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Title
Direct visualization of surface acoustic waves along substrates using smoke particles
Permalink
https://escholarship.org/uc/item/6hp6398z
Journal
Applied Physics Letters, 91(22)
ISSN
0003-6951
Authors
Tan, MK
Friend, JR
Yeo, LY
Publication Date
2007-12-06
DOI
10.1063/1.2814054
Peer reviewed
eScholarship.org Powered by the California Digital Library
University of California
Direct visualization of surface acoustic waves along substrates
using smoke particles
Ming K. Tan, James R. Friend,
a!
and Leslie Y. Yeo
Micro/Nanophysics Research Laboratory, Monash University, Clayton, Victoria 3800, Australia
!Received 30 August 2007; accepted 29 October 2007; published online 26 November 2007"
Smoke particles !SPs" are used to directly visualize surface acoustic waves !SAWs" propagating on
a 128°-rotated Y-cut X-propagating lithium niobate !LiNbO
3
" substrate. By electrically exciting a
SAW device in a compartment filled with SP, the SP were found to collect along the regions where
the SAW propagates on the substrate. The results of the experiments show that SPs are deposited
adjacent to regions of large vibration amplitude and form a clear pattern corresponding to the
surface wave profile on the substrate. Through an analysis of the SAW-induced acoustic streaming
in the air adjacent to the substrate and the surface acceleration measured with a laser Doppler
vibrometer, we postulate that the large transverse surface accelerations due to the SAW ejects SP
from the surface and carries them aloft to relatively quiescent regions nearby via acoustic streaming.
Offering finer detail than fine powders common in Chladni figures #E. Chladni, Entdeckungen über
die Theorie des Klanges !Weidmanns, Erben und Reich, Leipzig, Germany, 1787"$ the approach is
an inexpensive and a quick counterpart to laser interferometric techniques, presenting a means to
explore the controversial phenomena of particle agglomeration on surfaces. © 2007 American
Institute of Physics. #DOI: 10.1063/1.2814054$
Visualization of vibration in structures using the agglom-
eration of loose particles was first reported by Chladni in
1787.
1
This technique has been used over the years in some-
times surprising circumstances,
2
yet it has direct application
to micro- and nanotechnology
3
and, in particular, surface
acoustic wave !SAW" propagation.
4,5
The particle collection
controversially relies on two phenomena
6
depending on the
particle size and density relative to the ambient fluid.
Faraday
7
found large particles collected along the nodal re-
gions, as described by Chladni; he also found smaller par-
ticles collected at antinodal regions due to acoustic stream-
ing. Here, we demonstrate a new technique using adherent
nanoscale smoke particles !SPs" to overcome problems
5
with
Chladni patterns specifically in visualization of SAW on a
128°-rotated Y-cut X-propagating LiNbO
3
. Cigarette SP is
reported to have particle sizes of 40–500 nm with a mean
diameter of 170 nm;
8
however, the cigarette SP used in this
work was measured using a surface mobility particle spec-
trometer !3936 SMPS, TSI, Shoreview, MN, USA" and was
found to have a nearly monodisperse distribution in size of
around 250 nm in diameter. Though this method lacks the
precision of noncontact interferometry and stroboscopic
techniques,
9,10
it is simpler and inexpensive.
SAW propagating along lithium niobate !LiNbO
3
, LN"
generates extremely large accelerations !10
6
–10
8
m/ s
2
" per-
pendicular to the surface, resulting in a high impact force
onto particles coming into contact with the surface. This
force can be estimated from F
I
%m
p
a
s
, where m
p
is the mass
of the particle and a
s
is the acceleration of the piezoelectric
substrate. Once airborne, the acoustic radiation
11
and viscous
drag forces act to transport individual SP. Using King’s
expression
12
to estimate the acoustic radiation force on the
particle,
F
R
% 2
!"
0
&A&
2
'
#
c
R
!
(
6
1+
2
9
#1− !
"
0
/
"
p
"
2
$
!2+
"
0
/
"
p
"
2
, !1"
where
"
0
is the density of air, A is the complex amplitude of
the velocity potential of the incident wave,
#
is the angular
frequency of the incident wave, c is the speed of sound in air,
and R
!
and
"
p
are the radius and density of the particle,
respectively. The acoustic streaming drag is approximately
F
D
%
!
