurements and
are used for indirect flow field measurements. A prevailing flow field caused by acoustic
streaming in the continuous phase would affect and deflect the uniform one-dimensional
concentration streak. Two vertical directions of mass transfer, up and down, are investi-
Micromachines 2023,14, 1923 14 of 18
gated. In addition to measuring the flow field, this technique can also be used to determine
the dispersion of the inhomogeneous dissolved substance.
Butyl acetate with ρd<ρc
,
slightly soluble
: Figure 10a shows the injection of a
butyl acetate drop; initially, a weak and disturbed concentration field is visible. Pulling
out the capillary creates a turbulent flow field in the continuous phase. After about
30 s
,
the turbulence of the concentration field disappears (Figure 10b). From this point on,
the concentration
streak in the vicinity of the drop has a stationary shape, and the streak
points upwards and tilts in the
−
y-direction. It can be assumed that no flow field is
induced by acoustic streaming in close vicinity above the drop. The standing waves
affect the dissolved butyl acetate and prevent it from reaching the tip of the ultrasonic
transducer. It is repelled by the nodal plane halfway between the anti-node and the tip of
the ultrasonic transducer.
Figure 10.
RSD images of a butyl acetate drop in water (
ρd<ρc
) of one measurement at different
times: (a)t=0s,(b)t= 30 s and (c)t= 8 min.
1-butanol with ρd<ρc, sparingly soluble
: Figure 11a shows the injection of a
1-butanol
drop; initially a strong and rapidly forming concentration field is visible.
The complete
measurement is shown in Video S3 of the Supplementary Material.
The turbulence caused by the withdrawal of the capillary has a slight and brief im-
pact on the concentration streak. The aqueous solubility results in a rapidly dissolving
drop with high mass transfer rates by observing the diameter of the drop (Figure 11b,c).
The transferred and dissolved 1-butanol is trapped below the centre of the ultrasonic horn.
The dissolved 1-butanol cannot pass through the volume around the edge of the plate
tip (Figure 11c). In this region, the acoustic particle velocity is at its maximum and keeps
1-butanol away. It can be clearly seen that even dissolved substances can be strongly
affected by standing waves.
Figure 11.
RSD images of a 1-butanol drop in water (
ρd<ρc
) of one measurement at different times:
(a)t=0s,(b)t= 30 s and (c)t= 8 min.
Micromachines 2023,14, 1923 15 of 18
5 vol% propylene carbonate in toluene with ρTC >ρc, freely soluble
: To levitate
propylene carbonate (
φ>0
) in the anti-node, it is mixed with toluene, which acts as
a carrier for acoustic levitation. The density of propylene carbonate is higher than that
of water, so the concentration streaks in the continuous phase should theoretically only
point downward. Propylene carbonate is the main transfer component (TC) in the system.
The slow
mass transfer of toluene is not seen in this setup, which is very slightly soluble
in water. Figure 12 shows the behaviour of propylene carbonate as it is transferred to the
continuous phase. The entire measurement is shown in Video S4 of the Supplementary Ma-
terial. The high aqueous solubility (240 g/L) of the TC results in rapid mass transfer, leading
to Marangoni eruptions driven by surface tension gradients. When the concentration of the
TC in the drop falls below a threshold, the eruptions stop.
Figure 12.
RSD images of a 5vol% propylene carbonate/toluene drop in water (
ρTC >ρc
) of one
measurement at different times: (a)t=0s,(b)t= 30 s and (c)t= 8 min.
Although the density of the TC is higher than that of water, there are two opposite
directions of mass transfer (Figure 12b). This behaviour is not caused by acoustic streaming;
there is no superimposed turbulence visible in the spread of the TC. The acoustic field also
creates two distinct barriers for the TC at two nodal planes, comparable to butyl acetate
(Figure 10c) with one nodal plane as a barrier. The TC slides along these curved planes
and slowly descends to the bottom of the cuvette, as it continues to dissolve. Thus, for the
RSD technique, the TC visually disappears in the continuous phase. The measurement
shows that the acoustic field can influence the vertical direction of mass transfer and the
propagation of an inhomogeneous dissolved TC.
5. Conclusions
With this work, we developed a one-dimensional low-impact acoustic levitation
system and investigated the application in the field of mass transfer of immobilised single
drops in liquid–liquid systems in a quiescent environment.
