Acoustic resonances in microfluidic chips:
full-image micro-PIV experiments and numerical simulations
S. M. Sundin, T. Glasdam Jensen, H. Bruus and J. P. Kutter
MIC – Department of Micro and Nanotechnology, Technical University of Denmark
DTU Bldg. 345 east, DK-2800 Kongens Lyngby, Denmark
(Dated: 30 March 2007)
We show that full-image micro-PIV analysis in combination with images of transient particle
motion is a powerful tool for experimental studies of acoustic radiation forces and acoustic streaming
in microfluidic chambers under piezo-actuation in the MHz range. The measured steady-state motion
of both large 5 µm and small 1 µm particles can be understood in terms of the acoustic eigenmodes or
standing ultra-sound waves in the given experimental microsystems. This interpretation is supported
by numerical solutions of the corresponding acoustic wave equation.
I. INTRODUCTION
For the typical dimensions of microfluidic structures
there are two acoustic effects of main importance: the
acoustic radiation force [1, 2, 3], which moves suspended
particles either towards or away from pressure nodes de-
pending on their acoustic material properties, and acous-
tic streaming [4, 5], which imparts movement onto the
entire solvent. Both of these forces have been utilized,
alone or in combination, for several lab-on-a-chip appli-
cations. Yasuda et al. [6, 7], demonstrated concentration
of particles by acoustic radiation forces, and separation
of particles by acoustic forces in combination with elec-
trostatic forces. One of the most attractive applications
for acoustics in microfluidics is for mixing [8, 9, 10], as
this process typically is diffusion limited in microscale
devices. Valveless ultrasonic pumps, utilizing acoustic
streaming, have also been presented [11, 12]. Numer-
ous examples of microsystems where acoustics are ap-
plied to handling and analysis of biological material have
been suggested. Among others these include: trapping of
microorganisms [13], bioassays [14], and separation and
cleaning of blood [15, 16, 17]. Apart from on chip de-
vices, acoustic forces have also been suggested for use in
other µm-scale applications [18].
There are different imaging strategies and tools, which
can be used in order to enhance the understanding, and
to visualize the function of acoustic micro-devices during
operation. For acoustic mixers the effect can be illus-
trated and measured by partly filling the mixing cham-
ber with a dye prior to piezo-actuation [9, 10]. However,
this approach is mainly limited to determine the total,
and not the local, mixing behavior within the cham-
ber. A more refined method, which is not limited to
the study of micromixers, is to apply streak- or stream-
line analysis. This was shown by Lutz et al. [19, 20], who
neatly demonstrated 3D steady micro streaming around a
cylinder. Although streamline analysis can be employed
to illustrate flow behaviour, it is not suitable in deter-
mining local variations in velocity. For that purpose,
the micron-resolution particle image velocimetry (micro-
PIV) technique is the method of choice [21]. With this
technique the motion of tracer particles, acquired from
consecutive image frames, is utilized to obtain velocity
vector fields. In a large chamber, local measurements
of particle motion induced by acoustic radiation forces
and acoustic streaming have been performed by Spen-
gler et al. [22, 23], and further developed by Kuznetsova
et al. [24]. Li and Kenny derived velocity profiles in a
particle separating device utilizing the acoustic radiation
force [17]. Jang et al. used confocal scanning microscopy
to perform micro-PIV measurements on circulatory flows
in a piezo-actuated fluidic chamber [25]. Furthermore,
Manasseh et al. applied micro-PIV to measure stream-
ing velocites around a bubble trapped in a microfluidic
chamber [26].
As particles under the influence of acoustic fields do
no longer function as true independent tracers in all sit-
uations, and as several acoustic effects come into play
at the same time, extra caution and consideration have
to be taken when applying micro-PIV for microfluidic
acoustic studies. These considerations will be discussed
in more detail in section II C. The situation is further
complicated by the coupling from the actuator to the
structures and their acoustic resonances, which is a yet
poorly understood mechanism. The resonances depend
on the acoustic material parameters as well as the geom-
etry of both the chip and the chamber. For substrate
materials with low attenuation, such as silicon, the ac-
tuation will result in strong resonances over the whole
devices, whereas for substrate materials with high atten-
uation, the effect will be mostly confined to the prox-
imity of the actuator. Moreover, in a real system the
coupling strengths vary for different resonances, and am-
plitude fluctuations across the structures are often ob-
served. Therefore, if investigations striving to yield a
better understanding of acoustic resonances in low atten-
uation microfluidic chips are to be performed, it is not
sufficient only to study the acoustic phenomena locally.
In this work, full-image micro-PIV analysis in combi-
nation with images of transient particle motion is sug-
gested as a tool for studying acoustic resonances in mi-
crofluidic chambers under piezo-actuation. The acousto-
fluidic phenomena mentioned above can be investigated
by comparing these experimental images with plots of
acoustic eigenmodes of the device structure obtained by
http://arxiv.org/abs/0704.1314v1
FIG. 1: A top-view photograph of the silicon-glass chip (dark
gray) containing a square chamber with straight inlet and
outlet channels (light gray).
numerical solution of the corresponding acoustic wave
equation.
II. MATERIALS AND EXPERIMENTAL
METHODS
A. Microchip fabrication
In this study, two microfluidic chambers were inves-
tigated, one of quadratic footprint with a side-length of
2 mm and one of circular shape with a diameter of 2 mm.
The size was chosen to be a few times the acoustic wave-
length of 2 MHz ultrasound waves in water, and the spe-
cific shapes were employed to ensure simple patterns in
the pressure field at the acoustic resonances. Both cham-
bers were connected to 400 µm wide inlet and outlet
channels, and the depth was 200 µm throughout. The
microfluidic chips were fabricated in silicon via deep re-
active ion etching (DRIE). The same technique was also
applied on the backside of the chip to etch 300 µm diame-
ter round fluidic inlets. Anodic bonding was used to seal
the structures with a 500 µm thick pyrex glass lid on the
channel side. Silicon rubber tubings were glued to the
holes on the backside of the chip, for easy attachment of
teflon tubing. A picture of one of our microfluidic chips is
shown in Fig. 1, and a list of the geometrical parameters
is given in Table I.
B. Experimental setup and procedure
The piezo-actuator (Pz27, Ferroperm) was pressed to
the backside of the chip using an ultrasonic gel (ECO,
Ceracarta) and biased by a 20 V ac tone generator (Model
195, Wavetek). Images were captured with a progressive
scan interline CCD camera (Hisense MkII, Dantec Dy-
namics), mounted with a 0.63x TV-adapter on an epiflu-
orescent microscope (DMLB, Leica). The objective used
was a Plan 5x with a numerical aperture NA of 0.12.
For the given fluidic geometries, this combination allowed
capture of full-image PIV vector fields, while utilizing the
largest number of pixels on the CCD. A blue light emit-
ting diode, LED, (Luxeon Star 3W, Lumileds) was used
as illumination source in a front-lit configuration, which
TABLE I: The geometrical parameters of the fabricated mi-
crofluidic silicon-pyrex chip.
chip length L0 49 mm silicon thickness hs 500 µm
chip width w0 15 mm pyrex thickness hp 500 µm
channel length Lc 26 mm chamber height h 200 µm
channel width wc 400 µm chamber width w 2 mm
is described elsewhere [27]. The LED was powered by an
in-house built power supply controlled by a PIV timing
system (Dantec Dynamics). Image acquisition was per-
formed on a PC with Flowmanager software (Dantec Dy-
namics). As tracer fluids solutions of 1 µm polystyrene
micro-beads (Duke Scientific), 5 µm polyamide micro-
beads (Danish Phantom Design), diluted milk, and fluo-
rescein have been used.
The investigations were performed by scanning the
applied frequency from the tone generator and identi-
fying those frequencies which led to a strong response,
an acoustic resonance, in the microfluidic chamber. At
the resonance frequencies, the behavior of the different
tracer particle solutions was observed. Between succes-
sive recordings the chip was flushed to assure homoge-
neous seeding. Furthermore, to make sure that only par-
ticle motion caused by acoustic forces were recorded, no
external flow was applied during measurements.
