We investigate the dynamics of two identical artificial active particles suspended in a free-standing fluid film with a trap of finite radius in an acoustic tweezer. In the two dimensional Oseen approximation, their hydrodynamic coupling is long ranged, which naturally raises the question as under what conditions they can simultaneously reside in the trap. We determine a critical value of the hydrodynamic coupling below which that happens and study the ensuing active pair dynamics inside the trap. For larger couplings, only one particle sits in the trap, while the other diffuses freely until it eventually replaces the particle in the trap. Such a mechanism repeats itself with a characteristic noise-dependent mean residence-retrapping time.
REFERENCES
1.
Janus Particle Synthesis, Self-Assembly and Applications
, edited by S.
Jiang
and S.
Granick
(RSC Publishing
, Cambridge
, 2012
).2.
A.
Walther
and A. H. E.
Müller
, “Janus particles: Synthesis, self-assembly, physical properties, and applications
,” Chem. Rev.
113
, 5194
(2013
).3.
J.
Elgeti
, R. G.
Winkler
, and G.
Gompper
, “Physics of microswimmers, single particle motion and collective behavior: A review
,” Rep. Prog. Phys.
78
, 056601
(2015
).4.
R.
Golestanian
, T. B.
Liverpool
, and A.
Adjari
, “Designing phoretic micro- and nano-swimmers
,” New J. Phys.
9
, 126
(2007
).5.
W. E.
Uspal
, H.
Burak Eral
, and P. S.
Doyle
, “Engineering particle trajectories in microfluidic flows using particle shape
,” Nat. Commun.
4
, 2666
(2015
).6.
S.
Das
, A.
Garg
, A. I.
Campbell
, J.
Howse
, A.
Sen
, D.
Valegol
, R.
Golestanian
, and S. J.
Ebbens
, “Boundaries can steer active Janus spheres
,” Nat. Commun.
6
, 8999
(2015
).7.
A.
Zöttl
and H.
Stark
, “Emergent behavior in active colloids
,” J. Phys.: Condens. Matter
28
, 253001
(2016
).8.
J.
Palacci
, S.
Sacanna
, A.
Abramian
, J.
Barral
, K.
Hanson
, A. Y.
Grosberg
, D. J.
Pine
, and P. M.
Chaikin
, “Artificial rheotaxis
,” Sci. Adv.
1
, e1400214
(2015
).9.
E.
Lauga
and T. R.
Powers
, “The hydrodynamics of swimming microorganisms
,” Rep. Prog. Phys.
72
, 096601
(2009
).10.
M. C.
Marchetti
, J. F.
Joanny
, S.
Ramaswamy
, T. B.
Liverpool
, J.
Prost
, and M.
Rao
, “Hydrodynamics of soft active matter
,” Rev. Mod. Phys.
85
, 1143
(2013
).11.
T.
Debnath
, Y.
Li
, P. K.
Ghosh
, and F.
Marchesoni
, “Hydrodynamic interaction of trapped active Janus particles in two dimensions
,” Phys. Rev. E
97
, 042602
(2018
).12.
C.
Cheung
, Y. H.
Hwang
, X.-I.
Wu
, and H. J.
Choi
, “Diffusion of particles in free standing liquid films
,” Phys. Rev. Lett.
76
, 2531
(1996
).13.
B.
Cui
, H.
Diamant
, B.
Lin
, and S. A.
Rice
, “Anomalous hydrodynamic interaction in a quasi-two-dimensional suspension
,” Phys. Rev. Lett.
92
, 258301
(2004
).14.
R.
Di Leonardo
, S.
Keen
, F.
Ianni
, J.
Leach
, M. J.
Padgett
, and G.
Ruocco
, “Hydrodynamic interactions in two dimensions
,” Phys. Rev. E
78
, 031406
(2008
).15.
S.
Sengupta
, M. E.
Ibele
, and A.
Sen
, “Fantastic voyage: Designing self-powered nanorobots
,” Angew. Chem., Int. Ed.
51
, 8434
(2012
).16.
D.
Takagi
, A. B.
Braunschweig
, J.
Zhang
, and M. J.