For a systematic study, the levitation period of a long-term measurement was divided
into three intervals for different behaviours: injection, short-term, and long-term. When
a drop is injected, the initial movement disappears within the first 16 s. The shape is
stationary after two seconds, with a circularity C> 0.98 regardless of the diameter; the
measured volume is reliable from this point on, with an absolute volume error of
±
0.5%.
Short-term investigations have shown that the signal noise of the volume of a levitating
drop is about
±
0.05%, which is caused by the optical acquisition system. The shift of the
centroid over one minute is <7.5
µ
m and, therefore, in the sub-pixel range, resulting in an
idle velocity of
vi,10Hz
< 0.5 mm/min. The covered distance has been shown to be a good
visual indicator of the condition of the acoustically levitated drop. A constant slope of the
covered distance, resulting in a constant idle velocity, indicates uniform and stationary
levitation. The long-term measurements showed a deflection length below 7.5
µ
m, which
is also in the sub-pixel range, ending up with an idle velocity
vi,10Hz < 0.25 mm/min
. Our
observations show that the acoustic field does not induce drop vibrations during operation.
Measurements of dissolving drops with similar idle speeds and continuous phase tempera-
Micromachines 2023,14, 1923 16 of 18
tures are expected to have similar mass transfer rates,
and these
measurements have shown
good reproducibility. The importance of degassing the liquid phases has been addressed
to perform reproducible measurements with this technique. When gas is dissolved in the
dispersed and in the continuous phase, significant vibrations can be observed with an idle
velocity vi,10Hz > 15 mm/min, resulting in enhanced mass transfer.
Rainbow schlieren deflectometry measurements have shown that the standing waves
do not induce a flow field caused by acoustic streaming in the vicinity of the drop.
Any compressibility
in the liquid environment will result in an acoustic streaming flow,
such as
gas bubbles, submerged materials (e.g., PTFE), or dissolved gases in the liquid
phases. However, the dispersion of inhomogeneous dissolved substances in the continuous
phase was significantly affected by the standing waves in two different ways. One group
of substances is prevented from spreading through the nodal planes and is additionally
pulled towards these planes against its natural buoyancy. The inhomogeneous dissolved
substance shows an alternative acoustic contrast factor compared to the pure substance in
water.
The other
group of substances can pass through the nodal planes without interfer-
ence and is stopped by regions of maximum particle velocity of the acoustic field.
In this
case,
the substance
is trapped under the horn of the ultrasonic transducer and shows a
negative contrast factor as an inhomogeneous dissolved substance. These observations
require further investigations to understand this mechanism in more detail.
Acoustic levitation can be a unique tool for many directions of fundamental research
in liquid–liquid systems, such as mass transfer measurements, medical ageing tests with-
out contact with any surfaces, and micro-reactors with excellent tempering conditions,
to mention
a few. To perform measurements in a system with continuous phases other
than water, it is essential to adapt the design of the acoustic levitation cell and its resonance
behaviour to the specific physical properties of the chosen substance.
Supplementary Materials:
The following supporting information can be downloaded at: www.mdpi.
com/xxx/s1. Video S1: Injection of a toluene drop (20 s, HSC), Video S2: Long-term measurement of
a toluene drop (8 h, HSC), Video S3: 1-butanol drop (8 min, RSD) and Video S4: 5vol% propylene
carbonate in toluene drop (8 min, RSD).
Author Contributions:
Conceptualization, J.-P.R.; Data curation, J.-P.R.; Formal analysis, J.-P.R.;
Funding acquisition, J.V.; Investigation, J.-P.R.; Methodology, J.-P.R.; Project administration, J.V.;
Software , J.-P.R.; Supervision, M.K.; Validation, J.-P.R.; Visualization, J.-P.R.; Writing—original draft,
J.-P.R.; Writing—review and editing, J.V. and M.K. All authors have read and agreed to the published
version of the manuscript.
Funding:
The authors gratefully acknowledge the funding of a scholarship by the Max Buchner
Research Foundation (No. 3766) administrated by DECHEMA e.V., the support by the German
Research Foundation, and the Open Access Publication Fund of TU Berlin.