C. Micro-PIV considerations
In micro-PIV tracer particles are chosen for their abil-
ity to truthfully follow the motion of the flow that is
to be investigated. Particles under the influence of an
acoustic field do no longer fulfil this criterium in all situ-
ations. Therefore, extra caution and considerations have
to be taken regarding what movements are actually mea-
sured when applying micro-PIV for these types of stud-
ies. Given that particle motion caused by thermal or
gravitational forces can be neglected, the main task is to
determine if particle motion is caused by acoustic radi-
ation forces, acoustic streaming or a combination of the
two. In this study, this problem was tackled by applying
three tracer solutions with different physical properties.
Typically, the large polyamide particles are more
strongly affected by the acoustic radiation forces than
by the forces due to acoustic streaming of the surround-
ing water. In contrast, since the acoustic radiation
force scales with the volume of the particle, the small
polystyrene particles will follow the motion of the water,
if relatively strong acoustic streaming is present. How-
ever, there is no simple relation between the two forces,
and for an arbitrary frequency and geometry one can be
strong whereas the other is not, and vice versa. There-
fore, in order to determine whether particle motion is
caused by acoustic radiation forces or acoustic streaming
it is necessary to utilize the dependance of the acoustic
radiation forces on the compressibility of the particle.
TABLE II: The susceptibility to acoustic radiation forces for
the particles used in this study, as well as for some other
particles common to microfluidic applications.
tracer type force direction
beads (1 µm) weak nodes
beads (5 µm) strong nodes
red blood cells strong nodes
milk particles weak anti-nodes
large micelles strong anti-nodes
fluorescein none -
The polymer particles will move towards the pressure
nodes since their compressibility is smaller than that of
water. The opposite is true for the lipid particles in milk:
their compressibility is larger than that of water, and
consequently they will move towards pressure antinodes.
Like the small polystyrene particles, the lipid particles
we used were small enough to typically follow the net
acoustic streaming flow of the water. Thus, if similar mo-
tion is recorded with two types of tracers with different
compressibilities compared to the medium, the acoustic
radiation forces can be ruled out as cause of the motion.
As an alternative or complementary technique to micro-
PIV measurements, fluorescein can be used to investigate
acoustic streaming. A summary of the acoustic behav-
ior of the different particles used in this study, and some
other bodies that are common in microfluidic applica-
tions, is given in Table II.
The speed of sound c in water has a significant de-
pendence on temperature T given by the large deriva-
tive ∂c/∂T ≃ 4 m s−1K−1. All tracer fluids were there-
fore kept at room temperature, so that the temperature
was not changed when the microchip was flushed dur-
ing tracer particle exchange. The microchips used in
this study are comparable in size and mode of actua-
tion to those used for ultrasonic agitation in a study by
Bengtsson and Laurell [28]. They performed sensitive
temperature measurements on the reactor outlet, where
no temperature increase caused by the acoustic power
could be detected. In our study, the piezo-actuator was
run at a moderate power-level and only for the short
intervals during recordings (typically less than one sec-
ond). Therefore, it can be ruled out that heating from
the piezo-actuator would have any measurable impact on
the measurements.
One important factor, which needs to be accounted for
when applying micro-PIV on systems affected by acoustic
forces, is that the local seeding density will be distorted
during actuation. This is normally not a problem when
measuring on particle motion caused solely by acoustic
streaming, as this motion generally will be of a circulat-
ing nature. On the other hand, in the case of particle
motion induced by acoustic radiation forces, it will typi-
cally lead to total expulsion of particles from certain re-
gions into others. If PIV-vector statistics is applied, only
the first few image-pairs recorded after piezo-actuation
TABLE III: The acoustic material parameters of the microsys-
tem at 20 ◦C: sound velocities ci and densities ρi from the
CRC Handbook of Chemistry and Physics.
material speed of sound density
water cw = 1483 m/s ρw = 998 kg/m
silicon cs = 8490 m/s ρs = 2331 kg/m
pyrex cp = 5640 m/s ρp = 2230 kg/m
has been initiated can be used, and in this study, im-
ages from a number of consecutively recorded sets have
been used for averaging. Moreover, in the case of scan-
ning, or mapping, techniques the expulsion of particles is
especially problematic, as the seeding conditions in the
device, or chamber, need to be restored for each measure-
ment position. Also, the conditions may change during
these lengthy recordings, leading to results that are dif-
ficult to interpret.
The acoustic resonances in low attenuation piezo-
actuated microfluidic devices are formed over the whole
devices, and they are also depending on the geometry
of the whole device. As a consequence, there will typ-
ically be amplitude fluctuations over the devices, due
to unwanted artifacts, or deliberate designs. Therefore,
when investigating acoustic resonances, and the influence
caused by different modifications to the sample, it is im-
portant to study the effects globally. If the acoustic ef-
fects are only measured in a part of the device, this kind
of information will not be yielded, independently on how
detailed the flow is mapped within that region. There-
fore, we suggest full-image micro-PIV for the investiga-
tion of acoustic resonances in microfluidic devices.
In this study, emphasis has been put on how to present
the measured data in such a way that still images and
PIV-vector plots give the best illustration of the tran-
sient particle motion caused by the acoustic forces. To
achieve this, we have chosen to superimpose the PIV-
vector plots of the initial transient velocities on top of
the pictures of the steady-state patterns of the particles
obtained after a few seconds of actuation. After longer
actuation times, secondary patterns will form, so images
taken at this point can give a false impression of the parti-
cle motion. This method of combining the transient PIV-
vector plots and steady-state pictures has shown useful
when comparing numerical simulations with micro-PIV
measurements, especially for measuring amplitude fluc-
tuations across the structures, and when discriminating
between different numerical models. This will be demon-
strated in Sec. IV.
III. NUMERICAL SIMULATIONS
In the experiments, the acoustic pressure field, which
is superimposed on the ambient constant pressure, is
driven by a harmonically oscillating piezo-actuator, i.e.,
the time-dependence can be described as cos(ωt). In this
(a) 3D side-view (b) 3D side-view
(c) 3D top-view (d) 3D top-view
(e) 2D chip model (f) 2D chip model
n, eigenmode no.
0 10 20 30 40 50✻
3D model
2D chip
model
FIG. 2: Numerical simulations of the pressure eigenmodes
pn(x, y, z) shown in gray-scale plots. (a) and (b) 3D model:
side-view (xz-plane) of p1 and p31, respectively. (c) and (d)
3D model: top-view (xy-plane) of p1 and p31, respectively.
(e) and (f) 2D chip model: top-view (xy-plane) of p1 and
p31, respectively. (g) The eigenfrequencies ωn/2π versus mode
number n for the 3D model and the 2D chip model.
work, we focus on the acoustic resonances where the re-
sponse of the bead solution is particularly strong. As the
attenuation of the acoustic waves is relatively small, we
can approximate the actual frequency-broadened acous-
tic resonances of the driven system by the infinitely sharp
eigenmodes of the isolated dissipationless chip.
The pressure eigenmodes p
(x, y, z) cos(ω
t), labelled
by an integer index n, and the angular eigenfrequencies
or resonance frequencies ω
are found as solutions to
the Helmholtz eigenvalue equation ∇2p
= −(ω2
where the index i is referring to the three material do-
mains of silicon, water and glass in the chip. The bound-
ary conditions at the outer edges of the system are given
by the soft-wall condition p
= 0 except at the bottom
plane, where a hard-wall condition n ·∇p
= 0 is chosen
to mimic the piezo-actuator which fixes the velocity of
the wall. At the internal interfaces between the different
material regions the boundary conditions are continuity
of the pressure p
as well as of the wall-velocity. The lat-
ter is ensured by continuity of the field (1/ρ
. A list
of the acoustic material parameters, i.e., sound velocities
and densities ρ
, is given in Table III.
The Helmholtz equation was solved numerically using
the COMSOL finite element method software. However,
the large aspect ratio of the flat device made it impossible
to simulate the actual device in 3D due to limited com-
puter memory. We therefore investigated the possibility
of making 2D simulations. The rationale for doing this
is that the total height of the chip is only 1 mm. Given a
weighted average speed of sound in the silicon-glass chip
of 6900 m/s, the wavelength of a wave at the highest used
frequency f = 2.5 MHz is 3 mm and thus three times the
chip height. Similarly, at the same frequency the wave-
length in water is 0.6 mm or three times the chamber
height. Consequently, there is not room enough for even
half a standing wave in the vertical direction neither in
the water filled chamber nor in the silicon-glass chip.
