Microscopic swimming devices hold promise for radically new applications in lab-on-a-chip and microfluidic technology, including diagnostics and drug delivery. In this paper, we realize a macroscopic single particle ferromagnetic swimmer experimentally and investigate its swimming properties. The flagella-based swimmer is comprised of a hard ferromagnetic head attached to a flexible tail. We investigate the dynamic performance of the swimmer on the air-liquid interface as a function of the external magnetic field parameters (frequency and amplitude of an applied magnetic field). We show that the speed of the swimmer can be controlled by manipulating the strength and frequency of the external magnetic field (<3.5 mT) and that the propagation direction has a dependence on parameters of the external magnetic field. The experimental results are compared to a theoretical model based on three beads, one of which having a fixed magnetic moment and the other two non-magnetic, connected via elastic filaments. The model shows sufficient complexity to satisfy the “non-reciprocity” condition and gives good agreement with experiment. Via a simple conversion, we also demonstrate a fluid pump and investigate the induced flow. This investigation paves the way to the fabrication of such swimmers and fluid pump systems on a micro-scale, promising a variety of microfluidic applications.

1.
E. M.
Purcell
, “
Life at low Reynolds number
,”
Am. J. Phys.
45
,
3
(
1977
).
2.
A.
Shapere
and
F.
Wilczek
, “
Geometry of self-propulsion at low Reynolds number
,”
J. Fluid Mech.
198
,
557
(
1989
).
3.
E.
Lauga
and
T. R.
Powers
, “
The hydrodynamics of swimming microorganisms
,”
Rep. Prog. Phys.
72
,
096601
(
2009
).
4.
A.
Najafi
and
R.
Golestanian
, “
Simple swimmer at low Reynolds number: Three linked spheres
,”
Phys. Rev. E
69
,
062901
(
2004
).
5.
A.
Najafi
and
R.
Zargar
, “
Two-sphere low-Reynolds-number propeller
,”
Phys. Rev. E
81
,
067301
(
2010
).
6.
M.
Leoni
,
B.
Bassetti
,
J.
Kotar
,
P.
Cicuta
, and
M.
Cosentino Lagomarsino
, “
Minimal two-sphere model of the generation of fluid flow at low Reynolds numbers
,”
Phys. Rev. E
81
,
036304
(
2010
).
7.
D.
Salazar
,
A. M.
Roma
, and
H. D.
Ceniceros
, “
Numerical study of an inextensible, finite swimmer in Stokesian viscoelastic flow
,”
Phys. Fluids
28
,
063101
(
2016
).
8.
E. J.
Campbell
and
P.
Bagchi
, “
A computational model of amoeboid cell swimming
,”
Phys. Fluids
29
,
101902
(
2017
).
9.
S.
Yazdi
and
A.
Borhan
, “
Effect of a planar interface on time-averaged locomotion of a spherical squirmer in a viscoelastic fluid
,”
Phys. Fluids
29
,
093104
(
2017
).
10.
K. J.
Rao
,
F.
Li
,
L.
Meng
,
H.
Zheng
,
F.
Cai
, and
W.
Wang
, “
A force to be reckoned with: A review of synthetic microswimmers powered by ultrasound
,”
Small
11
,
2836
(
2015
).
11.
S. T.
Chang
,
V. N.
Paunov
,
D. N.
Petsev
, and
O. D.
Velev
, “
Remotely powered self-propelling particles and micropumps based on miniature diodes
,”
Nat. Mater.
6
,
235
(
2007
).
12.
K.
Ishiyama
,
M.
Sendoh
,
A.
Yamazaki
, and
K. I.
Arai
, “
Swimming micro-machine driven by magnetic torque
,”
Sens. Actuators, A
91
,
141
(
2001
).
13.
P.
Tierno
,
R.
Golestanian
,
I.
Pagonabarraga
, and
F.
Sagués
, “
Magnetically actuated colloidal microswimmers
,”
J. Phys. Chem. B
112
,
16525
(
2008
).
14.
S.
Tottori
,
L.
Zhang
,
F.
Qiu
,
K. K.
Krawczyk
,
A.
Franco-Obregõn
, and
B. J.
Nelson
, “
Magnetic helical micromachines: Fabrication, controlled swimming, and cargo transport
,”
Adv. Mater.
