Theoretical and experimental characterizations of gigahertz acoustic streaming in
Weiwei Cui, Wei Pang, Yang Yang, Tiechuan Li, Xuexin Duan ⁎
State Key Laboratory of Precision Measuring Technology & Instruments, College of Precision
Precision Instrument and Optoelectronics Engineering, Tianjin University, Tianjin 300072, China
Even as gigahertz (GHz) acoustic streaming has developed into a multi-functional platform technology for bio-
chemical applications, including ultrafast microﬂuidic mixing, microparticle operations, and cellar or vesicle sur-
gery, its theoretical principles haveyet to be established. Thisis because few studies have been conducted on the
use of such high frequency acoustics in microscale ﬂuids. Another difﬁculty is the lack of velocimetry methodsfor
microscale and nanoscaleﬂuidic streaming.In this work,we focus on the basicaspects of GHz acoustic streaming,
including its micro-vortex generation principles, theoretical model, and experimental characterization technolo-
gies. We present details of a weak-coupled ﬁnite simulation that represents our current understanding of the
GHz-acoustic-streaming phenomenon. Both our simulation and experimental results show that the GHz-
acoustic-induced interfacial body force plays a determinative role in vortex generation. We carefully studied
changes in the formation of GHz acoustic streaming at different acoustic powers and ﬂow rates. In particular,
we developed a microﬂuidic-particle-image velocimetry method that enables the quantiﬁcation of streaming
at the microscale and even nanoscale. This work provides a full map of GHz acoustoﬂuidics and highlights the
way to further theoretical study of this topic.
Copyright © 2019 Tianjin University. Publishing Service by Elsevier B.V. on behalf of KeAi Communications Co., Ltd.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
The term acoustoﬂuidics refers to a new ﬁeld that combines acous-
tics with microﬂuidics by conﬁning acoustic waves or energy within a
microﬂuidic system to stimulate the micro/nanoscale motions of ﬂuids
and particles, and interactions between them.
In recent decades, re-
searchers have developed different kinds of acoustoﬂuidic strategies.
From the acoustic wave form perspective, there are two basic wave
types, i.e., standing waves and travelling waves. Generally, acoustic
waves with frequencies ranging from kHz to several MHz are generated
by a PZT plate, which is placed on the substrate of a microchannel
Standing waves form in the microﬂuidic channel because the
acoustic wavelengths at such frequencies are similar to the
microchannel scale, i.e., from several hundred to tens of micrometers.
The spatial patterns of acoustic antinodes or nodes provide a gradient
physical ﬁeld for particle trapping and operations.
travelling on the substrate surface (typically a surface acoustic wave
(SAW)) can push the particle or ﬂuids away much like shooting pool.
The above strategies utilize the acoustic radiation force. It is very easy
perform microscale manipulations or even to manipulate millimeter-
scale particles. For example, both standing waves and SAW-based
travelling waves have been widely investigated for use in cell
The basic idea of these applications is to push the bigger
cells from the main ﬂow. From the frequency perspective, the most
commonly used frequencies range from kilohertz to tens of megahertz.
The acoustic frequency is determined by the resonators used. For exam-
ple, for PZT, the thickness vibration is related to the plane thickness.
The frequency of a SAW is determined by the interdigital (IDT) periodic
In other words, the reason that ultrahigh frequency (gener-
ally above 300 MHz) acoustoﬂuidics has rarely been explored is due to
the lack of high frequency resonators. GHz SAWs are fabricated for com-
munication purposes, but IDT distances are too small tofabricate by the
conventional fabrication process available to university researchers. On
the other hand, GHz SAWs cannot withstand high power, which also
limits their use in liquids.
Acousticstreaming is a simple yet practical means of effectively trig-
gering ﬂuid motion by directly introducing acoustic energy to a speciﬁc
region. Microscale vortex streaming induced by acoustic-driven
and sharp edges
have served as convenient
acoustoﬂuidic tools for microﬂuidic mixing and particle manipulations.
Construction and operation of these inserted components, however, re-
main a professional task, as does the difﬁculty of maintaining long-term
stability. SAW-driven microﬂuidics has become a very useful ﬂuid actu-
ation method due to its ability to transfer a large amount of momentum
into ﬂuids. Using this approach, complex ﬂuidic and particle operations
Nanotechnology and Precision Engineering 2 (2019) 15–22
E-mail address: email@example.com (X. Duan).