The first step towards a more rigorous justification for
doing 2D simulations was to make a smaller 3D version of
the system geometry. While keeping all the correct height
measures as well as the chamber width as listed in Ta-
ble I, we shrunk the planar dimensions of the surrounding
chip to L
= 8 mm, w
= 6 mm and L
= 6.8 mm. With
this reduced geometry we could carry out the full 3D
simulations, and the results thereof confirmed that the
variations in the vertical z-direction of the 3D eigenmodes
were modest, see the xz-plane plots of Figs. 2(a) and (b).
A 2D simulation was then carried out for the horizontal
xy center-plane of the chamber, i.e., a 2D water-filled
area surrounded by a 2D silicon region. Comparing the
50 lowest 3D and 2D eigenmodes gave the following re-
sults: (1) in the horizontal xy center-plane of the cham-
ber the 3D eigenmodes agreed with the 2D eigenmodes,
see Figs. 2(c–f); (2) due to the lack of the z-dependence
in the Laplacian of the 2D Helmholtz equation, the 2D
eigenfrequencies were systematically smaller than the 3D
eigenfrequencies, see Fig. 2(g). It has thus been justified
to simulate the experimentally observed resonances by
2D eigenmodes in the horizontal xy center-plane of the
chamber. This we denote the 2D chip model.
Due to the small acoustic impedance ratio
) = 0.08 between silicon and water,
the simulations could be simplified even further. As
demonstrated in Figs. 3(c) and (d), it suffices to find
the eigenmodes of the chamber itself using hard-wall
boundary conditions along its edges, except at the very
ends of the inlet channels where soft-wall boundary
conditions are employed to mimic in- and outlets. This
we will refer to as the 2D chamber model.
(c) (d)
FIG. 3: Acoustic radiation force. (a) Experiments on 5 µm
beads at the 1.936 MHz acoustic resonance. The white PIV-
vectors indicate the initial bead velocities pointing away from
pressure anti-nodes immediately after the piezo-actuation is
applied. The picture underneath the PIV-vector plot shows
the particles (black) gathered at the pressure nodal lines 3
seconds later. (b) As in panel (a) but now at 2.417 MHz. (c)
and (d) Gray-scale plots of numerical simulations in the 2D
chamber model of the corresponding acoustic pressure eigen-
modes. Nodal lines are shown in black.
IV. RESULTS AND DISCUSSION
We have measured the flow response to the acoustic
actuation in the frequency range from 0.5 to 2.5 MHz
paying special attention to the strong responses corre-
sponding to acoustic resonances. More than 30 of such
resonances have been detected, but we present only a few,
which we find to be representative for the method and the
problems associated with acoustics in microfluidics.
The most important results are the full-image micro-
PIV analyses. For these, two types of experimental re-
sults are presented. One type are the PIV-vector plots
(white arrows) of the motion of the tracer particles, in
most cases corresponding to the transient motion imme-
diately after the onset of the acoustic piezo-actuation.
The other type are micrographs of the microfluidic cham-
ber with the steady-state particle patterns (often visible
as narrow black bands) obtained after a few seconds of
actuation. These two types of images are superimposed
to illustrate the relation between the initial motion of the
tracer beads and their final steady-state positions.
The full-image micro-PIV analysis illustrations are also
accompanied by the results of our numerical simulations
in the form of gray-scale plots of the pressure eigenmodes
(x, y, z). The pressure antinodes appear as white (pos-
itive amplitude) and black (negative amplitude) regions.
The pressure nodal lines are shown as thin black lines in
the gray (small amplitude) regions.
Additionally, we show a close up measurement of a
streaming vortex, and provide a more in-depth compar-
ison between the measured velocities and the calculated
body force.
A. Acoustic radiation force
We first show results for the acoustic resonances at
1.936 and 2.417 MHz in the circular chamber containing
large 5 µm tracer particles.
In Figs. 3(a) and (b) are shown the measured tran-
sient PIV-vector plots superimposed on the micrographs
of the chamber with the static steady-state particle pat-
terns. The fact that the particles accumulate in static
patterns indicates that the dominant force on the tracer
particles is the acoustic radiation force, an observation
also expected from the relatively large size of the tracer
particles. The matching numerically calculated acoustic
eigenmodes of the 2D chamber model are shown in pan-
els (c) and (d). It is noteworthy that even for the com-
plicated resonance pattern of panels (b) and (d), the ob-
served transient particle motion towards the steady-state
positions, and the static steady-state patterns them-
selves, are in good agreement with the numerically cal-
culated pressure nodal lines. This demonstrates that
even the simple 2D chamber model can predict what
kind of fluidic behavior will be observed in the device.
It also demonstrates that full-image micro-PIV analysis
in combination with images of transient particle motion
is effective in visualizing in-plane acoustic phenomena in
micrometer-scale devices.
FIG. 4: Acoustic streaming and radiation forces at the
2.17 MHz acoustic resonance. (a) Experiments on 5 µm beads
similar to Fig. 3(a) showing that the acoustic radiation force
dominates for large particles. (b) Experiments on 1 µm beads.
Acoustic streaming dominates and the small beads act as trac-
ers for the motion of the liquid. The resulting vortex structure
in the flow-field prevents particle accumulation at the pres-
sure nodes. (c) Gray-scale plot of numerical simulation in
the 2D chamber model of the corresponding acoustic pressure
eigenmode. Nodal lines are shown in black.
B. Acoustic streaming
To illustrate the difference between the acoustic radi-
ation force and acoustic streaming, we now turn to the
acoustic resonance at 2.17 MHz in the square chamber
containing large 5 µm beads and small 1 µm beads as
shown in Figs. 4(a) and (b), respectively.
When micro-PIV is applied to investigate acoustic ef-
fects in microfluidic chambers, the simultaneous presence
of both acoustic radiation forces and acoustic streaming
needs to be taken into account. For the large beads in
Fig. 4(a) the acoustic radiation force dominates exactly
as in Figs. 3(a) and (b), which results in particle accu-
mulation at the pressure nodal lines. However, as shown
in Fig. 4(b) reduction of the particle volume by a fac-
tor of 125 leads to a qualitative change in the response.
The motion of the smaller particles is dominated by the
acoustic streaming of the water, and it manifests itself
as a 6×6 pattern of vortices. The same 6×6 pattern
was found by full-image micro-PIV when diluted milk
was used as tracer solution, and also by optical inspec-
tion with a fluorescein solution in the chamber (data not
shown). All three experimental results strongly support
the interpretation that the 6×6 vortex pattern is caused
by acoustic streaming.
In Fig. 4(b) is also seen a pronounced inhomogene-
ity in the strength of the vortices across the microfluidic
chamber. This effect cannot be ascribed to the geometry
of the chamber, but is probably due to either a geomet-
ric top-bottom asymmetry in the entire chip (similar to
the left-right asymmetry discussed in Sec. IVC), or to
an inhomogeneous coupling between the piezo-actuator
and the silicon chip. If the frequency is shifted slightly
in the vicinity of 2.17 MHz, the same vortex pattern will
still be visible, but the strength distribution between the
vortices will be altered. When investigating acoustic phe-
nomena the advantage of full-image micro-PIV compared
to partial-image micro-PIV is thus evident: partial-image
micro-PIV employed locally in a part of the chamber
would not have shown the symmetrical 6×6 vortex pat-
tern, nor would it supply us with information of the in-
homogeneity in strength for the same. Moreover, since
the same inhomogeneity is not seen in the acoustic ra-
diation force vector plot, this example shows that there
is no direct relation between the strength of the acoustic
streaming and the acoustic radiation force.
Finally, we note that our measurements show that the
acoustic radiation force on the large particles leads to a
much larger particle velocity than the acoustic streaming
velocities of the smaller particles.
Turning to the numerical simulation in the 2D chamber
model of the corresponding pressure eigenmode, shown in
Fig. 4(c), we find good agreement with the experimental
results. The calculated pressure nodal lines correspond
well to the static steady-state particle patterns obtained
with the large tracer particles dominated by the acous-
tic radiation force. Moreover, the calculated 3×3 antin-
ode pattern is also consistent with the observed period-
doubled 6×6 vortex pattern of the small tracer particles
dominated by acoustic streaming. The spatial period-
doubling arises from the non-zero time-average of the
non-linear term in the Navier–Stokes equation governing
the attenuated acoustic flows leading to acoustic stream-
ing [29].