Shelley
, “Dispersion of self-propelled rods undergoing fluctuation-driven flips
,” Phys. Rev. Lett.
110
, 038301
(2013
).17.
R. T.
Foister
and T. G. M.
van de Ven
, “Diffusion of Brownian particles in shear flows
,” J. Fluid Mech.
96
, 105
(1980
).18.
A.
Ziehl
, J.
Bammert
, L.
Holzer
, C.
Wagner
, and W.
Zimmermann
, “Direct measurements of shear-induced cross-correlations of Brownian motion
,” Phys. Rev. Lett.
103
, 230602
(2009
).19.
J.
Bammert
, L.
Holzer
, and W.
Zimmermann
, “Dynamics of two trapped Brownian particles: Shear-induced cross-correlations
,” Eur. Phys. J. E
33
, 313
(2010
).20.
B.
ten Hagen
, R.
Wittkowski
, and H.
Löwen
, “Brownian dynamics of a self-propelled particle in shear flow
,” Phys. Rev. E
84
, 031105
(2011
).21.
Y.
Li
, F.
Marchesoni
, T.
Debnath
, and P. K.
Ghosh
, “Dynamics of a trapped active swimmer in a shear flow
,” Phys. Rev. E
96
, 062138
(2017
).22.
J.-C.
Meiners
and S. R.
Quake
, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential
,” Phys. Rev. Lett.
82
, 2211
(1999
).23.
X.
Yang
, C.
Liu
, Y.
Li
, F.
Marchesoni
, P.
Hänggi
, and H. P.
Zhang
, “Colloidal diffusion in corrugated channels: Entropic versus hydrodynamic interactions
,” Proc. Natl. Acad. Sci. U. S. A.
114
, 9565
(2017
).24.
S. C.
Takatori
, R. D.
Dier
, J.
Vermant
, and J. F.
Brady
, “Acoustic trapping of active matter
,” Nat. Commun.
7
, 10694
(2016
).25.
R.
Golestanian
, T. B.
Liverpool
, and A.
Adjari
, “Self-Motile colloidal particles: From directed propulsion to random walk
,” Phys. Rev. Lett.
99
, 048102
(2007
).26.
D.
Debnath
, P. K.
Ghosh
, Y.
Li
, F.
Marchesoni
, and B.
Li
, “Diffusion of eccentric microswimmers
,” Soft Matter
12
, 2017
(2016
).27.
Y.
Zhong
, J.
Liu
, R.
Liu
, H.
Guo
, M.
Yang
, Z.
Li
, and K.
Chen
, “An optically driven bistable Janus rotor with patterned metal coatings
,” ACS Nano
9
, 10844
(2015
).28.
D. L.
Ermak
and J. A.
McCammon
, “Brownian dynamics with hydrodynamic interactions
,” J. Chem. Phys.
69
, 1352
(1978
).29.
B.
ten Hagen
, R.
Wittkowski
, D.
Takagi
, F.
Kümmel
, C.
Bechinger
, and H.
Löwen
, “Can the self-propulsion of anisotropic microswimmers be described by using forces and torques?
,” J. Phys.: Condens. Matter
27
, 194110
(2015
).30.
P.
Bayati
and A.
Najafi
, “Dynamics of two interacting active Janus particles
,” J. Chem. Phys.
144
, 134901
(2016
).31.
By means of a standard Mil’shtein algorithm, see
P. E.
Kloeden
and E.
Platen
, Numerical Solution of Stochastic Differential Equations
(Springer
, Berlin
, 1992
).32.
T.
Goldfriend
, H.
Diamant
, and T. A.
Witten
, “Hydrodynamic interactions between two forced objects of arbitrary shape. I. Effect on alignment
,” Phys. Fluids
27
, 123303
(2015
).33.
T.
Goldfriend
, H.
Diamant
, and T. A.
Witten
, “Hydrodynamic interactions between two forced objects of arbitrary shape. II. Relative translation
,” Phys. Rev. E
93
, 042609
(2016
).34.
W.
Feller
, An Introduction to Probability Theory and its Applications
, 3rd ed. (Wiley
, New York
, 1968
), Vol. 1.© 2019 Author(s).
2019
Author(s)
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