2589-5540/Copyright © 2019 Tianjin University. Publishing Service by ElsevierB.V. on behalfof KeAi Communications Co.,Ltd. This is an openaccess article under the C C BY-NC-ND license
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have been realized in microﬂuidic systems.
The typical amplitudes of
SAWs are on the order of nanometers or less, however, owing to the
high frequencies used (10–100 MHz), the accelerations induced by
these waves are enormous (over 10
In addition, the attenuation
length of high frequency SAWs is comparable with the scale of
microﬂuidic systems, which enables the coupling of most SAW energies
with ﬂuids. Shilton et al. experimentally demonstrated the ability of
SAWs with operating frequencies of up to 1.1 GHz with respect to re-
ﬁned nanoscale manipulation, thereby revealing the signiﬁcance of
the use of ultrahigh frequencies to effectively generate acoustoﬂuidic
streaming in microscale ﬂuids.
As well, Ye Ai et al. used focused ultra-
high frequency SAWs (193–636 MHz) to generate a micro-vortex, and
then developed this technique as a versatile tool for performing contin-
uous micro/nanoparticle manipulation.
Recently, we demonstrated the use of a GHz-acoustic-wave resona-
tor to generate a localized micro-vortex, which we applied to some ex-
citing applications including microﬂuidic mixing,
and cellar surgery.
However, at present, almost all of
the developed high frequency acoustoﬂuidic techniques are at their
very earliest developmental stages, and their theoretical principles
have yet to be established. In this work, we investigate and reveal the
properties of GHz-acoustic-induced vortex streaming, including GHz
acoustic device, streaming generation, and microscale streaming char-
acterizations, and present a full picture of GHz acoustic streaming and
its microﬂuidic applications. We develop an analysis model to quantita-
tively characterizevortex streaming, and offer a simple method for trac-
ing and characterizing microﬂuidic streaming motion to replace the use
of particle image velocimetry (PIV).
2. Theoretical description of GHz-acoustic-ﬂuid interaction
2.1. GHz acoustic device
The solid mounted piezoelectric acoustic resonator (SMR) is a typi-
cal ﬁlm bulk acoustic wave resonator. As shown in Fig. 1(a), the core
structure of an SMR is essentially a multi-layer sandwich, with a piezo-
electric ﬁlm in the center sandwiched by two electrodes. When an elec-
trical signal is applied to the electrodes, the electric ﬁelds trigger a
mechanical vibration within the piezoelectric ﬁlm by the piezoelectric
effect. Behind the sandwich structure is a Bragg reﬂector, which blocks
any leakage of acoustic energy into the substrate and conﬁnes the
acoustic waves to within the piezoelectric layer. Fig. 1(b) shows the vi-
bration mode of an SMR. The SMR works in the thickness extensional
mode, which is excited in a vertically grown piezoelectric material
ﬁlm by coupling the vertical electric ﬁeld through the d
coefﬁcient. Both the wave velocity and resonant frequency of the TE
mode are much higher than those of any other possible modes for a
given piezoelectric ﬁlm, and offers the highest energy transduction.
The frequency of an SMR can be estimated by the following
where dis the thickness of the piezoelectric ﬁlm, and c,ρare, respec-
tively, the stiffness coefﬁcient and density of the piezoelectric ﬁlm ma-
terial, i.e., alumina nitride here. We note that the thickness of the
piezoelectric layer of an SMR can be precisely controlled to within
from several nanometers to several micrometers during the ﬁlm depo-
sition process, which enables the accurate fabrication of acoustic de-
vices witha frequency from hundreds of megahertz to tens of gigahertz.