C. Effects of geometric asymmetries
For the results presented so far the simple 2D cham-
ber model proved sufficient to interpret the experimental
observations. However, as explained already in Sec. III
the pressure eigenmodes are not confined to the chamber
region but fill the entire chip. The acoustic resonances
even propagate in all media (air and piezo-actuator) in
contact with the chip. In the following we show one ex-
ample of asymmetric resonance patterns that can only
be explained by employing the more complete 2D chip
model or by introducing asymmetries in the 2D chamber
model.
In Figs. 5(a) and (b) we consider the square cham-
ber containing the large 5 µm beads at two nearby res-
onance frequencies, 2.06 and 2.08 MHz. As before, the
acoustic radiation force dominates and the beads accu-
mulate at the pressure nodal lines. Note that the two
patterns are similar, but that the first has a higher am-
plitude on the left side, while the second has a higher
amplitude on the right side. Both resonance patterns
are similar to the acoustic pressure eigenmode shown in
Fig. 5(c), which is found by numerical simulation using
the 2D chamber model. However, since the chamber itself
is left-right symmetric, the calculated eigenmode is also
left-right symmetric, so to explain the observed asymme-
try we have to break the left-right symmetry in the the-
oretical model. We investigate two ways of doing this:
first, in the 2D chip model by placing a symmetric cham-
ber asymmetrically on the chip, and second, in the 2D
chamber model by letting the inlet channel have a differ-
ent length than the outlet channel.
In Figs. 6(a-d) is shown the result of a numerical simu-
lation in the 2D chip model where the left-right symme-
try has been broken by displacing the chamber 1 mm left
of the symmetry center of the chip. This displacement
corresponds to the geometry of the actual chip used in
the experiment. Panels (a) and (b) show the entire chip
while panels (c) and (d) are the corresponding closeups
of the chamber region. With this left-right asymmetric
geometry, we do find asymmetric solutions at nearby fre-
quencies that resemble the measured patterns: Figs. 6(c)
and (d) correspond to Figs. 5(a) and (b), respectively.
In the left-right symmetric case the left-right acoustic
resonance is two-fold degenerate, i.e., two different res-
onances have the same frequency. When the symme-
try is broken the two resonances are affected differently:
one gets a slightly higher eigenfrequency and the other a
slightly lower, i.e., a splitting of the two-fold degenerate
eigenfrequency into two non-degenerate nearly identical
eigenfrequencies. The two closely spaced eigenmodes of
the asymmetric 2D chamber model shown in Figs. 6(e)
and (f) also resemble the measured patterns in Figs. 5(a)
and (b). The calculated frequency splitting is 28 kHz,
which is in fair agreement with the measured 20 kHz.
Unquestionably, advanced models, like the chip model,
are necessary for more complete theoretical investigations
of how different factors contribute to the breaking of the
FIG. 5: Splitting of a two-fold degenerate acoustic resonance
due to geometrical asymmetry. (a) Acoustic radiation force
as in Fig. 4(a) on 5 µm beads at the 2.06 MHz resonance.
(b) The closely related 2.08 MHz resonance for the same sys-
tem. (c) Gray-scale plot of numerical simulation in the left-
right symmetric 2D chamber model of the corresponding two-
fold degenerate, un-split, acoustic pressure eigenmode. Nodal
lines are shown in black.
symmetry of the simple chamber model. Experimentally
this effect could be studied by measuring on a range of
devices, with strictly controlled geometries of both struc-
tures and substrates. We have only investigated two de-
vices, and special concern was not taken as to the unifor-
mity of the substrate. It is therefore not possible in the
present study to determine whether the observed sym-
metry breaking was due to geometric asymmetries in the
chip, in the chip-actuator coupling, or in other parts of
(c) (d)
(e) (f)
FIG. 6: (a) ad (b) Gray-scale plots of numerical simulations
in the 2D chip model of two closely spaced acoustic pressure
eigenmodes. The chamber is displaced 1 mm to the left of
the symmetry center of the chip thereby breaking the left-
right symmetry and splitting the two-fold eigenmode degen-
eracy. The difference in eigenfrequency is only 1 kHz. (c) and
(d) Closeups of the chamber region showing the asymmetric
eigenmodes similar to the experimentally observed resonances
seen in Fig. 5. (e) and (f) Gray-scale plots of numerically
simulated pressure eigenmodes in the asymmetric 2D cham-
ber model, where the left lead is 1 mm shorter than the right
lead. The difference in eigenfrequency is 28 kHz, which is close
to the observed difference of 20 kHz in Figs. 5(a) and (b).
the system (such as air-bubbles trapped at the fluidic
inlet and outlet).
D. Validation of method
Fig. 7 shows a micro-PIV vector plot of streaming mo-
tion in the center of the square chamber at 2.17 MHz,
recorded with a 20x microscope objective. With this kind
of recording, detailed information of a section of the de-
vice can be obtained, but it will not supply any informa-
tion about the amplitude fluctuations over the device, nor
does it reveal the 6x6 vortex pattern as seen in Fig. 4(b).
Clearly, more detailed measurements of specific features
are valuable, but for studies of resonances in low atten-
uation microfluidic devices, full-image recordings are of
100 µm
500 µm/s
FIG. 7: Micro-PIV velocity vector plot of streaming motion
in the center of the square chamber at 2.17 MHz. Images were
recorded with a 20x objective and a 0.63x Tv-adapter, and
milk was used as tracer particles.
most importance.
By regarding the suspended particles as springs gov-
erned by Hooke’s law, we can estimate the acoustic ra-
diation force Fac, from the potential elastic energy. We
find F = −τp
, where τ is a constant parameter for
each kind of particles, and p
is the time-averaged second-
order pressure field. As τ is an unknown positive constant
for blood-cell like particles, the amplitude becomes a fit-
ting parameter. Assuming the particles move in a quasi-
stationary steady state, we can directly compare calcu-
lated force patterns to measured velocity patterns. Such
a comparison is seen in Fig. 8, where the calculated force
pattern is compared with a scalar map of the velocity in
y-direction, extruded from the measurement presented in
Fig. 4(a). A comparison between the two is also seen in
Fig. 9, where two vertical cross-sectional views, each lo-
cated 330 µm away from the center of the chamber, are
compared with the theoretical estimate. Both micro-PIV
velocity plots show a good agreement with the calculated
forces, and the fluctuations in amplitude over the device
can be seen by comparing the two micro-PIV velocity
plots with each other.
V. CONCLUSION
Using full-image micro-PIV we have made direct obser-
vations of the acoustic resonances in piezo-actuated, flat
microfluidic chambers containing various tracer particles.
Depending on the size of the tracer particles either
the acoustic radiation force or acoustic streaming of the
solvent dominates their motion. Large particles are dom-
FIG. 8: (a) The force in y-direction calculated with COMSOL
finite element method software. (b) Scalar map of the velocity
in y-direction, measured with micro-PIV.
0 10 20 30 40 50
-0.00025
-0.00020
-0.00015
-0.00010
-0.00005
0.00000
0.00005
0.00010
0.00015
0.00020
0.00025
Point
theory
FIG. 9: Vertical cross-sectional plots of the velocity in the
y-direction (PIV1) 330 µm left and (PIV2) 330 µm right of
the center of the chamber. (theory) is the force in y-direction,
calculated in COMSOL with the amplitude as the only fitting
parameter.
inated by the acoustic radiation force that pushes them
to the static pressure nodal lines, while small particles
are dominated by acoustic streaming and end up forming
steady-state vortex patterns. However, for an arbitrary
frequency and geometry one of the forces can be strong
whereas the other is not, and it is therefore always nec-
essary to apply more than one tracer solution in order to
determine which forces are present.
The observed acoustic resonances correspond to the
pressure eigenmodes found by numerical simulation of
2D models of the system. The symmetric patterns can be
explained by using the simple 2D chamber model, while
asymmetric patterns can be explained by using the more
complete 2D chip model taking into account the geomet-
ric asymmetries of the surrounding chip, or in special
cases, by an asymmetric 2D chamber model.
We have demonstrated that full-image micro-PIV
is a useful tool for complete characterization of the
in-plane acoustically induced motion in piezo-actuated
microfluidic chambers.
Acknowledgement
SMS was supported through Copenhagen Graduate
School of Nanoscience and Nanotechnology, in a collab-
oration between Dantec Dynamics A/S, and MIC, Tech-
nical University of Denmark.
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  We show that full-image micro-PIV analysis in combination with images of
transient particle motion is a powerful tool for experimental studies of
acoustic radiation forces and acoustic streaming in microfluidic chambers under
piezo-actuation in the MHz range. The measured steady-state motion of both
large 5 um and small 1 um particles can be understood in terms of the acoustic
eigenmodes or standing ultra-sound waves in the given experimental
microsystems. This interpretation is supported by numerical solutions of the
corresponding acoustic wave equation.