Data Availability Statement:
The data that support the findings of this study are available on request.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
The following abbreviations are used in this manuscript:
FPGA Field programmable gate array
HSC High-speed camera
CMA Centred moving average
PTFE Polytetrafluoroethylene
PIV Particle image velocimetry
RSD Rainbow schlieren deflectometry
TC Transfer component
Micromachines 2023,14, 1923 17 of 18
Appendix A
Appendix A.1. MATLAB Example for Image Processing
1folder = uigetdir ; % select folder with monochrome PNG files showing drops
2files = dir([ folder ,’\*. png ’]); % find PNG files in selected folder
3pixel_size = 7.5*10^ -3; % for volume calculation , scale of PNGs [ mm / pixel ]
4
5for i=1: length( files ) % loop through images
6IMdump = []; % reset dump structure
7IM(i). path = [ files (i). folder ’\’ files (i). name ]; % get path of png no. i
8IMdump.IM_raw = imread(IM(i).path); % read monochrome image
9IMdump . IM_bin = ~ imbinarize ( IMdump . IM_raw , ’adaptive ’, ...
10 ’ForegroundPolarity’,’ dark ’,’ Sensitivity ’ ,0.5); % binarize adaptive with
variable threshold and dark foreground (drop)
11 IMdump . IM_filled = imfill ( IMdump . IM_bin , ’holes ’); % Fill objects
12 IMdump . IM_drop = bwareafilt ( IMdump . IM_filled ,1) ; % Extract largest object
13 IM (i) .IMAGE = imclearborder ( IMdump . IM_drop ); % Clear objects on border
14 IM (i) . volume = sum (pi () *( sum(IM(i). IMAGE ,2) .^2) /4* pixel_size ^3) ;% get
volume in microliters of a drop that is symmetric to the vertical axis
15 IMdump . regprops = regionprops ( IM (i). IMAGE , ’ all ’); % Get ’all ’ region
props , improve speed by calculating specific values
16 IMdump .fn = fieldnames ( IMdump . regprops ) ; % Get fieldnames of regprops
17
18 for j=1: length( IMdump .fn )
19 if ~isempty( IMdump . regprops ) % Wirte values to IM (i):
20 IM (i) .( IMdump .fn {j}) = IMdump . regprops .( IMdump .fn {j}) ;
21 else % Write NaN to values to IM (i) for empty IMAGE :
22 IM (i) .( IMdump .fn {j}) = NaN; IM (i). volume = NaN ;
23 end
24 end
25
26 % Add more calculations here ...
27
28 end; clearvars -except IM; % keep IM , containing the calculated values
References
1.
Lieber, C.; Melekidis, S.; Koch, R.; Bauer, H.J. Insights into the evaporation characteristics of saliva droplets and aerosols:
Levitation experiments and numerical modeling. J. Aerosol Sci. 2021,154, 105760. [CrossRef] [PubMed]
2.
Maruyama, Y.; Hasegawa, K. Evaporation and drying kinetics of water-NaCl droplets via acoustic levitation. RSC Adv.
2020
,
10, 1870–1877. [CrossRef] [PubMed]
3. Scheeline, A.; Behrens, R.L. Potential of levitated drops to serve as microreactors for biophysical measurements. Biophys. Chem.
2012,165–166, 1–12. [CrossRef] [PubMed]
4.
Dangi, B.B.; Dickerson, D.J. Design and Performance of an Acoustic Levitator System Coupled with a Tunable Monochromatic
Light Source and a Raman Spectrometer for In Situ Reaction Monitoring. ACS Omega
2021
,6, 10447–10453. [CrossRef] [PubMed]
5.
Nguyen, T.Y.; Roessler, E.A.; Rademann, K.; Emmerling, F. Control of organic polymorph formation: Crystallization pathways in
acoustically levitated droplets. Z. Krist.-Cryst. Mater. 2016,232, 15–24. [CrossRef]
6.
Hasegawa, K.; Murata, M. Oscillation Dynamics of Multiple Water Droplets Levitated in an Acoustic Field. Micromachines
2022
,
13, 1373. [CrossRef] [PubMed]
7.
Hirayama, R.; Plasencia, D.M.; Masuda, N.; Subramanian, S. A volumetric display for visual, tactile and audio presentation using
acoustic trapping. Nature 2019,575, 320–323. [CrossRef]
8.
