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Japanese Journal of Applied Physics 52 (2013) 07HE02
http://dx.doi.org/10.7567/JJAP.52.07HE02

Demonstration of Noncontact Ultrasonic Mixing of Droplets
Ryohei Nakamura, Yosuke Mizuno, and Kentaro Nakamura
Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503, Japan
Received November 23, 2012; accepted January 29, 2013; published online June 20, 2013
The noncontact ultrasonic mixing of two droplets is demonstrated, for the first time, by controlling the acoustic field using the following two
methods: (1) by changing the distance between the vibrator and the reflector and (2) by modulating the driving voltage amplitude applied to thevibrator. The operating principle is confirmed by measuring the acoustic pressure distribution and the temporal change in the acoustic pressurenear the mixing position. We also show that the stable mixing of droplets with high repeatability is feasible by method (2), which does not involvethe use of mechanically moving parts. # 2013 The Japan Society of Applied Physics

1. Introduction

In the biochemical, pharmaceutical, and new material
industries, the noncontact transport of small components,
powders, and liquids is highly demanded. Although anumber of methods based on air pressure and electric/
magnetic ﬁelds have been proposed, they suﬀer from noise,high cost, and applicability only to electric/magnetic
objects.1–11) To overcome these drawbacks, noncontact
ultrasonic transport has been extensively studied so far, inwhich various ultrasonic technologies for manipulatingsmall objects, particles, and cells in air12–19) and in liquid
are used.20–22) We are currently aiming at implementing allof its procedures, i.e., injection, linear transport, direction
switching, ejection, analysis, and dispensing, based on
ultrasonics. When the materials to be transported are liquids(or droplets), mixing of multiple droplets is also essential.
Up to now, linear transport,23–25) direction switching,26) andejection27) have been successfully demonstrated, but otherprocedures need to be developed to achieve our aim.
Here, we focus on the mixing of multiple droplets.
Droplets trapped and levitated at some particular points
can be mixed by controlling the acoustic ﬁeld, as shown in
Fig. 1, based on one of the following four methods: (1)by using traveling waves, (2) by switching the acoustic
modes, (3) by changing the distance between the vibrator
and the reﬂector, and (4) by modulating the driving voltage
amplitude applied to the vibrator. In this study, we demonstrate the noncontact ultrasonic mixing of two droplets using
methods (3) and (4). The operating principle is conﬁrmed
by measuring the acoustic pressure distribution and thetemporal change in the acoustic pressure near the mixing
position. Method (4), which does not involve the use of any
mechanically moving parts, is shown to have a higher
repeatability than method (3).
2. Experimental Procedure

Figure 2 shows the experimental setup, where a Langevintransducer with an exponential horn excited a breathingmode of an aluminum ring (vibrator) at 25.9 kHz, and an
85-mm-long acrylic cylinder (reﬂector) was ﬁxed in thering. The depth of the vibrator was 30 mm. As is shown in
the next section, the acoustic ﬁeld had one nodal circle andtwelve radial nodal lines, as shown in Fig. 3. Here, weshould note that the alignment of the nodal lines is notbilaterally symmetric due to the bolt cap shown in Fig. 2,
and that objects are levitated at the position located along the

Fig. 1. (Color online) Concept of noncontact ultrasonic mixing of two

droplets.

Fig. 2. (Color online) Experimental setup for droplet mixing.

nodal circle and at the midpoint of two neighboring nodal
lines.28) Water was converted into droplets, which weremanually injected using a syringe into the acoustic ﬁeld
between the vibrator and the reﬂector, and levitated at two
diﬀerent points. The maximum volume of the droplet
levitated with this setup was 19 l.
2.1 Experiments (I): Change in vibrator/reflector
distance

As the ﬁrst trial, by shaking the vibrator in the verticaldirection to change the distance between the vibrator and thereﬂector [which was initially set to 7 mm at an angular
position of 90 (see Fig. 3)], we successfully demonstrated
noncontact droplet mixing, as shown in Figs. 4(a)–4(d). The
two droplets were (a) levitated at diﬀerent points and (b)moved by changing the vibrator/reﬂector distance, until they(c) touched each other and (d) mixed using surface tension.
In Fig. 4(a), the volume of the bottom droplet was 1.8 l,and that of the other droplet was 0.4 l. The mixed droplet
was rotating, which apparently contributed to the stirring of
its content.29)
To conﬁrm the operating principle of this method, theacoustic ﬁeld distribution between the vibrator and thereﬂector was measured as the modulation in optical path

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Fig. 3. (Color online) Schematic acoustic ﬁeld. The dotted circle/lines

indicate the nodal circle/lines.
Fig. 6. (Color online) Measured circumferential acoustic pressure

distribution when the L values were 7.5 and 10 mm.

Fig. 4. (Color online) Photographs of droplet mixing by changing thevibrator/reﬂector distance: (a) two droplets levitated at diﬀerent points,(b) two droplets approaching each other, (c) beginning of droplet mixing,
and (d) mixed droplet.