Acoustic resonances in microfluidic chips:
full-image micro-PIV experiments and numerical simulations
S. M. Sundin, T. Glasdam Jensen, H. Bruus and J. P. Kutter
MIC – Department of Micro and Nanotechnology, Technical University of Denmark
DTU Bldg. 345 east, DK-2800 Kongens Lyngby, Denmark
(Dated: 30 March 2007)
We show that full-image micro-PIV analysis in combination with images of transient particle
motion is a powerful tool for experimental studies of acoustic radiation forces and acoustic streaming
in microfluidic chambers under piezo-actuation in the MHz range. The measured steady-state motion
of both large 5 µm and small 1 µm particles can be understood in terms of the acoustic eigenmodes or
standing ultra-sound waves in the given experimental microsystems. This interpretation is supported
by numerical solutions of the corresponding acoustic wave equation.
I. INTRODUCTION
For the typical dimensions of microfluidic structures
there are two acoustic effects of main importance: the
acoustic radiation force [1, 2, 3], which moves suspended
particles either towards or away from pressure nodes de-
pending on their acoustic material properties, and acous-
tic streaming [4, 5], which imparts movement onto the
entire solvent. Both of these forces have been utilized,
alone or in combination, for several lab-on-a-chip appli-
cations. Yasuda et al. [6, 7], demonstrated concentration
of particles by acoustic radiation forces, and separation
of particles by acoustic forces in combination with elec-
trostatic forces. One of the most attractive applications
for acoustics in microfluidics is for mixing [8, 9, 10], as
this process typically is diffusion limited in microscale
devices. Valveless ultrasonic pumps, utilizing acoustic
streaming, have also been presented [11, 12]. Numer-
ous examples of microsystems where acoustics are ap-
plied to handling and analysis of biological material have
been suggested. Among others these include: trapping of
microorganisms [13], bioassays [14], and separation and
cleaning of blood [15, 16, 17]. Apart from on chip de-
vices, acoustic forces have also been suggested for use in
other µm-scale applications [18].
There are different imaging strategies and tools, which
can be used in order to enhance the understanding, and
to visualize the function of acoustic micro-devices during
operation. For acoustic mixers the effect can be illus-
trated and measured by partly filling the mixing cham-
ber with a dye prior to piezo-actuation [9, 10]. However,
this approach is mainly limited to determine the total,
and not the local, mixing behavior within the cham-
ber. A more refined method, which is not limited to
the study of micromixers, is to apply streak- or stream-
line analysis. This was shown by Lutz et al. [19, 20], who
neatly demonstrated 3D steady micro streaming around a
cylinder. Although streamline analysis can be employed
to illustrate flow behaviour, it is not suitable in deter-
mining local variations in velocity. For that purpose,
the micron-resolution particle image velocimetry (micro-
PIV) technique is the method of choice [21]. With this
technique the motion of tracer particles, acquired from
consecutive image frames, is utilized to obtain velocity
vector fields. In a large chamber, local measurements
of particle motion induced by acoustic radiation forces
and acoustic streaming have been performed by Spen-
gler et al. [22, 23], and further developed by Kuznetsova
et al. [24]. Li and Kenny derived velocity profiles in a
particle separating device utilizing the acoustic radiation
force [17]. Jang et al. used confocal scanning microscopy
to perform micro-PIV measurements on circulatory flows
in a piezo-actuated fluidic chamber [25]. Furthermore,
Manasseh et al. applied micro-PIV to measure stream-
ing velocites around a bubble trapped in a microfluidic
chamber [26].
As particles under the influence of acoustic fields do
no longer function as true independent tracers in all sit-
uations, and as several acoustic effects come into play
at the same time, extra caution and consideration have
to be taken when applying micro-PIV for microfluidic
acoustic studies. These considerations will be discussed
in more detail in section II C. The situation is further
complicated by the coupling from the actuator to the
structures and their acoustic resonances, which is a yet
poorly understood mechanism. The resonances depend
on the acoustic material parameters as well as the geom-
etry of both the chip and the chamber. For substrate
materials with low attenuation, such as silicon, the ac-
tuation will result in strong resonances over the whole
devices, whereas for substrate materials with high atten-
uation, the effect will be mostly confined to the prox-
imity of the actuator. Moreover, in a real system the
coupling strengths vary for different resonances, and am-
plitude fluctuations across the structures are often ob-
served. Therefore, if investigations striving to yield a
better understanding of acoustic resonances in low atten-
uation microfluidic chips are to be performed, it is not
sufficient only to study the acoustic phenomena locally.
In this work, full-image micro-PIV analysis in combi-
nation with images of transient particle motion is sug-
gested as a tool for studying acoustic resonances in mi-
crofluidic chambers under piezo-actuation. The acousto-
fluidic phenomena mentioned above can be investigated
by comparing these experimental images with plots of
acoustic eigenmodes of the device structure obtained by
http://arxiv.org/abs/0704.1314v1
FIG. 1: A top-view photograph of the silicon-glass chip (dark
gray) containing a square chamber with straight inlet and
outlet channels (light gray).
numerical solution of the corresponding acoustic wave
equation.
II. MATERIALS AND EXPERIMENTAL
METHODS
A. Microchip fabrication
In this study, two microfluidic chambers were inves-
tigated, one of quadratic footprint with a side-length of
2 mm and one of circular shape with a diameter of 2 mm.
The size was chosen to be a few times the acoustic wave-
length of 2 MHz ultrasound waves in water, and the spe-
cific shapes were employed to ensure simple patterns in
the pressure field at the acoustic resonances. Both cham-
bers were connected to 400 µm wide inlet and outlet
channels, and the depth was 200 µm throughout. The
microfluidic chips were fabricated in silicon via deep re-
active ion etching (DRIE). The same technique was also
applied on the backside of the chip to etch 300 µm diame-
ter round fluidic inlets. Anodic bonding was used to seal
the structures with a 500 µm thick pyrex glass lid on the
channel side. Silicon rubber tubings were glued to the
holes on the backside of the chip, for easy attachment of
teflon tubing. A picture of one of our microfluidic chips is
shown in Fig. 1, and a list of the geometrical parameters
is given in Table I.
B. Experimental setup and procedure
The piezo-actuator (Pz27, Ferroperm) was pressed to
the backside of the chip using an ultrasonic gel (ECO,
Ceracarta) and biased by a 20 V ac tone generator (Model
195, Wavetek). Images were captured with a progressive
scan interline CCD camera (Hisense MkII, Dantec Dy-
namics), mounted with a 0.63x TV-adapter on an epiflu-
orescent microscope (DMLB, Leica). The objective used
was a Plan 5x with a numerical aperture NA of 0.12.
For the given fluidic geometries, this combination allowed
capture of full-image PIV vector fields, while utilizing the
largest number of pixels on the CCD. A blue light emit-
ting diode, LED, (Luxeon Star 3W, Lumileds) was used
as illumination source in a front-lit configuration, which
TABLE I: The geometrical parameters of the fabricated mi-
crofluidic silicon-pyrex chip.
chip length L0 49 mm silicon thickness hs 500 µm
chip width w0 15 mm pyrex thickness hp 500 µm
channel length Lc 26 mm chamber height h 200 µm
channel width wc 400 µm chamber width w 2 mm
is described elsewhere [27]. The LED was powered by an
in-house built power supply controlled by a PIV timing
system (Dantec Dynamics). Image acquisition was per-
formed on a PC with Flowmanager software (Dantec Dy-
namics). As tracer fluids solutions of 1 µm polystyrene
micro-beads (Duke Scientific), 5 µm polyamide micro-
beads (Danish Phantom Design), diluted milk, and fluo-
rescein have been used.
The investigations were performed by scanning the
applied frequency from the tone generator and identi-
fying those frequencies which led to a strong response,
an acoustic resonance, in the microfluidic chamber. At
the resonance frequencies, the behavior of the different
tracer particle solutions was observed. Between succes-
sive recordings the chip was flushed to assure homoge-
neous seeding. Furthermore, to make sure that only par-
ticle motion caused by acoustic forces were recorded, no
external flow was applied during measurements.
