How motile microorganisms or self-propelled synthetic swimmers interact with a curved surface is crucial in determining their locomotion patterns in complex geometry. We used a self-propelled micrsoswimmer model (i.e., the squirmer) and performed two-dimensional study on the hydrodynamic interaction between the microswimmers and a circular obstacle. We revealed that both pullers and pushers, i.e., the two types of squirmers, may exhibit flower-like paths as they are circling around the obstacle at nonzero Reynolds numbers. Flowers with various shapes and numbers of petals were created by a microswimmer by varying the Reynolds number, squirmer-type parameter, or relative curvature of the obstacle. Moreover, pullers showed quite different dynamical features from their counterparts in terms of their motion direction, swimming speed, and shape of flower-like paths. The possible mechanisms were revealed in detail. In particular, pullers interacting with a large obstacle may attain an enhanced speed. The findings of this study display potential usefulness in micro/nanofluidic applications associated with a collection or separation of microorganisms and artificial mircroswimmer navigation.
REFERENCES
1.
T.
Pedley
and
J. O.
Kessler
, “Hydrodynamic phenomena in suspensions of swimming microorganisms
,” Annu. Rev. Fluid Mech.
24
, 313
–358
(1992
).2.
D.
Koch
and
G.
Subramanian
, “Collective hydrodynamics of swimming microorganisms: Living fluids
,” Annu. Rev. Fluid Mech.
43
, 637
–659
(2011
).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.
S.
Ramaswamy
, “Active fluids
,” Nat. Rev. Phys.
1
, 640
–642
(2019
).5.
A. C. H.
Tsang
,
E.
Demir
,
Y.
Ding
, and
O. S.
Pak
, “Roads to smart artificial microswimmers
,” Adv. Intell. Syst.
2
, 1900137
(2020
).6.
P.
Sharan
,
A.
Nsamela
,
S. C.
Lesher-Pérez
, and
J.
Simmchen
, “Microfluidics for microswimmers: Engineering novel swimmers and constructing swimming lanes on the microscale—A tutorial review
,” Small
17
, 2007403
(2021
).7.
Z.
Zou
,
Y.
Liu
,
Y.-N.
Young
,
O. S.
Pak
, and
A. C. H.
Tsang
, “Gait switching and targeted navigation of microswimmers via deep reinforcement learning
,” Commun. Phys.
5
, 158
(2022
).8.
A. J. T. M.
Mathijssen
,
N.
Figueroa-Morales
,
G.
Junot
,
É.
Clément
,
A.
Lindner
, and
A.
Zöttl
, “Oscillatory surface rheotaxis of swimming E. coli bacteria
,” Nat. Commun.
10
, 3434
(2019
).9.
R.
Dey
,
C. M.
Buness
,
B. V.
Hokmabad
,
C.
Jin
, and
C. C.
Maass
, “Oscillatory rheotaxis of artificial swimmers in microchannels
,” Nat. Commun.
13
, 2952
(2022
).10.
E.
Lushi
,
H.
Wioland
, and
R.
Goldstein
, “Fluid flows generated by swimming bacteria drive self-organization in confined fluid suspensions
,” Proc. Natl. Acad. Sci. U. S. A.
111
, 9733
–9738
(2014
).11.
C.
Scholz
,
M.
Engel
, and
T.
Pöschel
, “Rotating robots move collectively and self-organize
,” Nat. Commun.
9
, 931
(2018
).12.
E.
Lauga
,
W. R.
DiLuzio
,
G. M.
Whitesides
, and
H. A.
Stone
, “Swimming in circles: Motion of bacteria near solid boundaries
,” Biophys. J.
90
, 400
–412
(2006
).13.
F.
Kümmel
,
B.
ten Hagen
,
R.
Wittkowski
,
I.
Buttinoni
,
R.
Eichhorn
,
G.
Volpe
,
H.
Löwen
, and
C.
Bechinger
, “Circular motion of asymmetric self-propelling particles
,” Phys. Rev. Lett.
110
, 198302
(2013
).14.