Andrade, M.A.B.; Camargo, T.S.A.; Marzo, A. Automatic contactless injection, transportation, merging, and ejection of droplets
with a multifocal point acoustic levitator. Rev. Sci. Instrum. 2018,89, 125105. [CrossRef]
9.
Watanabe, A.; Hasegawa, K.; Abe, Y. Contactless Fluid Manipulation in Air: Droplet Coalescence and Active Mixing by Acoustic
Levitation. Sci. Rep. 2018,8, 10221. [CrossRef]
10.
Marzo, A.; Ghobrial, A.; Cox, L.; Caleap, M.; Croxford, A.; Drinkwater, B.W. Realization of compact tractor beams using acoustic
delay-lines. Appl. Phys. Lett. 2017,110, 014102. [CrossRef]
11.
Foresti, D.; Nabavi, M.; Klingauf, M.; Ferrari, A.; Poulikakos, D. Acoustophoretic contactless transport and handling of matter in
air. Proc. Natl. Acad. Sci. USA 2013,110, 12549–12554. [CrossRef] [PubMed]
12.
Lim, H.G.; Kim, K.; Kim, Y.; Park, J.; Kim, H.; Kim, H.H.; Heo, D.; Yoo, J. High Frequency Ultrasonic Levitation of Red Blood Cells
Aggregation. In Proceedings of the IEEE International Ultrasonics Symposium (IUS), Kobe, Japan, 22–25 October 2018. [CrossRef]
13.
Hammarström, B.; Skov, N.R.; Olofsson, K.; Bruus, H.; Wiklund, M. Acoustic trapping based on surface displacement of resonance
modes. J. Acoust. Soc. Am. 2021,149, 1445–1453. [CrossRef] [PubMed]
Micromachines 2023,14, 1923 18 of 18
14.
Lenshof, A.; Magnusson, C.; Laurell, T. Acoustofluidics 8: Applications of acoustophoresis in continuous flow microsystems.
Lab Chip 2012,12, 1210. [CrossRef] [PubMed]
15.
Lv, H.; Chen, X.; Zhang, Y.; Wang, X.; Zeng, X.; Zhang, D. Two-stage particle separation channel based on standing surface
acoustic wave. J. Microsc. 2022,286, 42–54. [CrossRef] [PubMed]
16.
Luo, X.; Cao, J.; Gong, H.; Yan, H.; He, L. Phase separation technology based on ultrasonic standing waves: A review.
Ultrason. Sonochem. 2018,48, 287–298. [CrossRef] [PubMed]
17.
Drinkwater, B.W. Dynamic-field devices for the ultrasonic manipulation of microparticles. Lab Chip
2016
,16, 2360–2375.
[CrossRef] [PubMed]
18. Apfel, R.E. A Novel Technique for Measuring the Strength of Liquids. J. Acoust. Soc. Am. 1971,49, 145–155. [CrossRef]
19.
Trinh, E.; Zwern, A.; Wang, T.G. An experimental study of small-amplitude drop oscillations in immiscible liquid systems.
J. Fluid Mech. 1982,115, 453. [CrossRef]
20.
Asaki, T.J.; Marston, P.L.; Trinh, E.H. Shape oscillations of bubbles in water driven by modulated ultrasonic radiation pressure:
Observations and detection with scattered laser light. J. Acoust. Soc. Am. 1992,93, 706–713. [CrossRef]
21.
Schulz, J.M.; Junne, H.; Böhm, L.; Kraume, M. Measuring local heat transfer by application of Rainbow Schlieren Deflectometry
in case of different symmetric conditions. Exp. Therm. Fluid Sci. 2020,110, 109887. [CrossRef]
22.
Junne, H.; Jurtz, N.; Schulz, J.M.; Kraume, M.; Böhm, L. Rainbow Schlieren Deflectometry for spherical fields: A new algorithm
and numerical validation approach. Numer. Heat Transf. Part Fundam. 2023. [CrossRef]
23. Gor’kov, L.P. On the forces acting on a small particle in an acoustical field in an ideal fluid. Sov. Phys. Dokl. 1962,6, 773–775.
24. Rumble, J. CRC Handbook of Chemistry and Physics, 104th ed.; Taylor and Francis Group: Oxfordshire, UK, 2023.
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