C. Micro-PIV considerations
In micro-PIV tracer particles are chosen for their abil-
ity to truthfully follow the motion of the flow that is
to be investigated. Particles under the influence of an
acoustic field do no longer fulfil this criterium in all situ-
ations. Therefore, extra caution and considerations have
to be taken regarding what movements are actually mea-
sured when applying micro-PIV for these types of stud-
ies. Given that particle motion caused by thermal or
gravitational forces can be neglected, the main task is to
determine if particle motion is caused by acoustic radi-
ation forces, acoustic streaming or a combination of the
two. In this study, this problem was tackled by applying
three tracer solutions with different physical properties.
Typically, the large polyamide particles are more
strongly affected by the acoustic radiation forces than
by the forces due to acoustic streaming of the surround-
ing water. In contrast, since the acoustic radiation
force scales with the volume of the particle, the small
polystyrene particles will follow the motion of the water,
if relatively strong acoustic streaming is present. How-
ever, there is no simple relation between the two forces,
and for an arbitrary frequency and geometry one can be
strong whereas the other is not, and vice versa. There-
fore, in order to determine whether particle motion is
caused by acoustic radiation forces or acoustic streaming
it is necessary to utilize the dependance of the acoustic
radiation forces on the compressibility of the particle.
TABLE II: The susceptibility to acoustic radiation forces for
the particles used in this study, as well as for some other
particles common to microfluidic applications.
tracer type force direction
beads (1 µm) weak nodes
beads (5 µm) strong nodes
red blood cells strong nodes
milk particles weak anti-nodes
large micelles strong anti-nodes
fluorescein none -
The polymer particles will move towards the pressure
nodes since their compressibility is smaller than that of
water. The opposite is true for the lipid particles in milk:
their compressibility is larger than that of water, and
consequently they will move towards pressure antinodes.
Like the small polystyrene particles, the lipid particles
we used were small enough to typically follow the net
acoustic streaming flow of the water. Thus, if similar mo-
tion is recorded with two types of tracers with different
compressibilities compared to the medium, the acoustic
radiation forces can be ruled out as cause of the motion.
As an alternative or complementary technique to micro-
PIV measurements, fluorescein can be used to investigate
acoustic streaming. A summary of the acoustic behav-
ior of the different particles used in this study, and some
other bodies that are common in microfluidic applica-
tions, is given in Table II.
The speed of sound c in water has a significant de-
pendence on temperature T given by the large deriva-
tive ∂c/∂T ≃ 4 m s−1K−1. All tracer fluids were there-
fore kept at room temperature, so that the temperature
was not changed when the microchip was flushed dur-
ing tracer particle exchange. The microchips used in
this study are comparable in size and mode of actua-
tion to those used for ultrasonic agitation in a study by
Bengtsson and Laurell [28]. They performed sensitive
temperature measurements on the reactor outlet, where
no temperature increase caused by the acoustic power
could be detected. In our study, the piezo-actuator was
run at a moderate power-level and only for the short
intervals during recordings (typically less than one sec-
ond). Therefore, it can be ruled out that heating from
the piezo-actuator would have any measurable impact on
the measurements.
One important factor, which needs to be accounted for
when applying micro-PIV on systems affected by acoustic
forces, is that the local seeding density will be distorted
during actuation. This is normally not a problem when
measuring on particle motion caused solely by acoustic
streaming, as this motion generally will be of a circulat-
ing nature. On the other hand, in the case of particle
motion induced by acoustic radiation forces, it will typi-
cally lead to total expulsion of particles from certain re-
gions into others. If PIV-vector statistics is applied, only
the first few image-pairs recorded after piezo-actuation
TABLE III: The acoustic material parameters of the microsys-
tem at 20 ◦C: sound velocities ci and densities ρi from the
CRC Handbook of Chemistry and Physics.
material speed of sound density
water cw = 1483 m/s ρw = 998 kg/m
silicon cs = 8490 m/s ρs = 2331 kg/m
pyrex cp = 5640 m/s ρp = 2230 kg/m
has been initiated can be used, and in this study, im-
ages from a number of consecutively recorded sets have
been used for averaging. Moreover, in the case of scan-
ning, or mapping, techniques the expulsion of particles is
especially problematic, as the seeding conditions in the
device, or chamber, need to be restored for each measure-
ment position. Also, the conditions may change during
these lengthy recordings, leading to results that are dif-
ficult to interpret.
The acoustic resonances in low attenuation piezo-
actuated microfluidic devices are formed over the whole
devices, and they are also depending on the geometry
of the whole device. As a consequence, there will typ-
ically be amplitude fluctuations over the devices, due
to unwanted artifacts, or deliberate designs. Therefore,
when investigating acoustic resonances, and the influence
caused by different modifications to the sample, it is im-
portant to study the effects globally. If the acoustic ef-
fects are only measured in a part of the device, this kind
of information will not be yielded, independently on how
detailed the flow is mapped within that region. There-
fore, we suggest full-image micro-PIV for the investiga-
tion of acoustic resonances in microfluidic devices.
In this study, emphasis has been put on how to present
the measured data in such a way that still images and
PIV-vector plots give the best illustration of the tran-
sient particle motion caused by the acoustic forces. To
achieve this, we have chosen to superimpose the PIV-
vector plots of the initial transient velocities on top of
the pictures of the steady-state patterns of the particles
obtained after a few seconds of actuation. After longer
actuation times, secondary patterns will form, so images
taken at this point can give a false impression of the parti-
cle motion. This method of combining the transient PIV-
vector plots and steady-state pictures has shown useful
when comparing numerical simulations with micro-PIV
measurements, especially for measuring amplitude fluc-
tuations across the structures, and when discriminating
between different numerical models. This will be demon-
strated in Sec. IV.
III. NUMERICAL SIMULATIONS
In the experiments, the acoustic pressure field, which
is superimposed on the ambient constant pressure, is
driven by a harmonically oscillating piezo-actuator, i.e.,
the time-dependence can be described as cos(ωt). In this
(a) 3D side-view (b) 3D side-view
(c) 3D top-view (d) 3D top-view
(e) 2D chip model (f) 2D chip model
n, eigenmode no.
0 10 20 30 40 50✻
3D model
2D chip
model
FIG. 2: Numerical simulations of the pressure eigenmodes
pn(x, y, z) shown in gray-scale plots. (a) and (b) 3D model:
side-view (xz-plane) of p1 and p31, respectively. (c) and (d)
3D model: top-view (xy-plane) of p1 and p31, respectively.
(e) and (f) 2D chip model: top-view (xy-plane) of p1 and
p31, respectively. (g) The eigenfrequencies ωn/2π versus mode
number n for the 3D model and the 2D chip model.
work, we focus on the acoustic resonances where the re-
sponse of the bead solution is particularly strong. As the
attenuation of the acoustic waves is relatively small, we
can approximate the actual frequency-broadened acous-
tic resonances of the driven system by the infinitely sharp
eigenmodes of the isolated dissipationless chip.
The pressure eigenmodes p
(x, y, z) cos(ω
t), labelled
by an integer index n, and the angular eigenfrequencies
or resonance frequencies ω
are found as solutions to
the Helmholtz eigenvalue equation ∇2p
= −(ω2
where the index i is referring to the three material do-
mains of silicon, water and glass in the chip. The bound-
ary conditions at the outer edges of the system are given
by the soft-wall condition p
= 0 except at the bottom
plane, where a hard-wall condition n ·∇p
= 0 is chosen
to mimic the piezo-actuator which fixes the velocity of
the wall. At the internal interfaces between the different
material regions the boundary conditions are continuity
of the pressure p
as well as of the wall-velocity. The lat-
ter is ensured by continuity of the field (1/ρ
. A list
of the acoustic material parameters, i.e., sound velocities
and densities ρ
, is given in Table III.
The Helmholtz equation was solved numerically using
the COMSOL finite element method software. However,
the large aspect ratio of the flat device made it impossible
to simulate the actual device in 3D due to limited com-
puter memory. We therefore investigated the possibility
of making 2D simulations. The rationale for doing this
is that the total height of the chip is only 1 mm. Given a
weighted average speed of sound in the silicon-glass chip
of 6900 m/s, the wavelength of a wave at the highest used
frequency f = 2.5 MHz is 3 mm and thus three times the
chip height. Similarly, at the same frequency the wave-
length in water is 0.6 mm or three times the chamber
height. Consequently, there is not room enough for even
half a standing wave in the vertical direction neither in
the water filled chamber nor in the silicon-glass chip.