The SMR is fabricated using a standard complementary metal–
oxide–semiconductor (CMOS) process, as presented in our previous
This process is illustrated in Fig. 2 and can be described as fol-
lows. SMR devices are fabricated on 100-mmundoped Si wafers, begin-
ning with the deposition of the Bragg reﬂector. AlN and SiO
alternatively deposited through physical and chemical vapor deposition
(PVD and CVD), respectively. Then, a sandwiched structure comprising
a bottom electrode (BE), piezoelectric layer (AlN), and top electrode
(TE) is deposited andpatterned layer by layer: The BE of the acoustic de-
vice consists of 600-nm thick Mo deposited via PVD on top of the Bragg
reﬂector, and the ﬁlm is then patterned by photolithography and
plasma etching into a pentagon. PVD is used again to deposit the piezo-
electric layer—a 1000-nm thick AlN ﬁlm—on top of the BE,with a crystal
orientation along the c-axis. In the ﬁnal step, the SMR is capped with a
gold TE ﬁlm, which is deposited using E-beam evaporation followed
by a wet etch. The thicknesses of the Au electrodes and underlying Cr
adhesive layer are 300 nm and 50 nm, respectively. We conﬁgured the
electrode area to be 20,000 μm
such that the SMR had a characteristic
impedance of 50 Ωto match the impedance of the external circuits.
We then used a PDMS microchannel prepared with soft lithography to
ensure microscale conﬁnement of the liquid samples and acoustic
waves. Fig. 2(b) shows a schematic of the prepared GHz acoustoﬂuidic
chip consisting of an SMR and a microchannel.
Fig. 3(a) shows a scanning electron microscope (SEM) image of a
fabricated SMR device. The sandwich structure is pentagon-shaped
and conﬁnes the resonating region of the SMR. We measured the per-
formance of the SMR in air and water, respectively, with a network an-
alyzer (Agilent, E5071C). As Fig. 3(b) shows, the quality value (Q-value)
is dramatically decreased when the device is submerged in water,
which is considered to be mainly caused by acoustic leakage into the liq-
uid. Generally, the serial resonant frequency is used as the working fre-
quency of the acoustoﬂuidic chip, which is about 1560 MHz here.
2.2. Some key parameters
As shown in Fig. 2(b), the SMR vibrates at a resonant frequency in
the GHz range. The vibrating displacement (A) of the SMR surface can
be described simply as follows: A=ξsin(ωt). The acceleration can be
obtained by ∂
. With an assumed magnitude of about 10 nm, the
acceleration is greater than 10
, which is faster than any other
known technique except that of particle accelerators. For this reason,
it is possible to obtain extraordinary inertial behavior from ﬂuids and
particles down to the nanoscale. However, many other factors must be
considered that can affect the ﬁnal performances. When submerged in
water, it would be interesting to explore what would occur. Prior to de-
scribing our acoustoﬂuidic experiment, we introduce and discuss some
critical concepts and parameters, including the Stokes boundary layer,
acoustic decay length, and body force.
2.2.1. Stokes boundary layer
According to the classical Rayleigh–Schlichting streaming model,
the acoustic triggered ﬂuid bulk can be divided into two parts, as
shown in Fig. 4, in which the light blue region supports a horizontal
Fig. 1. (a) Schematic structure of the SMR, and (b) thickness-extensional vibration of the
SMR working at resonant frequency.
Values of parameters used in model calculation.
(m/s) μ′(Pa·s) μξ
1500 1.0087 × 10
1.0100 × 10
16 W. Cui et al. / Nanotechnology and Precision Engineering 2 (2019) 15–22
sinusoidal pressure wave (magenta line) of wavelength λin the hori-
zontal direction parallel to the wall. The dark blue region is the viscous
boundary layer of sub-micrometre thickness δ, wherein large shear
stress appears to generate the boundary layer (Schlichting) streaming
rolls (yellow arrow line), which then drive the bulk (Rayleigh) stream-
ing rolls (red). In traditional standing wave systems at ordinary acoustic
frequency, the streaming pattern is periodic in the horizontal direction
with periodicity λ/2, and thus only the top and bottom walls are subject
to the no-slip boundary condition. The energy within these two regions
is attributed to acoustic dissipation. The expression for the viscous
boundary layer thickness can be written as follows
are, respectively, the viscosity and density of the liquid, and
ωis the acoustic frequency. In viscous acoustics, the length is about 0.01
2.2.2. Acoustic decay length
When the acoustic wave transfers into the liquid, it is subject to an
acoustic damping effect and the acoustic energy is radiated into the liq-
uid with an attenuation coefﬁcient of β
are the density and sound speed in the liquid, respec-
tively; μand μ′represent the dynamic and bulk viscosities of the
ﬂows, respectively; and the attenuation length of the TE-mode acoustic
waves is deﬁned as βl
−1, which is proportional to ω
. This high fre-
quency will induce a short decay length, and enable rapid energy dissi-
pation within a rather short propagation distance near the SMR–liquid
interface. As shown in Fig. 5, we calculated the decay length of 1560-
MHz acoustic waves in water to be 7.5 μm, which is much shorter
than the channel height, thereby avoiding the formation of standing
The analysis of the decay length of GHz acoustic waves reveals that
most of the acoustic energy is dissipated within or near the thin viscous
boundary layer. Considering that the thickness of the GHz acoustic trig-
gered boundary layer is on the order of ~10 nm, the energy is ultra-
conﬁned and would generate a great stress force in the liquid.