Fig. 5. (Color online) Two directions in which the acoustic ﬁeld

distribution and its dependence on the vibrator/reﬂector distance L were
measured.

length using a laser Doppler vibrometer (LDV) with awavelength of 633 nm. Considering the acoustooptic eﬀectof air and the transformation of the path length modulation
into the resultant LDV output, the acoustic pressure p isexpressed as30)p¼

n c2 
vLDV ;n  1 2f l

ð1Þ

where n is the refractive index of air (¼ 1:0002764), c theacoustic velocity (¼ 346:51 m/s at 25  C),  the density ofair (¼ 1:184 kg/m3 ), f the frequency of the acoustic ﬁeld,
l the acoustic ﬁeld length (¼ 30 mm), and vLDV the velocity
measured with the LDV. As shown in Fig. 5, the acoustic
ﬁeld distribution and its dependence on the vibrator/reﬂector
distance L at 90 were measured in two directions: thecircumferential direction from 0 to 180 and the radial

Fig. 7. (Color online) Measured maximum acoustic pressure in the radial

direction at 65 vs L.

direction at 65 (where the droplets were mixed). In thecircumferential direction, the acoustic pressure distribution
was measured along the midline between the vibrator andthe reﬂector; in the radial direction, ﬁrst, the acoustic ﬁeld
distribution at 65 was measured, and then the maximum
pressure was obtained at each L. Figure 6 shows themeasured circumferential acoustic pressure distribution
when the L values were 7.5 and 10 mm. As L was changed,
the acoustic pressure also markedly changed, but thepositions of the nodal points at approximately 90 only
slightly changed. Figure 7 shows the measured maximum
acoustic pressure in the radial direction at 65 as a functionof L, which also indicated that the pressure was highly
dependent on L. When L was approximately 9 mm, themaximum acoustic pressure was highest; when L wasapproximately 7 mm (experimentally employed), a marked
change in the maximum pressure was observed. Thus, theoperating principle of this method appears to be as follows:ﬁrst, when the vibrating ring was shaken upward, L became
shorter, and consequently the acoustic pressure applied tothe droplets was temporarily reduced; then the droplets
shifted in the circumferential direction with gravity andmixed with each other. When the vibrating ring returned to
its initial position, the mixed droplet was also trapped at theinitial position.
We also measured the vibration mode of the vibrator in
the depth and circumferential directions with the LDV. The
vibration velocity was almost uniform in the depth direction.
The measured vibration velocity distribution in the circumferential direction is shown in Fig. 8, in which the number
and positions of nodal points were inconsistent with those

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Fig. 10. (Color online) Schematic of periodical amplitude modulation

applied to the driving voltage.
Fig. 8. (Color online) Measured vibration velocity distribution of vibrator

in the circumferential direction.

Fig. 11. (Color online) Photos of droplet mixing by amplitude

modulation of the driving voltage: (a) two droplets levitated at the diﬀerent
points, (b) two droplets moving circumferentially, and (c) mixed droplet.

Fig. 9. (Color online) Measured temporal change in the acoustic pressure

at the strongest antinode near the mixing position.

in Fig. 6. This indicates that the vibration modes of thevibrator and that of the air were diﬀerent, resulting in theselective excitation of the vibration mode of the air, which
is similar to that of the vibrator.
In addition, we measured the temporal change in the
acoustic pressure at the strongest antinode near the position
where the droplets were mixed, which is shown in Fig. 9.
When the vibrating ring was shaken upward and L became
shorter, the acoustic pressure was reduced; when the ring
returned to its initial position, the pressure also returnedto the initial value. The waveform was, however, distorted
probably owing to the mechanical movement of the vibrator,
resulting in poor repeatability. Other methods that involveno mechanical movement need to be developed to perform
noncontact droplet mixing with higher stability.

(a)

(b)

2.2 Experiments (II): Amplitude modulation of driving
voltageFig. 12. (Color online) Measured temporal changes in (a) driving voltage

Next, by periodically modulating the driving voltage
amplitude applied to the vibrator (schematically shown in
Fig. 10; modulation period: 50 ms), we demonstrated thenoncontact mixing of two droplets, as shown in Figs. 11(a)–11(c). The two droplets were (a) levitated at diﬀerent points,(b) moved by the amplitude modulation of the driving
voltage, and ﬁnally (c) mixed. In Fig. 11(a), the volume of
the bottom droplet was 1.5 l and that of the other droplet
was 0.4 l. The mixed droplet kept on oscillating in thecircumferential direction until the modulation was stopped.
The acoustic pressure distribution in the circumferential
direction was the same as the curve when L ¼ 7:5 mm inFig. 6, because the distance between the vibrator and theapplied to the vibrator and (b) acoustic pressure at the strongest antinodenear the mixing position.

reﬂector was ﬁxed at 7.5 mm in this experiment. The
temporal change in the acoustic pressure at the strongest
antinode near the mixing position was also measured.
Figures 12(a) and 12(b) show the measured driving voltage
applied to the vibrator and acoustic pressure as functions oftime, respectively. Despite the abrupt change in the driving
voltage amplitude, the corresponding change in the acousticpressure was gradual with a time constant of 10 ms, whichmight originate from the high quality factor of the vibration

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system employed in the experiment. The quality factor wasmeasured to be 925, corresponding to a time constant of
11.4 ms at 25.7 kHz, which is in good agreement with theresults in Fig. 12(b).31) Compared with the result describedin the previous section (see Fig. 9), the waveform of theacoustic pressure was signiﬁcantly improved with lessdistortion, which leads to a much higher repeatability. Thisis because the modulation-based method does not involve
any mechanically moving parts.

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3. Conclusions

8)
9)
10)

We demonstrated the noncontact ultrasonic mixing of two
droplets, for the ﬁrst time, by controlling the acoustic ﬁeld
using two methods: by changing the distance between
the vibrator and the reﬂector and by modulating thedriving voltage amplitude applied to the vibrator. Then we
conﬁrmed their operating principle by measuring theacoustic pressure distribution and the temporal change in
the acoustic pressure near the mixing position. We also
showed that the stable mixing of droplets with a highrepeatability can be performed by the modulation-based
method, which does not involve the use of any mechanicallymoving parts. We think that our work is an important
technological step toward the implementation of noncontact
ultrasonic transport/analysis systems for droplets in the near
future.

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Acknowledgement

This work was partially supported by a Grant-in-Aid for
Scientiﬁc Research (Challenging Exploratory Research,
23656163) from the Japan Society for the Promotion of
Science (JSPS).

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