The first step towards a more rigorous justification for
doing 2D simulations was to make a smaller 3D version of
the system geometry. While keeping all the correct height
measures as well as the chamber width as listed in Ta-
ble I, we shrunk the planar dimensions of the surrounding
chip to L
= 8 mm, w
= 6 mm and L
= 6.8 mm. With
this reduced geometry we could carry out the full 3D
simulations, and the results thereof confirmed that the
variations in the vertical z-direction of the 3D eigenmodes
were modest, see the xz-plane plots of Figs. 2(a) and (b).
A 2D simulation was then carried out for the horizontal
xy center-plane of the chamber, i.e., a 2D water-filled
area surrounded by a 2D silicon region. Comparing the
50 lowest 3D and 2D eigenmodes gave the following re-
sults: (1) in the horizontal xy center-plane of the cham-
ber the 3D eigenmodes agreed with the 2D eigenmodes,
see Figs. 2(c–f); (2) due to the lack of the z-dependence
in the Laplacian of the 2D Helmholtz equation, the 2D
eigenfrequencies were systematically smaller than the 3D
eigenfrequencies, see Fig. 2(g). It has thus been justified
to simulate the experimentally observed resonances by
2D eigenmodes in the horizontal xy center-plane of the
chamber. This we denote the 2D chip model.
Due to the small acoustic impedance ratio
) = 0.08 between silicon and water,
the simulations could be simplified even further. As
demonstrated in Figs. 3(c) and (d), it suffices to find
the eigenmodes of the chamber itself using hard-wall
boundary conditions along its edges, except at the very
ends of the inlet channels where soft-wall boundary
conditions are employed to mimic in- and outlets. This
we will refer to as the 2D chamber model.
(c) (d)
FIG. 3: Acoustic radiation force. (a) Experiments on 5 µm
beads at the 1.936 MHz acoustic resonance. The white PIV-
vectors indicate the initial bead velocities pointing away from
pressure anti-nodes immediately after the piezo-actuation is
applied. The picture underneath the PIV-vector plot shows
the particles (black) gathered at the pressure nodal lines 3
seconds later. (b) As in panel (a) but now at 2.417 MHz. (c)
and (d) Gray-scale plots of numerical simulations in the 2D
chamber model of the corresponding acoustic pressure eigen-
modes. Nodal lines are shown in black.
IV. RESULTS AND DISCUSSION
We have measured the flow response to the acoustic
actuation in the frequency range from 0.5 to 2.5 MHz
paying special attention to the strong responses corre-
sponding to acoustic resonances. More than 30 of such
resonances have been detected, but we present only a few,
which we find to be representative for the method and the
problems associated with acoustics in microfluidics.
The most important results are the full-image micro-
PIV analyses. For these, two types of experimental re-
sults are presented. One type are the PIV-vector plots
(white arrows) of the motion of the tracer particles, in
most cases corresponding to the transient motion imme-
diately after the onset of the acoustic piezo-actuation.
The other type are micrographs of the microfluidic cham-
ber with the steady-state particle patterns (often visible
as narrow black bands) obtained after a few seconds of
actuation. These two types of images are superimposed
to illustrate the relation between the initial motion of the
tracer beads and their final steady-state positions.
The full-image micro-PIV analysis illustrations are also
accompanied by the results of our numerical simulations
in the form of gray-scale plots of the pressure eigenmodes
(x, y, z). The pressure antinodes appear as white (pos-
itive amplitude) and black (negative amplitude) regions.
The pressure nodal lines are shown as thin black lines in
the gray (small amplitude) regions.
Additionally, we show a close up measurement of a
streaming vortex, and provide a more in-depth compar-
ison between the measured velocities and the calculated
body force.
A. Acoustic radiation force
We first show results for the acoustic resonances at
1.936 and 2.417 MHz in the circular chamber containing
large 5 µm tracer particles.
In Figs. 3(a) and (b) are shown the measured tran-
sient PIV-vector plots superimposed on the micrographs
of the chamber with the static steady-state particle pat-
terns. The fact that the particles accumulate in static
patterns indicates that the dominant force on the tracer
particles is the acoustic radiation force, an observation
also expected from the relatively large size of the tracer
particles. The matching numerically calculated acoustic
eigenmodes of the 2D chamber model are shown in pan-
els (c) and (d). It is noteworthy that even for the com-
plicated resonance pattern of panels (b) and (d), the ob-
served transient particle motion towards the steady-state
positions, and the static steady-state patterns them-
selves, are in good agreement with the numerically cal-
culated pressure nodal lines. This demonstrates that
even the simple 2D chamber model can predict what
kind of fluidic behavior will be observed in the device.
It also demonstrates that full-image micro-PIV analysis
in combination with images of transient particle motion
is effective in visualizing in-plane acoustic phenomena in
micrometer-scale devices.
FIG. 4: Acoustic streaming and radiation forces at the
2.17 MHz acoustic resonance. (a) Experiments on 5 µm beads
similar to Fig. 3(a) showing that the acoustic radiation force
dominates for large particles. (b) Experiments on 1 µm beads.
Acoustic streaming dominates and the small beads act as trac-
ers for the motion of the liquid. The resulting vortex structure
in the flow-field prevents particle accumulation at the pres-
sure nodes. (c) Gray-scale plot of numerical simulation in
the 2D chamber model of the corresponding acoustic pressure
eigenmode. Nodal lines are shown in black.
B. Acoustic streaming
To illustrate the difference between the acoustic radi-
ation force and acoustic streaming, we now turn to the
acoustic resonance at 2.17 MHz in the square chamber
containing large 5 µm beads and small 1 µm beads as
shown in Figs. 4(a) and (b), respectively.
When micro-PIV is applied to investigate acoustic ef-
fects in microfluidic chambers, the simultaneous presence
of both acoustic radiation forces and acoustic streaming
needs to be taken into account. For the large beads in
Fig. 4(a) the acoustic radiation force dominates exactly
as in Figs. 3(a) and (b), which results in particle accu-
mulation at the pressure nodal lines. However, as shown
in Fig. 4(b) reduction of the particle volume by a fac-
tor of 125 leads to a qualitative change in the response.
The motion of the smaller particles is dominated by the
acoustic streaming of the water, and it manifests itself
as a 6×6 pattern of vortices. The same 6×6 pattern
was found by full-image micro-PIV when diluted milk
was used as tracer solution, and also by optical inspec-
tion with a fluorescein solution in the chamber (data not
shown). All three experimental results strongly support
the interpretation that the 6×6 vortex pattern is caused
by acoustic streaming.
In Fig. 4(b) is also seen a pronounced inhomogene-
ity in the strength of the vortices across the microfluidic
chamber. This effect cannot be ascribed to the geometry
of the chamber, but is probably due to either a geomet-
ric top-bottom asymmetry in the entire chip (similar to
the left-right asymmetry discussed in Sec. IVC), or to
an inhomogeneous coupling between the piezo-actuator
and the silicon chip. If the frequency is shifted slightly
in the vicinity of 2.17 MHz, the same vortex pattern will
still be visible, but the strength distribution between the
vortices will be altered. When investigating acoustic phe-
nomena the advantage of full-image micro-PIV compared
to partial-image micro-PIV is thus evident: partial-image
micro-PIV employed locally in a part of the chamber
would not have shown the symmetrical 6×6 vortex pat-
tern, nor would it supply us with information of the in-
homogeneity in strength for the same. Moreover, since
the same inhomogeneity is not seen in the acoustic ra-
diation force vector plot, this example shows that there
is no direct relation between the strength of the acoustic
streaming and the acoustic radiation force.
Finally, we note that our measurements show that the
acoustic radiation force on the large particles leads to a
much larger particle velocity than the acoustic streaming
velocities of the smaller particles.
Turning to the numerical simulation in the 2D chamber
model of the corresponding pressure eigenmode, shown in
Fig. 4(c), we find good agreement with the experimental
results. The calculated pressure nodal lines correspond
well to the static steady-state particle patterns obtained
with the large tracer particles dominated by the acous-
tic radiation force. Moreover, the calculated 3×3 antin-
ode pattern is also consistent with the observed period-
doubled 6×6 vortex pattern of the small tracer particles
dominated by acoustic streaming. The spatial period-
doubling arises from the non-zero time-average of the
non-linear term in the Navier–Stokes equation governing
the attenuated acoustic flows leading to acoustic stream-
ing [29].
