A method is presented for measurements of secondary acoustic radiation forces acting on solid particles in a plain ultrasonic standing wave. The method allows for measurements of acoustic interaction forces between particles located in arbitrary positions such as in between a pressure node and a pressure antinode. By utilizing a model that considers both density- and compressibility-dependent effects, the observed particle−particle interaction dynamics can be well understood. Two differently sized polystyrene micro-particles (4.8 and 25 μm, respectively) were used in order to achieve pronounced interaction effects. The particulate was subjected to a 2-MHz ultrasonic standing wave in a microfluidic channel, such as commonly used for acoustophoresis. Observation of deflections in the particle pathways shows that the particle interaction force is not negligible under this circumstance and has to be considered in accurate particle manipulation applications. The effect is primarily pronounced when the distance between two particles is small, the sizes of the particles are different, and the acoustic properties of the particles are different relative to the media. As predicted by theory, the authors also observe that the interaction forces are affected by the angle between the inter-particle centerline and the axis of the standing wave propagation direction.

1.
Antfolk
,
M.
, and
Laurell
,
T.
(
2017
). “
Continuous flow microfluidic separation and processing of rare cells and bioparticles found in blood—A review
,”
Anal. Chim. Acta
965
,
9
35
.
2.
Apfel
,
R. E.
(
1988
). “
Acoustically induced square law forces and some speculations about gravitation
,”
Am. J. Phys.
56
,
726
729
.
3.
Augustsson
,
P.
,
Barnkob
,
R.
,
Wereley
,
S. T.
,
Bruus
,
H.
, and
Laurell
,
T.
(
2011
). “
Automated and temperature-controlled micro-PIV measurements enabling long-term-stable microchannel acoustophoresis characterization
,”
Lab Chip
11
,
4152
4164
.
4.
Baasch
,
T.
,
Leibacher
,
I.
, and
Dual
,
J.
(
2017
). “
Multibody dynamics in acoustophoresis
,”
J. Acoust. Soc. Am.
141
,
1664
1674
.
5.
Barani
,
A.
,
Paktinat
,
H.
,
Janmaleki
,
M.
,
Mohammadi
,
A.
,
Mosaddegh
,
P.
,
Fadaei-Tehrani
,
A.
, and
Sanati-Nezhad
,
A.
(
2016
). “
Microfluidic integrated acoustic waving for manipulation of cells and molecules
,”
Biosens. Bioelectron.
85
,
714
725
.
6.
Barnkob
,
R.
,
Augustsson
,
P.
,
Laurell
,
T.
, and
Bruus
,
H.
(
2010
). “
Measuring the local pressure amplitude in microchannel acoustophoresis
,”
Lab Chip
10
,
563
570
.
7.
Barnocky
,
G.
, and
Davis
,
R. H.
(
1989
). “
The lubrication force between spherical drops, bubbles and rigid particles in a viscous fluid
,”
Int. J. Multiph. Flow.
15
,
627
638
.
8.
Bjerknes
,
V. F. K.
(
1906
).
Fields of Force
(
Columbia University Press
,
New York
).
9.
Brenner
,
H.
(
1961
). “
The slow motion of a sphere through a viscous a plane surface
,”
Chem. Eng. Sci.
16
,
242
251
.
10.
Brown
,
D.
(
2017
). “
Tracker 4.11.0: Free video analysis and modeling tool for physics education
,” https://physlets.org/tracker/index.html (Last viewed May 7, 2018).
11.
Crum
,
L. A.
(
1971
). “
Acoustic force on a liquid droplet in an acoustic stationary wave
,”
J. Acoust. Soc. Am.
50
,
157
163
.
12.
Crum
,
L. A.
(
1975
). “
Bjerknes forces on bubbles in a stationary sound field
,”
J. Acoust. Soc. Am.
57
,
1363
1370
.
13.
Davis
,
R. H.
,
Schonberg
,
J. A.
, and
Rallison
,
J. M.
(
1989
). “
The lubrication force between two viscous drops
,”
Phys. Fluids A
1
,
77
81
.
14.
Doinikov
,
A. A.
(
1999
). “
Bjerknes forces between two bubbles in a viscous fluid
,”
J. Acoust. Soc. Am.
106
,
3305
3312
.
15.
Doinikov
,
A. A.
(
2002
). “
Viscous effects on the interaction force between two small gas bubbles in a weak acoustic field
,”
J. Acoust. Soc. Am.
111
,
1602
1609
.
16.
Dual
,
J.
,
Möller
,
D.
,
Neild
,
A.
,
Oberti
,
S.
,
Schwarz
,
T.
, and
Wang
,
J.