M.
Polin
,
I.
Tuval
,
K.
Drescher
,
J. P.
Gollub
, and
R. E.
Goldstein
, “Chlamydomonas swims with two “gears” in a eukaryotic version of run-and-tumble locomotion
,” Science
325
, 487
–490
(2009
).15.
H.
Karani
,
G. E.
Pradillo
, and
P. M.
Vlahovska
, “Tuning the random walk of active colloids: from individual run-and-tumble to dynamic clustering
,” Phys. Rev. Lett.
123
, 208002
(2019
).16.
J.
Hill
,
O.
Kalkanci
,
J. L.
McMurry
, and
H.
Koser
, “Hydrodynamic surface interactions enable Escherichia coli to seek efficient routes to swim upstream
,” Phys. Rev. Lett.
98
, 068101
(2007
).17.
E.
Perez Ipiña
,
S.
Otte
,
R.
Pontier-Bres
,
D.
Czerucka
, and
F.
Peruani
, “Bacteria display optimal transport near surfaces
,” Nat. Phys.
15
, 610
–615
(2019
).18.
B.
Liebchen
and
H.
Löwen
, “Optimal navigation strategies for active particles
,” EPL
127
, 34003
(2019
).19.
A. P.
Berke
,
L.
Turner
,
H. C.
Berg
, and
E.
Lauga
, “Hydrodynamic attraction of swimming microorganisms by surfaces
,” Phys. Rev. Lett.
101
, 038102
(2008
).20.
K.
Ishimoto
and
E. A.
Gaffney
, “Squirmer dynamics near a boundary
,” Phys. Rev. E
88
, 062702
(2013
).21.
G. J.
Li
and
A. M.
Ardekani
, “Hydrodynamic interaction of microswimmers near a wall
,” Phys. Rev. E
90
, 013010
(2014
).22.
S. E.
Spagnolie
and
E.
Lauga
, “Hydrodynamics of self-propulsion near a boundary: Predictions and accuracy of far-field approximations
,” J. Fluid Mech.
700
, 105
–147
(2012
).23.
M. J.
Lighthill
, “On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers
,” Commun. Pure Appl. Math.
5
, 109
–118
(1952
).24.
J. R.
Blake
, “A spherical envelope approach to ciliary propulsion
,” J. Fluid Mech.
46
, 199
–208
(1971
).25.
J. R.
Blake
, “Self propulsion due to oscillations on the surface of a cylinder at low Reynolds number
,” Bull. Aust. Math. Soc.
5
, 255
–264
(1971
).26.
D.
Giacché
,
T.
Ishikawa
, and
T.
Yamaguchi
, “Hydrodynamic entrapment of bacteria swimming near a solid surface
,” Phys. Rev. E
82
, 056309
(2010
).27.
S. M.
Mousavi
,
G.
Gompper
, and
R. G.
Winkler
, “Wall entrapment of peritrichous bacteria: A mesoscale hydrodynamics simulation study
,” Soft Matter
16
, 4866
–4875
(2020
).28.
M.
Molaei
and
J.
Sheng
, “Succeed escape: Flow shear promotes tumbling of Escherichia coli near a solid surface
,” Sci. Rep.
6
, 35290
(2016
).29.
M.
Molaei
,
M.
Barry
,
R.
Stocker
, and
J.
Sheng
, “Failed escape: Solid surfaces prevent tumbling of Escherichia coli
,” Phys. Rev. Lett.
113
, 068103
(2014
).30.
K.
Ishimoto
,
E. A.
Gaffney
, and
D. J.
Smith
, “Squirmer hydrodynamics near a periodic surface topography
,” Front. Cell Dev. Biol.
11
, 1123446
(2023
).31.
J.
Simmchen
,
J.
Katuri
,
W. E.
Uspal
,
M. N.
Popescu
,
M.
Tasinkevych
, and
S.
Sánchez
, “Topographical pathways guide chemical microswimmers
,” Nat. Commun.
7
, 10598
(2016
).32.
