We present a variant of the immersed boundary (IB) method that implements acoustic perturbation theory to model acoustically levitated fluid droplets. Instead of resolving sound waves numerically, our hybrid method solves acoustic scattering semi-analytically to obtain the corresponding time-averaged acoustic forces on the droplet. This framework allows the droplet to be simulated on inertial timescales of interest, and therefore works with much larger time steps than traditional compressible flow solvers. To benchmark this technique and demonstrate its utility, we implement the hybrid IB method for a single droplet in a standing wave. Simulated droplet shape deformations and streaming profiles agree with available theoretical predictions. Our simulations also yield insights into the streaming profiles for elliptical droplets, for which a comprehensive analytic solution does not yet exist.
REFERENCES
1.
S.
Santesson
and
S.
Nilsson
, “
Airborne chemistry: Acoustic levitation in chemical analysis
,” Anal. Bioanal. Chem.
378
, 1704
–1709
(2004
).2.
M. A.
Andrade
,
N.
Pérez
, and
J. C.
Adamowski
, “
Review of progress in acoustic levitation
,” Braz. J. Phys.
48
, 190
–213
(2018
).3.
C.
Mu
,
J.
Wang
,
K. M.
Barraza
,
X.
Zhang
, and
J. L.
Beauchamp
, “
Mass spectrometric study of acoustically levitated droplets illuminates molecular-level mechanism of photodynamic therapy for cancer involving lipid oxidation
,” Angew. Chem. Int. Ed.
58
, 8082
–8086
(2019
).4.
A.
Marzo
and
B. W.
Drinkwater
, “
Holographic acoustic tweezers
,” Proc. Natl. Acad. Sci. U. S. A.
116
, 84
–89
(2019
).5.
M. A.
Abdelaziz
,
J.-L.
Aider
,
D. J.
Pine
,
D. G.
Grier
,
M.
Hoyos
et al, “
Ultrasonic chaining of emulsion droplets
,” Phys. Rev. Res.
3
, 043157
(2021
).6.
G. T.
Silva
and
B. W.
Drinkwater
, “
Acoustic radiation force exerted on a small spheroidal rigid particle by a beam of arbitrary wavefront: Examples of traveling and standing plane waves
,” J. Acoust. Soc. Am.
144
, EL453
–EL459
(2018
).7.
J. T.
Karlsen
and
H.
Bruus
, “
Forces acting on a small particle in an acoustical field in a thermoviscous fluid
,” Phys. Rev. E
92
, 043010
(2015
).8.
L.
Wang
,
F.-B.
Tian
, and
J. C.
Lai
, “
An immersed boundary method for fluid–structure–acoustics interactions involving large deformations and complex geometries
,” J. Fluids Struct.
95
, 102993
(2020
).9.
H.
Bruus
, “
Acoustofluidics 7: The acoustic radiation force on small particles
,” Lab Chip
12
, 1014
–1021
(2012a
).10.
W. L.
Nyborg
, “
Acoustic streaming near a boundary
,” J. Acoust. Soc. Am.
30
, 329
–339
(1958
).11.
Q.
Qi
, “
The effect of compressibility on acoustic streaming near a rigid boundary for a plane traveling wave
,” J. Acoust. Soc. Am.
94
, 1090
–1098
(1993
).12.
C. P.
Lee
and
T. G.
Wang
, “
Outer acoustic streaming
,” J. Acoust. Soc. Am.
88
, 2367
–2375
(1990
).13.
P. J.
Westervelt
, “
The theory of steady rotational flow generated by a sound field
,” J. Acoust. Soc. Am.
25
, 60
–67
(1953
).14.
T.
Baasch
,
A. A.
Doinikov
, and
J.
Dual
, “
Acoustic streaming outside and inside a fluid particle undergoing monopole and dipole oscillations
,” Phys. Rev. E
101
, 013108
(2020
).15.
P. L.
Marston
, “
Shape oscillation and static deformation of drops and bubbles driven by modulated radiation stresses—theory
,” J. Acoust. Soc. Am.
67
, 15
–26
(1980
).16.
H.
Bruus
, “
Acoustofluidics 2: Perturbation theory and ultrasound resonance modes
,” Lab Chip
12
, 20
–28
(2012b
).17.
F.
Mitri
, “
Axial acoustic radiation force on rigid oblate and prolate spheroids in bessel vortex beams of progressive, standing and quasi-standing waves
,” Ultrasonics
74
, 62
–71
(2017
).18.
P.
Waterman
, “
T-matrix methods in acoustic scattering
,” J. Acoust. Soc. Am.
125
, 42
–51
(2009
).19.
C. S.
Peskin
, “
Flow patterns around heart valves: A numerical method
,” J. Comput. Phys.
10
, 252
–271
(1972
).20.
C. S.
Peskin
, “
The immersed boundary method
,” Acta Numer.