$
UR
!
, where
$
is the fluid viscosity and U is the
velocity of the surrounding fluid.
Figure 1 illustrates the fluid-solid half-space model of
the first-order acoustic field.
13
When coupled with air, the
elastic solid-medium moves along an elliptical locus in the
counterclockwise direction due to the SAW. The acoustic
a"
Electronic mail: james.friend@eng.monash.edu.au
FIG. 1. !Color online" SAW on the semi-infinite LN substrate coupled with
the half-space air. The x
1
and x
3
components of streaming body force density
are plotted along the direction of the waves propagation in the fluid and at
x
1
=0. The inset shows the motion of the solid particle elements of the LN
substrate.
APPLIED PHYSICS LETTERS 91, 224101 !2007"
0003-6951/2007/91"22!/224101/3/$23.00 © 2007 American Institute of Physics91, 224101-1
Downloaded 27 Nov 2007 to 130.194.13.104. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
streaming body force density is given by solving
14,15
− F
dc
=
1
c
2
)
P
1
#
u
1
#
t
*
+
"
0
+!u
1
· $"u
1
,, !2"
obtained numerically for 30 MHz SAW propagating on a
128°-rotated Y-cut X-propagating LN coupled with air in
Fig. 1. The symbol +,in Eq. !2" refers to time averaging, the
subscript “dc” refers to second-order steady-state terms, P
1
is
the first-order fluid pressure, and u
1
is the first-order fluid
velocity. The numerical results are plotted in Fig. 1!b" for the
x
1
and x
3
components of the body force density at the solid-
liquid interface; the body force density tangent to the sub-
strate surface !F
x1
" is 100 times higher in the viscous bound-
ary layer than in the bulk fluid region, and is in the positive
x
1
direction at the solid-fluid interface because of the coun-
terclockwise surface motion that gives rise to a large inertia
force in the fluid at the interface. Due to the low viscosity of
air, the weak attenuation of this longitudinal surface accel-
eration suggests that only the fluid adjacent to the surface is
accelerated in the same direction as that of the propagating
SAW. The inertial effects quickly die out and hence a rever-
sal in the direction of F
x1
is observed; the maximum ampli-
tude of F
x1
is at the edge of the viscous boundary layer,
given by
16
d
v
=
-
!2
$
"/ !
"
0
#
", away from the surface, about
0.4
$
m for 30 MHz.
Conversely, the viscous boundary layer does not affect
the body force density perpendicular to the substrate surface
F
x3
. This body force density F
x3
is caused by the normal
displacement of the solid, and is associated with the first
term on the right-hand side of Eq. !2", the local acceleration.
The F
x1
and F
x3
components of the body force density are
then substituted into F
dc
=$p
dc
−
$
$
2
u
dc
,
14,15
and solved nu-
merically using the Gauss-Seidel method with the
SIMPLER
algorithm
17
for a staggered mesh to correct for the pressure
term. Within the viscous boundary layer, the streaming ve-
locities parallel and normal to the surface !x
1
and x
3
direc-
tions in Fig. 3" are on the order of 10
−6
and 10
−5
m/ s, re-
spectively, for a particle displacement of the surface of the
solid on the order of 10
−10
m. A traveling-wave 30 MHz
focusing—elliptical single—phase—unidirectional—
transducer
18
!SPUDT" device is shown here as an example.
Figure 2 shows the formation of the SP pattern along with
the measured acceleration and displacement amplitudes per-
pendicular to the substrate surface using a scanning laser
Doppler vibrometer !MSA-400, Polytec PI, Waldbrunn, Ger-
many". The distinct nodal and antinodal lines on the substrate
due to the standing surface wave are clearly associated with
the location of the deposited SP. At an acceleration of
10
8
m/ s
2
, the surface displacement is on the order of 10 nm.