(
2012
). “
Particle manipulation using acoustic radiation forces in micromachined devices
,”
AIP Conf. Proc.
1433
,
27
32
.
17.
Engebrecht
,
C. P.
(
2009
). “
Bubble dynamics in ultrasound
,” M.Sc. thesis,
University of Washington
.
18.
Garcia-Sabaté
,
A.
,
Castro
,
A.
,
Hoyos
,
M.
, and
González-Cinca
,
R.
(
2014
). “
Experimental study on inter-particle acoustic forces
,”
J. Acoust. Soc. Am.
135
,
1056
1063
.
19.
Gor'kov
,
L. P.
(
1962
). “
On the forces acting on a small particle in an acoustical field in an ideal fluid
,”
Sov. Phys. Dokl.
6
,
773
775
.
20.
Gröschl
,
M.
(
1998
). “
Ultrasonic separation of suspended particles—Part I: Fundamentals
,”
Acustica
84
,
432
447
.
21.
Habibi
,
R.
,
Devendran
,
C.
, and
Neild
,
A.
(
2017
). “
Trapping and patterning of large particles and cells in a 1D ultrasonic standing wave
,”
Lab Chip
17
,
3279
3290
.
22.
Hammarström
,
B.
,
Evander
,
M.
,
Wahlström
,
J.
, and
Nilsson
,
J.
(
2014b
). “
Frequency tracking in acoustic trapping and system surveillance
,”
Lab Chip
14
,
1005
1013
.
23.
Hammarström
,
B.
,
Laurell
,
T.
, and
Nilsson
,
J.
(
2012
). “
Seed particle-enabled acoustic trapping of bacteria and nanoparticles in continuous flow systems
,”
Lab Chip
12
,
4296
4304
.
24.
Hammarström
,
B.
,
Nilson
,
B.
,
Laurell
,
T.
,
Nilsson
,
J.
, and
Ekström
,
S.
(
2014a
). “
Acoustic trapping for bacteria identification in positive blood cultures with MALDI-TOF MS
,”
Anal. Chem.
86
,
10560
10567
.
25.
Happel
,
J.
, and
Brenner
,
H.
(
1983
).
Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media
(
Springer Netherlands
,
The Hague
).
26.
Huang
,
P.
,
Nama
,
N.
,
Mao
,
Z.
,
Li
,
P.
,
Rufo
,
J.
,
Chen
,
Y.
,
Xie
,
Y.
,
Wei
,
C. H.
,
Wang
,
L.
, and
Huang
,
T. J.
(
2014
). “
A reliable and programmable acoustofluidic pump powered by oscillating sharp-edge structures
,”
Lab Chip
14
,
4319
4323
.
27.
Israelachvili
,
J. N.
(
2011
).
Intermolecular and Surface Forces
(
Academic
,
New York
).
28.
Karlsen
,
J. T.
, and
Bruus
,
H.
(
2015
). “
Forces acting on a small particle in an acoustical field in a thermoviscous fluid
,”
Phys. Rev. E
92
,
043010
.
29.
King
,
L. V.
(
1934
). “
On the acoustic radiation pressure on spheres
,”
Proc. R. Soc. London Ser. A
147
,
212
240
.
30.
Lambert
,
B.
,
Weynans
,
L.
, and
Bergmann
,
M.
(
2018
). “
Local lubrication model for spherical particles within incompressible Navier-Stokes flows
,”
Phys Rev E
97
,
033313
.
31.
Leach
,
J.
,
Mushfique
,
H.
,
Keen
,
S.
,
Di Leonardo
,
R.
,
Ruocco
,
G.
,
Cooper
,
J. M.
, and
Padgett
,
M. J.
(
2009
). “
Comparison of Faxén's correction for a microsphere translating or rotating near a surface
,”
Phys. Rev. E
79
,
026301
.
32.
Lee
,
J.
,
Jeong
,
J. S.
, and
Shung
,
K. K.
(
2013
). “
Microfluidic acoustic trapping force and stiffness measurement using viscous drag effect
,”
Ultrasonics
53
,
249
254
.
33.
Li
,
P.
,
Mao
,
Z.
,
Peng
,
Z.
,
Zhou
,
L.
,
Chen
,
Y.
,
Huang
,
P. H.
,
Truica
,
C. I.
,
Drabick
,
J. J.
,
El-Deiry
,
W. S.
, and
Dao
,
M.
(
2015
). “
Acoustic separation of circulating tumor cells
,”
Proc. Natl. Acad. Sci.
112
,
4970
4975
.
34.
Li
,
S.
,
Glynne-Jones
,
P.