24
,
811
(
2012
).
15.
M.
Medina-Sánchez
,
L.
Schwarz
,
A. K.
Meyer
,
F.
Hebenstreit
, and
O. G.
Schmidt
, “
Cellular cargo delivery: Toward assisted fertilization by sperm-carrying micromotors
,”
Nano Lett.
16
,
555
(
2015
).
16.
G.
Grosjean
,
G.
Lagubeau
,
A.
Darras
,
M.
Hubert
,
G.
Lumay
, and
N.
Vandewalle
, “
Remote control of self-assembled microswimmers
,”
Sci. Rep.
5
,
16035
(
2015
).
17.
A. M.
Maier
,
C.
Weig
,
P.
Oswald
,
E.
Frey
,
P.
Fischer
, and
T.
Liedl
, “
Magnetic propulsion of microswimmers with DNA-based flagellar bundles
,”
Nano Lett.
16
,
906
(
2016
).
18.
R. M.
Erb
,
J. J.
Martin
,
R.
Soheilian
,
C.
Pan
, and
J. R.
Barber
, “
Actuating soft matter with magnetic torque
,”
Adv. Funct. Mater.
26
,
3859
(
2016
).
19.
G.
Grosjean
,
M.
Hubert
,
G.
Lagubeau
, and
N.
Vandewalle
, “
Realization of the Najafi-Golestanian microswimmer
,”
Phys. Rev. E
94
,
021101
(
2016
).
20.
J. R.
Howse
,
R. A. L.
Jones
,
A. J.
Ryan
,
T.
Gough
,
R.
Vafabakhsh
, and
R.
Golestanian
, “
Self-motile colloidal particles: From directed propulsion to random walk
,”
Phys. Rev. Lett.
99
,
048102
(
2007
).
21.
S. J.
Ebbens
and
J. R.
Howse
, “
In pursuit of propulsion at the nanoscale
,”
Soft Matter
6
,
726
(
2010
).
22.
A. A.
Solovev
,
W.
Xi
,
D. H.
Gracias
,
S. M.
Harazim
,
C.
Deneke
,
S.
Sanchez
, and
O. G.
Schmidt
, “
Self-propelled nanotools
,”
ACS Nano
6
,
1751
(
2012
).
23.
S.
Das
,
A.
Garg
,
A. I.
Campbell
,
J. R.
Howse
,
A.
Sen
,
D.
Velegol
,
R.
Golestanian
, and
S. J.
Ebbens
, “
Boundaries can steer active Janus spheres
,”
Nat. Commun.
6
,
8999
(
2015
).
24.
G.
Natale
,
C.
Datt
,
S. G.
Hatzikiriakos
, and
G. J.
Elfring
, “
Autophoretic locomotion in weakly viscoelastic fluids at finite Péclet number
,”
Phys. Fluids
29
,
123102
(
2017
).
25.
M.
Camacho-Lopez
,
H.
Finkelmann
,
P.
Palffy-Muhoray
, and
M.
Shelley
, “
Fast liquid-crystal elastomer swims into the dark
,”
Nat. Mater.
3
,
307
(
2004
).
26.
W.
Li
,
X.
Wu
,
H.
Qin
,
Z.
Zhao
, and
H.
Liu
, “
Light-driven and light-guided microswimmers
,”
Adv. Funct. Mater.
26
,
3164
(
2016
).
27.
A.
Cebers
and
I.
Javaitis
, “
Dynamics of a flexible magnetic chain in a rotating magnetic field
,”
Phys. Rev. E
69
,
021404
(
2004
).
28.
R.
Dreyfus
,
J.
Baudry
,
M. L.
Roper
,
M.
Fermigier
,
H. A.
Stone
, and
J.
Bibette
, “
Microscopic artificial swimmers
,”
Nature
437
,
862
(
2005
).
29.
T. S.
Yu
,
E.
Lauga
, and
A. E.
Hosoi
, “
Experimental investigations of elastic tail propulsion at low Reynolds number
,”
Phys. Fluids
18
,
091701
(
2006
).
30.
O. S.
Pak
,
W.
Gao
,
J.
Wang
, and
E.
Lauga
, “
High-speed propulsion of flexible nanowire motors: Theory and experiments
,”
Soft Matter
7
,
8169
(
2011
).
31.