11
, 479
–517
(2002
).21.
S.
Maramizonouz
,
M.
Rahmati
,
A.
Link
,
T.
Franke
, and
Y.
Fu
, “
Numerical and experimental studies of acoustic streaming effects on microparticles/droplets in microchannel flow
,” Int. J. Eng. Sci.
169
, 103563
(2021
).22.
Y.
Kim
and
C. S.
Peskin
, “
Penalty immersed boundary method for an elastic boundary with mass
,” Phys. Fluids
19
, 053103
(2007
).23.
Y.
Kim
and
C. S.
Peskin
, “
A penalty immersed boundary method for a rigid body in fluid
,” Phys. Fluids
28
, 033603
(2016
).24.
T. G.
Fai
,
B. E.
Griffith
,
Y.
Mori
, and
C. S.
Peskin
, “
Immersed boundary method for variable viscosity and variable density problems using fast constant-coefficient linear solvers I: Numerical method and results
,” SIAM J. Sci. Comput.
35
, B1132
–B1161
(2013
).25.
Y.
Kim
and
C. S.
Peskin
, “
Numerical study of incompressible fluid dynamics with nonuniform density by the immersed boundary method
,” Phys. Fluids
20
, 062101
(2008
).26.
J.
Happel
and
H.
Brenner
, Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media
, Vol.
1
(
Springer Science & Business Media
, 1983
).27.
M.
Settnes
and
H.
Bruus
, “
Forces acting on a small particle in an acoustical field in a viscous fluid
,” Phys. Rev. E
85
, 016327
(2012
).28.
S.
Danilov
and
M.
Mironov
, “
Mean force on a small sphere in a sound field in a viscous fluid
,” J. Acoust. Soc. Am.
107
, 143
–153
(2000
).29.
P. J.
Westervelt
, “
Acoustic radiation pressure
,” J. Acoust. Soc. Am.
29
, 26
–29
(1957
).30.
G. T.
Silva
, “
An expression for the radiation force exerted by an acoustic beam with arbitrary wavefront (l)
,” J. Acoust. Soc. Am.
130
, 3541
–3544
(2011
).31.
W. L. M.
Nyborg
, “
Acoustic streaming
,” in Physical Acoustics
(
Elsevier
, 1965
), Vol.
2
, pp. 265
–331
.32.
M. A.
Yurkin
and
A. G.
Hoekstra
, “
The discrete dipole approximation: An overview and recent developments
,” J. Quant. Spectrosc. Radiat. Transfer
106
, 558
–589
(2007
).33.
F. G.
Mitri
, “
Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid
,” IEEE Trans. Ultrason, Ferroelect, Freq. Control
62
, 1809
–1818
(2015
).34.
L.
Wang
and
F.-B.
Tian
, “
Numerical study of sound generation by three-dimensional flexible flapping wings during hovering flight
,” J. Fluids Struct.
99
, 103165
(2020
).35.
J. H.
Seo
and
R.
Mittal
, “
A high-order immersed boundary method for acoustic wave scattering and low-Mach number flow-induced sound in complex geometries
,” J. Comput. Phys.
230
, 1000
–1019
(2011
).36.
E. H.
Trinh
and
C.-J.
Hsu
, “
Equilibrium shapes of acoustically levitated drops
,” J. Acoust. Soc. Am.
79
, 1335
–1338
(1986
).37.
H.
Jackson
,
M.
Barmatz
, and
C.
Shipley
, “
Equilibrium shape and location of a liquid drop acoustically positioned in a resonant rectangular chamber
,” J. Acoust. Soc. Am.
84
, 1845
–1862
(1988
).38.
P. L.
Marston
,
S. E.
LoPorto-Arione
, and
G. L.
Pullen
, “
Quadrupole projection of the radiation pressure on a compressible sphere
,” J. Acoust. Soc. Am.
69
, 1499
–1501
(1981
).39.
J. P.
Leão-Neto
,
J. H.
Lopes
, and
G. T.
Silva
, “
Acoustic radiation torque exerted on a subwavelength spheroidal particle by a traveling and standing plane wave
,” J. Acoust. Soc. Am.
147
, 2177
–2183
(2020
).40.
J.
Kim
,
D.
Kim
, and
H.
Choi
, “
An immersed-boundary finite-volume method for simulations of flow in complex geometries
,” J. Comput. Phys.
171
, 132
–150
(2001
).41.
R.
Mittal
and
G.
Iaccarino
, “
Immersed boundary methods
,” Annu. Rev. Fluid Mech.
37
, 239
–261
(2005
).42.
Y.
Bao
,
A.
Donev
,
B. E.
Griffith
,
D. M.
McQueen
, and
C. S.
Peskin
, “
An immersed boundary method with divergence-free velocity interpolation and force spreading
,” J. Comput. Phys.
347
, 183
–206
(2017
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
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