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Theoretical and experimental characterizations of gigahertz acoustic streaming in
microscale fluids
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
abstractarticle info
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/).
Keywords:
Acoustic streaming
Gigahertz
Body force
Microfluidic PIV
1. Introduction
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.
1–3
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
chip.
4,5
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.
6,7
Acoustic waves
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
separations.
8,9
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.
10
The frequency of a SAW is determined by the interdigital (IDT) periodic
distance.
1,3
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
bubbles
11,12
and sharp edges
13,14
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
⁎Corresponding author.
E-mail address: xduan@tju.edu.cn (X. Duan).
https://doi.org/10.1016/j.npe.2019.03.004
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
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Contents lists available at ScienceDirect
Nanotechnology and Precision Engineering
journal homepage: http://www.keaipublishing.com/en/journals/nanotechnology-
and-precision-engineering/
have been realized in microfluidic systems.
3,15
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
7
m/s
2
).
2
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.
16
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.
17
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,
18
acoustofluidic
tweezering,
19
and cellar surgery.
20
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
33
piezoelectric
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
equation
21
:
f0¼1
2dffiffiffi
c
ρ
r;ð1Þ
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
paper.
22
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
2
layers are
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
2
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 ∂
2
A/∂t
2
. With an assumed magnitude of about 10 nm, the
acceleration is greater than 10
10
m/s
2
, 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,
23
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.
18
Table 1
Values of parameters used in model calculation.
ρ
l
(kg/m
3
)c
l
(m/s) μ′(Pa·s) μξ
0
(nm) F(MHz)
10
3
1500 1.0087 × 10
−3
1.0100 × 10
−3
10 1560
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
23
:
δv¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2μ=ωρf0
q;ð2Þ
where μ,ρ
f0
are, respectively, the viscosity and density of the liquid, and
ωis the acoustic frequency. In viscous acoustics, the length is about 0.01
μmforwaterat2GHz.
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
l18
:
βl¼4
3μþμ0ω2
ρlcl
;ð3Þ
where ρ
l
and c
l
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
−2
. 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
waves.
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
follows
18
:
FB¼ρξ2bω4
ρlcl3;ð4Þ
where ξis the maximum amplitude of the acoustic waves at the SMR–
liquid interface. Eq. (4) indicates that the body force scales with ω
4
,
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
13
N/m
3
. 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
2
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:
ρV∙∇Vþ∇∙P−μ∇2V¼FBð5Þ
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.
24
Localized heat has
been demonstrated to generate vortex streaming in various optofluidic
systems at velocities on the order of μm/s.
25
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
previous paper.
The preset conditions of the heat-streaming simulation are shown in
Fig. 6(b). The heat-streaming effect is expressed in the following:
∇∙ −k∇TþρCTvðÞ¼Q;ð6Þ
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.
23
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,
18
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
i
)intheregionof
interest (ROI) to characterize the concentrations,
18
as follows:
MI ¼1−
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
NX
N
i¼1
Ii−I
2
v
u
u
t
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
NX
N
i¼1
Ii0−I0
2
v
u
u
t
;ð7Þ
where Nis the number of pixels along the line of the ROI, I
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
unmixed region.
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
f
,defines the mixing length from the un-
mixed to the mixed region. The vortex area is confined by the edges of
V/V
f
= 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
f
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-
streaming effect.
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
f
=1defines the vortex edges, as well as
the mixing region wherein the flow of UP water enters the mixed region with flow
velocity, V
f
.(b)V/V
f
distributions for different flow rates. The simulated water vortex
streaming represents the velocity field inside static microfluids, and the plotted V/V
f
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
f
) 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
experiment.
6. Conclusions
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-
acoustic-fluid interactions.
Acknowledgements
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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