C. Effects of geometric asymmetries
For the results presented so far the simple 2D cham-
ber model proved sufficient to interpret the experimental
observations. However, as explained already in Sec. III
the pressure eigenmodes are not confined to the chamber
region but fill the entire chip. The acoustic resonances
even propagate in all media (air and piezo-actuator) in
contact with the chip. In the following we show one ex-
ample of asymmetric resonance patterns that can only
be explained by employing the more complete 2D chip
model or by introducing asymmetries in the 2D chamber
model.
In Figs. 5(a) and (b) we consider the square cham-
ber containing the large 5 µm beads at two nearby res-
onance frequencies, 2.06 and 2.08 MHz. As before, the
acoustic radiation force dominates and the beads accu-
mulate at the pressure nodal lines. Note that the two
patterns are similar, but that the first has a higher am-
plitude on the left side, while the second has a higher
amplitude on the right side. Both resonance patterns
are similar to the acoustic pressure eigenmode shown in
Fig. 5(c), which is found by numerical simulation using
the 2D chamber model. However, since the chamber itself
is left-right symmetric, the calculated eigenmode is also
left-right symmetric, so to explain the observed asymme-
try we have to break the left-right symmetry in the the-
oretical model. We investigate two ways of doing this:
first, in the 2D chip model by placing a symmetric cham-
ber asymmetrically on the chip, and second, in the 2D
chamber model by letting the inlet channel have a differ-
ent length than the outlet channel.
In Figs. 6(a-d) is shown the result of a numerical simu-
lation in the 2D chip model where the left-right symme-
try has been broken by displacing the chamber 1 mm left
of the symmetry center of the chip. This displacement
corresponds to the geometry of the actual chip used in
the experiment. Panels (a) and (b) show the entire chip
while panels (c) and (d) are the corresponding closeups
of the chamber region. With this left-right asymmetric
geometry, we do find asymmetric solutions at nearby fre-
quencies that resemble the measured patterns: Figs. 6(c)
and (d) correspond to Figs. 5(a) and (b), respectively.
In the left-right symmetric case the left-right acoustic
resonance is two-fold degenerate, i.e., two different res-
onances have the same frequency. When the symme-
try is broken the two resonances are affected differently:
one gets a slightly higher eigenfrequency and the other a
slightly lower, i.e., a splitting of the two-fold degenerate
eigenfrequency into two non-degenerate nearly identical
eigenfrequencies. The two closely spaced eigenmodes of
the asymmetric 2D chamber model shown in Figs. 6(e)
and (f) also resemble the measured patterns in Figs. 5(a)
and (b). The calculated frequency splitting is 28 kHz,
which is in fair agreement with the measured 20 kHz.
Unquestionably, advanced models, like the chip model,
are necessary for more complete theoretical investigations
of how different factors contribute to the breaking of the
FIG. 5: Splitting of a two-fold degenerate acoustic resonance
due to geometrical asymmetry. (a) Acoustic radiation force
as in Fig. 4(a) on 5 µm beads at the 2.06 MHz resonance.
(b) The closely related 2.08 MHz resonance for the same sys-
tem. (c) Gray-scale plot of numerical simulation in the left-
right symmetric 2D chamber model of the corresponding two-
fold degenerate, un-split, acoustic pressure eigenmode. Nodal
lines are shown in black.
symmetry of the simple chamber model. Experimentally
this effect could be studied by measuring on a range of
devices, with strictly controlled geometries of both struc-
tures and substrates. We have only investigated two de-
vices, and special concern was not taken as to the unifor-
mity of the substrate. It is therefore not possible in the
present study to determine whether the observed sym-
metry breaking was due to geometric asymmetries in the
chip, in the chip-actuator coupling, or in other parts of
(c) (d)
(e) (f)
FIG. 6: (a) ad (b) Gray-scale plots of numerical simulations
in the 2D chip model of two closely spaced acoustic pressure
eigenmodes. The chamber is displaced 1 mm to the left of
the symmetry center of the chip thereby breaking the left-
right symmetry and splitting the two-fold eigenmode degen-
eracy. The difference in eigenfrequency is only 1 kHz. (c) and
(d) Closeups of the chamber region showing the asymmetric
eigenmodes similar to the experimentally observed resonances
seen in Fig. 5. (e) and (f) Gray-scale plots of numerically
simulated pressure eigenmodes in the asymmetric 2D cham-
ber model, where the left lead is 1 mm shorter than the right
lead. The difference in eigenfrequency is 28 kHz, which is close
to the observed difference of 20 kHz in Figs. 5(a) and (b).
the system (such as air-bubbles trapped at the fluidic
inlet and outlet).
D. Validation of method
Fig. 7 shows a micro-PIV vector plot of streaming mo-
tion in the center of the square chamber at 2.17 MHz,
recorded with a 20x microscope objective. With this kind
of recording, detailed information of a section of the de-
vice can be obtained, but it will not supply any informa-
tion about the amplitude fluctuations over the device, nor
does it reveal the 6x6 vortex pattern as seen in Fig. 4(b).
Clearly, more detailed measurements of specific features
are valuable, but for studies of resonances in low atten-
uation microfluidic devices, full-image recordings are of
100 µm
500 µm/s
FIG. 7: Micro-PIV velocity vector plot of streaming motion
in the center of the square chamber at 2.17 MHz. Images were
recorded with a 20x objective and a 0.63x Tv-adapter, and
milk was used as tracer particles.
most importance.
By regarding the suspended particles as springs gov-
erned by Hooke’s law, we can estimate the acoustic ra-
diation force Fac, from the potential elastic energy. We
find F = −τp
, where τ is a constant parameter for
each kind of particles, and p
is the time-averaged second-
order pressure field. As τ is an unknown positive constant
for blood-cell like particles, the amplitude becomes a fit-
ting parameter. Assuming the particles move in a quasi-
stationary steady state, we can directly compare calcu-
lated force patterns to measured velocity patterns. Such
a comparison is seen in Fig. 8, where the calculated force
pattern is compared with a scalar map of the velocity in
y-direction, extruded from the measurement presented in
Fig. 4(a). A comparison between the two is also seen in
Fig. 9, where two vertical cross-sectional views, each lo-
cated 330 µm away from the center of the chamber, are
compared with the theoretical estimate. Both micro-PIV
velocity plots show a good agreement with the calculated
forces, and the fluctuations in amplitude over the device
can be seen by comparing the two micro-PIV velocity
plots with each other.
V. CONCLUSION
Using full-image micro-PIV we have made direct obser-
vations of the acoustic resonances in piezo-actuated, flat
microfluidic chambers containing various tracer particles.
Depending on the size of the tracer particles either
the acoustic radiation force or acoustic streaming of the
solvent dominates their motion. Large particles are dom-
FIG. 8: (a) The force in y-direction calculated with COMSOL
finite element method software. (b) Scalar map of the velocity
in y-direction, measured with micro-PIV.
0 10 20 30 40 50
-0.00025
-0.00020
-0.00015
-0.00010
-0.00005
0.00000
0.00005
0.00010
0.00015
0.00020
0.00025
Point
theory
FIG. 9: Vertical cross-sectional plots of the velocity in the
y-direction (PIV1) 330 µm left and (PIV2) 330 µm right of
the center of the chamber. (theory) is the force in y-direction,
calculated in COMSOL with the amplitude as the only fitting
parameter.
inated by the acoustic radiation force that pushes them
to the static pressure nodal lines, while small particles
are dominated by acoustic streaming and end up forming
steady-state vortex patterns. However, for an arbitrary
frequency and geometry one of the forces can be strong
whereas the other is not, and it is therefore always nec-
essary to apply more than one tracer solution in order to
determine which forces are present.
The observed acoustic resonances correspond to the
pressure eigenmodes found by numerical simulation of
2D models of the system. The symmetric patterns can be
explained by using the simple 2D chamber model, while
asymmetric patterns can be explained by using the more
complete 2D chip model taking into account the geomet-
ric asymmetries of the surrounding chip, or in special
cases, by an asymmetric 2D chamber model.
We have demonstrated that full-image micro-PIV
is a useful tool for complete characterization of the
in-plane acoustically induced motion in piezo-actuated
microfluidic chambers.
Acknowledgement
SMS was supported through Copenhagen Graduate
School of Nanoscience and Nanotechnology, in a collab-
oration between Dantec Dynamics A/S, and MIC, Tech-
nical University of Denmark.
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