2.2.3. Body force
The attenuation of SMR-generated acoustic waves into liquid intro-
duces a body force at the SMR–liquid interface, which is expressed as
where ξis the maximum amplitude of the acoustic waves at the SMR–
liquid interface. Eq. (4) indicates that the body force scales with ω
which reveals the signiﬁcance of applying ultrahigh frequency to gener-
ate greater momentum to actuate the microﬂuids. Fig. 5 shows the
body-force distribution generated by the SMR with an initial value on
the order of 10
. Another critical issue is the localization or
Fig. 2. (a) Fabrication of SMR and SMR-based acoustoﬂuidic chip,including Bragg reﬂector deposition (1), BE deposition andpattern (2), piezoelectric layerdeposition and pattern (3), TE
deposition and wet etch (4). (b) Cross-sectional illustration of the multilayered device structure of GHz acoustoﬂuidic chip. From bottom to top are the high-resistivity silicon substrate,
Bragg reﬂector (containing three pairs of AlN and SiO
layers to attenuate acoustic waves leaking into the Si substrate (inset)), bottom electrode (BE, Moly), piezoelectric layer, top
electrode (TE, Au), and PDMS channel.
Fig. 3. (a) SEM image of a fabricated SMR. (b) Measured performance of the SMR both in air and liquid.
17W. Cui et al. / Nanotechnology and Precision Engineering 2 (2019) 15–22
focus of the bodyforce region. Because the resonantregion of the SMR is
deﬁned by the pentagon-shaped sandwiched structure, the body force
is naturally focused within the locally conﬁned region.
3. Weak-coupled ﬁnite-element simulations
To evaluate the microﬂuidic streaming triggered by GHz acoustic
waves, we used COMSOL software to perform a ﬁnite-element simula-
tion of the ﬂuid motion in a spatially conﬁned area with a height of 50
μm (as shown in Fig. 6(a)). Considering the fact that the interaction be-
tweensuchhighfrequencyacousticsandﬂuids is as yet not clearly un-
derstood, we conducted a weak-coupled simulation and neglected the
nonlinear effects. Investigations of GHz acoustic streaming in micro/
nanoscale ﬂuids are ongoing. The acoustic streaming response of the
ﬂuid is characterized using a second-order system of equations, which
in turn is driven by ﬁrst-order equations. The ﬂuid response is governed
by the standard Navier–Stokes equation for a linear, viscous compress-
ible ﬂuid. As discussed above, we introduced the GHz-acoustic-wave-
induced body force into the Navier–Stokes equation by presetting a
boundary condition, as follows:
where Vis the velocity vector, Pis the pressure, and ρ,μdenote the den-
sity and viscosity of ﬂuid, respectively.
We considered the SMR to be the ideal device with a perfect match
layer on the substrate, despite the fact that the fabricated device con-
tains ﬂaws that can provide various pathways for acoustic energy leak-
age into the substrate. Another factor is the heating effect caused by the
acoustic energy dissipation. The heating ability of the SMR has been
characterized within the microﬂuidic system.
Localized heat has
been demonstrated to generate vortex streaming in various optoﬂuidic
systems at velocities on the order of μm/s.
Here, we studied the heat-
streaming effect using a two-dimensional ﬁnite-element simulation,
and we used parameters from the experimental data described in our
The preset conditions of the heat-streaming simulation are shown in
Fig. 6(b). The heat-streaming effect is expressed in the following:
where Qis the input heat ﬂux, and Cand kdenote the heat capacity and
thermal conductivity of the ﬂuid, respectively. The input heat source is
assumed to be at the liquid–solid interface. The proﬁle of the heat ﬂux
is assumed to be Gaussian and focused in the center of the source. The
Fig. 4. Schematic of the Rayleigh–Schlichting streaming model.