W.
Gao
,
D.
Kagan
,
O. S.
Pak
,
C.
Clawson
,
S.
Campuzano
,
E.
Chuluun-Erdene
,
E.
Shipton
,
E. E.
Fullerton
,
L.
Zhang
,
E.
Lauga
, and
J.
Wang
, “
Cargo-towing fuel-free magnetic nanoswimmers for targeted drug delivery
,”
Small
8
,
460
(
2012
).
32.
R.
Livanovičs
and
A.
Cebers
, “
Magnetic dipole with a flexible tail as a self-propelling microdevice
,”
Phys. Rev. E
85
,
041502
(
2012
).
33.
H.
Gadêlha
, “
On the optimal shape of magnetic swimmers
,”
Regular Chaotic Dyn.
18
,
75
(
2013
).
34.
J.
Espinosa-Garcia
,
E.
Lauga
, and
R.
Zenit
, “
Fluid elasticity increases the locomotion of flexible swimmers
,”
Phys. Fluids
25
,
031701
(
2013
).
35.
I. S. M.
Khalil
,
K.
Youakim
,
A.
Sanchez
, and
S.
Misra
, in
IEEE International Conference on Intelligent Robots and Systems
(
IEEE
,
2014
), p.
4686
.
36.
I. S. M.
Khalil
,
H. C.
Dijkslag
,
L.
Abelmann
, and
S.
Misra
, “
MagnetoSperm: A microrobot that navigates using weak magnetic fields
,”
Appl. Phys. Lett.
104
,
223701
(
2014
).
37.
A.
Cebers
and
K.
Erglis
, “
Flexible magnetic filaments and their applications
,”
Adv. Funct. Mater.
26
,
3783
(
2016
).
38.
F.
Box
,
E.
Han
,
C. R.
Tipton
, and
T.
Mullin
, “
On the motion of linked spheres in a Stokes flow
,”
Exp. Fluids
58
,
29
(
2017
).
39.
F. Y.
Ogrin
,
P. G.
Petrov
, and
C. P.
Winlove
, “
Ferromagnetic microswimmers
,”
Phys. Rev. Lett.
100
,
218102
(
2008
).
40.
A. D.
Gilbert
,
F. Y.
Ogrin
,
P. G.
Petrov
, and
C. P.
Winlove
, “
Ferromagnetic microswimmers
,”
Q. J. Mech. Appl. Math.
64
,
239
(
2011
).
41.
A. D.
Gilbert
,
F. Y.
Ogrin
,
P. G.
Petrov
, and
C. P.
Winlove
, “
Motion and mixing for multiple ferromagnetic microswimmers
,”
Eur. Phys. J. E
34
,
121
(
2011
).
42.
M. T.
Bryan
,
S. R.
Shelley
,
M. J.
Parish
,
P. G.
Petrov
,
C. P.
Winlove
,
A. D.
Gilbert
, and
F. Y.
Ogrin
, “
Emergent propagation modes of ferromagnetic swimmers in constrained geometries
,”
J. Appl. Phys.
121
,
073901
(
2017
).
43.
J. K.
Hamilton
,
P. G.
Petrov
,
C. P.
Winlove
,
A. D.
Gilbert
,
M. T.
Bryan
, and
F. Y.
Ogrin
, “
Magnetically controlled ferromagnetic swimmers
,”
Sci. Rep.
7
,
44142
(
2017
).
44.
J. K.
Hamilton
,
M. T.
Bryan
,
A. D.
Gilbert
,
F. Y.
Ogrin
, and
T. O.
Myers
, “
A new class of magnetically actuated pumps and valves for microfluidic applications
,”
Sci. Rep.
8
,
933
(
2018
).
45.
D.
Brown
, Open Source Physics, 2017.
46.
C. P.
Lowe
, “
Dynamics of filaments: Modelling the dynamics of driven microfilaments
,”
Philos. Trans. R. Soc., B
358
,
1543
(
2003
).
47.
J.
Happel
and
H.
Brenner
,
Low Reynolds Number Hydrodynamics
(
Kluwer
,
Dordrecht
,
1983
).
48.
L.
Landau
and
E.
Lifshitz
,
Fluid Mechanics
(
Butterworth–Heinemann
,
1959
).

Supplementary Material

You do not currently have access to this content.