The SP and acceleration distributions are well correlated,
with SP particles located predominantly at low-acceleration
regions #see Figs. 2!b" and 2!c"$. Figure 3!a" summarizes the
mechanism. Once an electrical signal is applied to the
SPUDT, a SAW propagates across the substrate surface and,
within seconds, the randomly deposited SPs are ejected from
regions of large transverse acceleration. Three mechanisms
are possible for the lifting of the particles off the surface: the
acoustic radiation pressure on the particles, the ejection of
the particles due to a large impact force when a particle
comes into contact with the accelerating substrate surface,
and the drag force due to the acoustic streaming, as illus-
trated in Fig. 3!b". At equilibrium, the particle weight m
p
g
%R
!
3
must balance the acoustic radiation force F
R
%R
!
6
, the
impact force F
I
%R
!
3
, and the streaming drag force F
D
%R
!
1
.
The surface acceleration is the dominant factor in sus-
pension of SP. Assuming that it has a mean mass of 10 ng
!Ref. 19" and a mean diameter of 250 nm, the particle expe-
riences a force F
I
due to impact acceleration on the order of
FIG. 2. !Color online"!a" SP deposited on the substrate after 15 s exposure,
and !b" after 30 s exposure. !c" The magnitude of surface acceleration in
millions of m/ s
2
and !d" the instantaneous surface displacement amplitude
in nanometer, across the surface of the 30 MHz FE-SPUDT SAW device
while the drive signal is being applied to the IDT.
FIG. 3. !a" Schematic illustrating the mechanism of SP aggregation along
the x
1
and x
3
directions and !b" the forces responsible for the suspension and
transport of a particular particle in the agglomeration process.
224101-2 Tan, Friend, and Yeo Appl. Phys. Lett. 91, 224101 "2007!
Downloaded 27 Nov 2007 to 130.194.13.104. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
10
−4
N for a surface displacement amplitude of 10
−10
m and
excitation frequency of 30 MHz. From Eq. !1", the acoustic
radiation force F
R
is on the order of 10
−24
N, while the drag
force F
D
is on the order of 10
−16
N from the streaming cal-
culation. Further, the adhesion characteristics of SP reduce
the ability of the particles to roll or slide to a new location
without the ejection caused by the SAW. This has been con-
firmed by depositing SP onto a substrate, irradiating the sur-
face with a 30 MHz SAW to redistribute the SP into a pat-
tern, and then leaving it aside in a clean room for 20 min
while exposed to strong air currents. No changes in the SP
profiles were observed after 20 min. yet, if the SP were able
to roll or slide along the surface, one would expect at least
some changes in the SP distribution in this time.
Acoustic streaming then transports the suspended par-
ticles from high to low vibration amplitude regions. The air-
flow is due to the boundary layer streaming force, resulting
in higher air velocities in the direction transverse to the sub-
strate in the air layer adjacent to it #Fig. 3!c"$. This high air
velocity region exerts a drag on the lifted particle and trans-
ports it to regions where the acceleration is small enough to
permit redeposition of the SP. The drag force exerted on a
particle therefore increases proportionally with increasing
particle size and air velocity; larger particles !2R
!
%d
v
" thus
experience higher drag. Small particles !2 R
!
% d
v
", on the
other hand, tend to stay in their original locations. For a
30 MHz SAW at standard room temperature and humidity,
the viscous boundary layer thickness is approximately
0.4
$
m and, thus, most of the cigarette SPs !%0.25
$
m" are
transported to regions experiencing low surface acceleration.
Adopting the same assumptions above and together with the
calculated flow velocity along the x
1
direction, the streaming
drag force and acoustic radiation force are on the order of
10
−17
and 10
−26
N, respectively, suggesting that the acoustic
streaming is predominantly responsible for transport of the
suspended particles. As these particles accumulate in the re-
gions adjacent to the high surface vibration regions, they
begin to aggregate into large particle clumps, forming dark
regions on the substrate, as shown in Fig. 2. If the power is
turned off, the distribution of particles remains in place, pro-
viding a “fingerprint” of the SAW propagation.
In conclusion, this new technique offers a simple and
economical method to visualize and analyze SAW propaga-
tion patterns. This technique offers much finer detail than
SAW visualization with fine powders akin to Chladni figures,
is far less expensive than noncontact laser interferometric
techniques, and presents a new method to explore the con-
troversial phenomena of particle agglomeration on surfaces.
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224101-3 Tan, Friend, and Yeo Appl. Phys. Lett. 91, 224101 "2007!
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