Reproduced with permission.
Copyright 2012 The Royal Society of Chemistry
Fig. 5. Body-force distribution above the SMR surface. The decay length is labelled at the
point where the body force decreases to 1/e of the initial value. The inserted SEM image
shows the SMR devic e, in which the pentagon-shape is the resonant region. A two-
dimensional ﬁnite-element simulation of the acoustic ﬁeld across the red line on the
resonator generates a distribution of body force on the surface. An ultra-large body force
generates a strea ming beam into the liquid to drive away the liquid abo ve the SMR.
According to the mass continuous equation, the liquid from the surrounding area would
ﬂow to the surface of the SMR and ultimately form a closed rotating vortex. The value of
the parameters in Eqs. (3) and (4) are listed in Table 1.
Fig. 6. Two-dimensional ﬁnite-element simulation of UHF acoustic ﬁeld and acoustic-
heater-induced streaming within microchannels. (a)–(b) Preset boundary conditions for
acoustic-streaming and heat-streaming simulations, respectively. Body force and heat
source are resp ectively applied at the boundary with a w idth of 100 μm, and other
parameters are the same as those in the acoustic streaming simulation.
18 W. Cui et al. / Nanotechnology and Precision Engineering 2 (2019) 15–22
ﬂuid motion obeys the Navier-Stokes equation, and we set the external
force term to be proportional to the temperature gradient.
4. Two experimental characterization methods
4.1. Setup of the experimental characterization system
The SMR is excited by a radio frequency (RF) signal generator (MXG
Analog Signal Generator, Agilent, N5181A 100 kHz–3GHz)andapower
ampliﬁer (Mini-Circuits, with 35 dBm enhancement of the original RF
source power). Prior to the microﬂuidic mixing experiments, we
cleaned the channels by ﬂushing them with ultrapure (UP) water at a
ﬂow rate of 20 μL/min. We then introduced the UP water with and with-
out ﬂuorescent dye (FITC, 20 μg/mL) into the chip via two inlets using a
syringe pump (New Era Pump Systems, Inc.). We maintained equal ﬂow
rates for both streaming experiments, and set their total ﬂow rates Qto
5μL/min, 10 μL/min, 20 μL/min, 40 μL/min, 60 μL/min, and 80 μL/min.
We measured the operating frequency of the SMR by frequency sweep-
ing and used the serial resonant value as the working frequency. All ex-
periments were recorded using a ﬂorescent microscope (Olympus,
BX53) integrated with a CCD camera (DP73), with the images captured
at 25 frames per second.
4.2. Microﬂuidic mixing
As localized micro-streaming can generate laminar ﬂows within
microﬂuidic systems, different laminar ﬂows can be mixed to reﬂect
and characterize the strength of the acoustic streaming. We described
the mixing effect of a GHz acoustoﬂuidic chip in our previous paper,
as well as detailing the characterization method. Brieﬂy, the mixing per-
formance is determined by examining a cross-sectional area of the
microﬂuidic mixer perpendicular to the ﬂow direction in terms of a
mixing index (MI). In theexperiment, we used an FITC solution and ac-
quired the ﬂuorescence intensity value of i-th pixel (I
interest (ROI) to characterize the concentrations,
where Nis the number of pixels along the line of the ROI, I
and Iare the
intensity values of the i-th pixel and the average value of Npixels in the
mixed region, respectively, and I′represents the intensity value in the
4.3. Microﬂuidic “particle image velocimetry”(μ-PIV)
To better understand the vortex mixing principles, we developed a
dynamic model by analyzing the molecule transfer process at the inter-
face of the vortex and ﬂowing ﬂuids. Fig. 7(a) shows the mass transfer of
two laminar ﬂows at the vortex edge, wherein the vortex velocity, V,
equals the ﬂow velocity, and V
,deﬁnes the mixing length from the un-
mixed to the mixed region. The vortex area is conﬁned by the edges of
= 1, and the inﬂuence of the ﬂow rate on the vortex area is deter-
mined by normalizing the vortex velocity ﬁeld with the ﬂow velocity.
Fig. 7(b) shows the values of V/V
on the labelled line on the simulated
vortex velocity ﬁeld. The inner edge of the vortex is closer to the center
of the device (x= 300 μm), and the vortex area is primarily tuned by
adjusting its outside edges according to the experimental results.