,
Andriotis
,
O. G.
,
Ching
,
K. Y.
,
Jonnalagadda
,
U. S.
,
Oreffo
,
R. O. C.
,
Hill
,
M.
, and
Tare
,
R. S.
(
2014
). “
Application of an acoustofluidic perfusion bioreactor for cartilage tissue engineering
,”
Lab Chip
14
,
4475
4485
.
35.
Lopes
,
J. H.
,
Azarpeyvand
,
M.
, and
Silva
,
G. T.
(
2016
). “
Acoustic interaction forces and torques acting on suspended spheres in an ideal fluid
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
63
,
186
197
.
36.
Manneberg
,
O.
,
Svennebring
,
J.
,
Hertz
,
H. M.
, and
Wiklund
,
M.
(
2008
). “
Wedge transducer design for two-dimensional ultrasonic manipulation in a microfluidic chip
,”
J. Micromech. Microeng.
18
,
095025
.
37.
Mohapatra
,
A. R.
,
Sepehrirahnama
,
S.
, and
Lim
,
K.
(
2018
). “
Experimental measurement of interparticle acoustic radiation force in the Rayleigh limit
,”
Phys. Rev. E
97
,
053105
.
38.
Nilsson
,
J.
,
Evander
,
M.
,
Hammarström
,
B.
, and
Laurell
,
T.
(
2009
). “
Review of cell and particle trapping in microfluidic systems
,”
Anal. Chim. Acta
649
,
141
157
.
39.
Pelekasis
,
N. A.
,
Gaki
,
A.
,
Doinikov
,
A.
, and
Tsamopoulos
,
J. A.
(
2004
). “
Secondary Bjerknes forces between two bubbles and the phenomenon of acoustic streamers
,”
J. Fluid. Mech.
500
,
313
347
.
40.
Sepehrirahnama
,
S.
,
Lim
,
K. M.
, and
Chau
,
F. S.
(
2015
). “
Numerical study of interparticle radiation force acting on rigid spheres in a standing wave
,”
J. Acoust. Soc. Am.
137
,
2614
2622
.
41.
Silva
,
G. T.
, and
Bruus
,
H.
(
2014
). “
Acoustic interaction forces between small particles in an ideal fluid
,”
Phys. Rev. E.
90
,
063007
.
42.
Svennebring
,
J.
,
Manneberg
,
O.
, and
Wiklund
,
M.
(
2007
).“
Temperature regulation during ultrasonic manipulation for long-term cell handling in a microfluidic chip
,”
J. Micromech. Microeng.
17
,
2469
2474
.
43.
Tenje
,
M.
,
Xia
,
H.
,
Evander
,
M.
,
Hammarström
,
B.
,
Tojo
,
A.
,
Belák
,
S.
,
Laurell
,
T.
, and
LeBlanc
,
N.
(
2015
). “
Acoustic trapping as a generic non-contact incubation site for multiplex bead-based assays
,”
Anal. Chim. Acta
853
,
682
688
.
44.
Vázquez-Quesada
,
A.
, and
Ellero
,
M.
(
2016
). “
Analytical solution for the lubrication force between two spheres in a bi-viscous fluid
,”
Phys. Fluids
28
,
073101
.
45.
Weiser
,
M. A. H.
,
Apfel
,
R. E.
, and
Neppiras
,
E. A.
(
1984
). “
Interparticle forces on red cells in a standing wave field
,”
Acta Acust. united Acust.
56
,
114
119
.
46.
Wiklund
,
M.
,
Green
,
R.
, and
Ohlin
,
M.
(
2012
). “
Acoustofluidics 14: Applications of acoustic streaming in microfluidic devices
,”
Lab Chip
12
,
2438
2451
.
47.
Yamakoshi
,
Y.
, and
Koganezawa
,
M.
(
2005
). “
Bubble manipulation by self organization of bubbles inside ultrasonic wave
,”
Jpn. J. Appl. Phys.
44
,
4583
4587
.
48.
Yasui
,
K.
,
Iida
,
Y.
,
Tuziuti
,
T.
,
Kozuka
,
T.
, and
Towata
,
A.
(
2008
). “
Strongly interacting bubbles under an ultrasonic horn
,”
Phys. Rev. E
77
,
016609
.
49.
Yosioka
,
K.
, and
Kawasima
,
Y.
(
1955
). “
Acoustic radiation pressure on a compressible sphere
,”
Acustica
5
,
167
173
.
50.
Zheng
,
X.
, and
Apfel
,
R. E.
(
1995
). “
Acoustic interaction forces between two fluid spheres in an acoustic field
,”
J. Acoust. Soc. Am.
97
,
2218
2226
.
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