C. K.
Tung
,
F.
Ardon
,
A. G.
Fiore
,
S. S.
Suarez
, and
M.
Wu
, “Cooperative roles of biological flow and surface topography in guiding sperm migration revealed by a microfluidic model
,” Lab Chip
14
, 1348
–1356
(2014
).33.
C.
Kurzthaler
and
H. A.
Stone
, “Microswimmers near corrugated, periodic surfaces
,” Soft Matter
17
, 3322
–3332
(2021
).34.
D.
Takagi
,
J.
Palacci
,
A. B.
Braunschweig
,
M. J.
Shelley
, and
J.
Zhang
, “Hydrodynamic capture of microswimmers into sphere-bound orbits
,” Soft Matter
10
, 1784
–1789
(2014
).35.
O.
Sipos
,
K.
Nagy
,
R.
Di Leonardo
, and
P.
Galajda
, “Hydrodynamic trapping of swimming bacteria by convex walls
,” Phys. Rev. Lett.
114
, 258104
(2015
).36.
Y.
Takaha
and
D.
Nishiguchi
, “Quasi-two-dimensional bacterial swimming around pillars: Enhanced trapping efficiency and curvature dependence
,” Phys. Rev. E
107
, 014602
(2023
).37.
S. E.
Spagnolie
,
G. R.
Moreno-Flores
,
D.
Bartolo
, and
E.
Lauga
, “Geometric capture and escape of a microswimmer colliding with an obstacle
,” Soft Matter
11
, 3396
–3411
(2015
).38.
M.
Kuron
,
P.
Stärk
,
C.
Holm
, and
J.
de Graaf
, “Hydrodynamic mobility reversal of squirmers near flat and curved surfaces
,” Soft Matter
15
, 5908
–5920
(2019
).39.
S.
Das
and
A.
Cacciuto
, “Colloidal swimmers near curved and structured walls
,” Soft Matter
15
, 8290
–8301
(2019
).40.
G. J.
Li
, “Slow motion of a sphere near a sinusoidal surface
,” J. Fluid Mech.
975
, A31
(2023
).41.
K. V. S.
Chaithanya
and
P. T.
Sumesh
, “Wall-curvature driven dynamics of a microswimmer
,” Phys. Rev. Fluids
6
, 083101
(2021
).42.
K.
Zheng
,
J.
Wang
,
P.
Zhang
, and
D.
Nie
, “Study on the motion of squirmers close to a curved boundary
,” AIP Adv.
13
, 075011
(2023
).43.
E. B.
van der Wee
,
B. C.
Blackwell
,
F.
Balboa Usabiaga
,
A.
Sokolov
,
I. T.
Katz
,
B.
Delmotte
, and
M. M.
Driscoll
, “A simple catch: Fluctuations enable hydrodynamic trapping of microrollers by obstacles
,” Sci. Adv.
9
, eade0320
(2023
).44.
S.
Ghosh
and
A.
Poddar
, “Slippery rheotaxis: New regimes for guiding wall-bound microswimmers
,” J. Fluid Mech.
967
, A14
(2023
).45.
S.
Ghosh
,
S.
Ghoshal
, and
A.
Poddar
, “Harnessing wall slip towards tunable microswimming in Poiseuille flow
,” J. Fluid Mech.
997
, A59
(2024
).46.
G.
Guan
,
Y.
Ying
, and
J.
Lin
, “Effect of the shape of microswimmers and slip boundary conditions on the dynamic characteristics of near-wall microswimmers
,” J. Fluid Mech.
999
, A42
(2024
).47.
A.
Hamel
,
C.
Fisch
,
L.
Combettes
,
P.
Dupuis-Williams
, and
C. N.
Baroud
, “Transitions between three swimming gaits in paramecium escape
,” Proc. Natl. Acad. Sci. U. S. A.
108
, 7290
–7295
(2011
).48.
L. N.
Wickramarathna
,
C.
Noss
, and
A.