5. Results and discussion
5.1. Generation of acoustic streaming
Fig. 8(a) shows the maximum velocity of the vortex as a function of
the applied power, which reveals alinear relationship between velocity
and power. The insert in Fig. 8(a) shows the results of the experimental
vortex generation in microﬂows, which demonstrate the formation of
vortex streaming, and which ﬁt well with the simulation results. Fig. 8
(b) shows the heat-streaming effect simulated by a 2-D model, with
the conditions preset as in Fig. 6(b). The results show that acoustic-
dissipation-generated heat can induce a pair of vortices similar to the
acoustic-streaming effect. We plotted and ﬁtted the relationship be-
tween maximum velocity and temperature. Compared with the vortex
induced by the acoustic ﬁelds, for which the velocity is on the order of
m/s, the streaming generated by heat is much weaker, on the order of
μm/s. Thus, the streaming induced by the acoustic-heating effect can
be neglected, as the vortex is mainly induced by the acoustic-
5.2. Mixing index characterizations
As shown in Fig. 8(a), vortex streaming is effectively generated in
the microﬂuids. We can clearly see that there are multiple vortices
(those in the downstream are hidden by the well-mixed ﬂorescence
ﬂow) around the resonator device, which agrees well with the simula-
tion results. The vortex can efﬁciently mix the laminar ﬂows, thereby
Fig. 7. The relative balance of the vortex streaming and ﬂow velocities determines the
vortex shape and area. (a) The location of V/V
=1deﬁnes the vortex edges, as well as
the mixing region wherein the ﬂow of UP water enters the mixed region with ﬂow
distributions for different ﬂow rates. The simulated water vortex
streaming represents the velocity ﬁeld inside static microﬂuids, and the plotted V/V
distributions are obtained by dividing the static-case velocity value on the labelled red
dash line by the ﬂow velocity.
19W. Cui et al. / Nanotechnology and Precision Engineering 2 (2019) 15–22
Fig. 8. (a) Simulated velocity ﬁeld of acoustic streaming (insert)and ﬁtted relationship between simulated maximum velocity and applied power. (b) Simulated heat-streamingvelocity
ﬁeld and ﬁtted relationship between temperature and maximum velocity. The insert in (a) is the experimental result of the micro-vortex within the microchannels, and the insert in
(b) shows the heat transfer inside ﬂuids when heated by the resonator at a power of 500 mW.
Fig. 9. (a) The ﬂow rate is maintained at 5 μL/min,and the applied powerwas set at 100 mW, 300 mW,and 500 mW from left to right, respectively. Thecurves represent the ﬂuorescence
intensity on the labelled line in the mixed region (downstream). (b) The applied power is maintained at500 mW, and the ﬂow rate was varied from 10 μL/min, 40 μL/min, to 80 μL/min,
respectively. (c)–(d) Mixing index in response to applied power and ﬂow rate, respectively. The red dashed line in (c) represents the saturated mixing index value.
20 W. Cui et al. / Nanotechnology and Precision Engineering 2 (2019) 15–22
enabling a homogenous mixed ﬂow in the downstream (i.e., mixed re-
gion). Fig. 9(a) and (b) show the streaming ﬁelds of the vortices for dif-
ferent power and ﬂow-rate conditions. In the upstream, two vortices
can be clearly observed by the border lines of the ﬂuorescent dye.
First, we evaluated the power effects on the formation of the micro-
vortex. The simulation result shows that the power input of the device
has a strong effect on the rotation speed of the micro-vortex, which is
directly related to the ﬂuid mixing efﬁciency in the microchannel. Ex-
perimentally, we studied this issue by analyzing the shape of the vortex
formed at different input powers. Fig. 9(a) shows the streaming ﬁeld in-
duced by the SMR with applied power values of 100 mW, 300 mW, and
500 mW, respectively, at the same ﬂow rate (5 μL/min). At a lower input
power (100 mW),the vortex remains approximately symmetrical along
the ﬂow direction and the streaming area does not cover the full
microchannel, which results in poor mixing. When the power is in-
creased to 500 mW, the behavior of the vortex array becomes much
more intense, and disturbs the ﬂuids in a larger area until it is conﬁned
by the boundaries of the microchannel, thereby improving the mixing
efﬁciency. This result conﬁrms the simulation results, which indicated
that a higher power input will induce faster vortex formation, and
thus improve the ﬂuid mixing efﬁciency. Next, we experimentally in-
vestigated the effect of the ﬂow velocity (V
) in the microchannel. We
obtained the ﬂow velocity by dQ
dA, where Qis the ﬂow rate and Ais the
cross-section area of the microchannel. Here, we use the average veloc-
ity (Vf) to represent the ﬂow velocity ﬁeld. While keeping the same
input power (500 mW), we varied the ﬂow rate (Q)at10μL/min, 40
μL/min, and 80 μL/min. As shown in Fig. 9(b), a higher ﬂow rate reduces
the vortex area and conﬁnes the shape, which is a similar result to the
lower power case in Fig. 9(a), and therefore weakens the mixing effect.
We can conclude that both the input power and the ﬂow conditions
conﬁne the vortex, and the ﬂuid mixing efﬁciency can be ﬁnely tuned
by these parameters. To further quantify the inﬂuence of different
input power and ﬂow conditions, we carefully characterized the mixing
efﬁciency using the mixing index presented in Eq. (7).AsshowninFig. 9
(c), for a given ﬂow rate, the mixing efﬁciency increases with increased
power. In the low-power range, the mixing index has an approximately
linear relationship to the applied power. Combined with the simulation
results, this reveals that the mixing efﬁciency is proportional to the ve-
locity of the vortex. The power applied to the SMR can be varied from
several milliwatts to several watts to tune the mixing efﬁciency over a
rather large range. Fig. 9(d) shows that for a given applied power, the
mixing efﬁciency increases with decreases in the ﬂow rate in most
cases. In particular, in the low-power case, the mixing efﬁciency is
greatly inﬂuenced by the ﬂow rate. This is due to the fact that the vortex
is conﬁned by the ﬂow, which limits the disturbance range inside the
microchannel. The inﬂuence of the ﬂow rate is less apparent in the
high-power case, since when high power is applied, the SMR induces
a much stronger vortex to offset the inﬂuence of the ﬂowing ﬂuids.
5.3. Microﬂuidic-particle-image velocimetry (μ-PIV)
Based on the deﬁnition of the vortex edge, the vortex area can be ob-
tained in both simulations and experiments by acquiringthe curve ratio
of the vortex area. The curves in Fig. 10(a) show the vortex edges at dif-
ferent ﬂow rates, with the corresponding radii obtained shown in Fig. 10
(b). As the vortex velocity on the edges is approximately equal to the
ﬂow velocity, the vortex velocity triggered by different power levels
and the velocity distribution within the vortex can be directly measured
using the ﬂow tuning method. The above analysis highlights a new ap-
proach for measuring the streaming velocity ﬁeld that can replace PIV
methods. Fig. 10(c) shows the radius values obtained from Fig. 7(b),
which show a similar functional relationship as those obtained in the
In conclusion, both our simulation and experimental results demon-
strated the determinative role of GHz acoustics in streaming generation.
To understand the GHz-acoustic-induced microscale vortex streaming,
we introduced the classical Rayleigh–Schlichting model to explore the
particular case of such high frequencies. Even though the theoretical
principles can be illustrated rather reasonably, there remain many as-
pects of the acoustic-ﬂuid interaction process that are unclear. In addi-
tion to a mixing index, we developed a micro-PIV method in which
the vortex edges are deﬁned, which enables a determination of the pre-
cise velocimetry within microscale and even nanoscale ﬂuids. For the
ﬁrst time, in this work, we introduced a whole map of GHz
acoustoﬂuidics from its theoretical principles to experimental charac-
terizations, which contribute to broadening the understanding of GHz-
The authors gratefully acknowledge ﬁnancial support from the Na-
tional Natural Science Foundation of China (Grant Nos. 91743110,
61674114, 21861132001), National Key R&D Program of China (Grant
No. 2017YFF0204600), Tianjin Applied Basic Research and Advanced
Technology (Grant No. 17JCJQJC43600), the Foundation for Talent Sci-
entists of Nanchang Institute for Microtechnology of Tianjin University,
and the 111 Project (Grant No. B07014). We also thank Prof. Mark Reed
at Yale University for useful discussions.
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