Lorke
, “Hydrodynamic trails produced by Daphnia: Size and energetics
,” PLoS One
9
, e92383
(2014
).49.
A.
Choudhary
,
S.
Paul
,
F.
Rühle
, and
H.
Stark
, “How inertial lift affects the dynamics of a microswimmer in Poiseuille flow
,” Commun. Phys.
5
, 14
(2022
).50.
A.
Daddi-Moussa-Ider
,
H.
Löwen
, and
B.
Liebchen
, “Hydrodynamics can determine the optimal route for microswimmer navigation
,” Commun. Phys.
4
, 15
(2021
).51.
S.
Wang
and
A.
Ardekani
, “Inertial squirmer
,” Phys. Fluids
24
, 101902
(2012
).52.
A. S.
Khair
and
N. G.
Chisholm
, “Expansions at small Reynolds numbers for the locomotion of a spherical squirmer
,” Phys. Fluids
26
, 011902
(2014
).53.
N.
Chisholm
,
D.
Legendre
,
E.
Lauga
, and
A.
Khair
, “A squirmer across Reynolds numbers
,” J. Fluid Mech.
796
, 233
–256
(2016
).54.
Y. H.
Qian
,
D.
D'Humières
, and
P.
Lallemand
, “Lattice BGK models for Navier–Stokes equation
,” Europhys. Lett.
17
, 479
–484
(1992
).55.
P.
Lallemand
and
L.-S.
Luo
, “Lattice Boltzmann method for moving boundaries
,” J. Comput. Phys.
184
, 406
–421
(2003
).56.
Y.
Ying
,
T.
Jiang
,
D.
Nie
, and
J.
Lin
, “Study on the sedimentation and interaction of two squirmers in a vertical channel
,” Phys. Fluids
34
, 103315
(2022
).57.
D.
Nie
,
Y.
Ying
,
G.
Guan
,
J.
Lin
, and
Z.
Ouyang
, “Two-dimensional study on the motion and interactions of squirmers under gravity in a vertical channel
,” J. Fluid Mech.
960
, A31
(2023
).58.
C. K.
Aidun
,
Y.
Lu
, and
E.
Ding
, “Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation
,” J. Fluid Mech.
373
, 287
–311
(1998
).59.
R.
Glowinski
,
T.-W.
Pan
,
T. I.
Hesla
,
D. D.
Joseph
, and
J.
Periaux
, “A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: Application to particulate flow
,” J. Comput. Phys.
169
, 363
–426
(2001
).60.
D.
Papavassiliou
and
G. P.
Alexander
, “The many-body reciprocal theorem and swimmer hydrodynamics
,” Europhys. Lett.
110
, 44001
(2015
).61.
A. M.
Leshansky
, “Enhanced low-Reynolds-number propulsion in heterogeneous viscous environments
,” Phys. Rev. E
80
, 051911
(2009
).62.
E.
Lauga
and
T. R.
Powers
, “The hydrodynamics of swimming microorganisms
,” Rep. Prog. Phys.
72
, 096601
(2009
).63.
H.
Xie
,
M.
Sun
,
X.
Fan
,
Z.
Lin
,
W.
Chen
,
L.
Wang
,
L.
Dong
, and
Q.
He
, “Reconfigurable magnetic microrobot swarm: Multimode transformation, locomotion, and manipulation
,” Sci. Rob.
4
, eaav8006
(2019
).64.
Q.
Yang
,
L.
Xu
,
W.
Zhong
,
Q.
Yan
,
Y.
Gao
,
W.
Hong
,
Y.
She
, and
G.
Yang
, “Recent advances in motion control of micro/nanomotors
,” Adv. Intell. Syst.
2
, 2000049
(2020
).65.
S.
Ketzetzi
,
M.
Rinaldin
,
P.
Dröge
,
J.
Graaf
, and
D. J.
Kraft
, “Activity-induced interactions and cooperation of artificial microswimmers in one-dimensional environments
,” Nat. Commun.
13
, 1772
(2022
).© 2025 Author(s). Published under an exclusive license by AIP Publishing.
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