We conduct experiments with flexible swimmers to address the impact of fluid viscoelasticity on their locomotion. The swimmers are composed of a magnetic head actuated in rotation by a frequency-controlled magnetic field and a flexible tail whose deformation leads to forward propulsion. We consider both viscous Newtonian and glucose-based Boger fluids with similar viscosities. We find that the elasticity of the fluid systematically enhances the locomotion speed of the swimmer and that this enhancement increases with Deborah number. Using particle image velocimetry to visualize the flow field, we find a significant difference in the amount of shear between the rear and leading parts of the swimmer head. We conjecture that viscoelastic normal stresses lead to a net elastic forces in the swimming direction and thus a faster swimming speed.

1.
G. I.
Taylor
, “
Analysis of the swimming of microscopic organisms
,”
Proc. R. Soc. London, Ser. A
209
,
447
461
(
1951
).
2.
T. L.
Jahn
and
J. J.
Votta
, “
Locomotion of protozoa
,”
Annu. Rev. Fluid Mech.
4
,
93
116
(
1972
).
3.
J.
Lighthill
,
Mathematical Biofluiddynamics
(
SIAM
,
Philadelphia
,
1975
).
4.
C.
Brennen
and
H.
Winet
, “
Fluid mechanics of propulsion by cilia and flagella
,”
Annu. Rev. Fluid Mech.
9
,
339
398
(
1977
).
5.
E. M.
Purcell
, “
Life at low Reynolds number
,”
Am. J. Phys.
45
,
3
11
(
1977
).
6.
S.
Childress
,
Mechanics of Swimming and Flying
(
Cambridge University Press
,
Cambridge, England
,
1981
).
7.
E.
Lauga
and
T. R.
Powers
, “
The hydrodynamics of swimming microorganisms
,”
Rep. Prog. Phys.
72
,
096601
(
2009
).
8.
M. A.
Sleigh
,
J. R.
Blake
, and
N.
Liron
, “
The propulsion of mucus by cilia
,”
Am. Rev. Respir. Dis.
137
,
726
741
(
1988
).
9.
S. S.
Suarez
and
A. A.
Pacey
, “
Sperm transport in the female reproductive tract
,”
Hum. Reprod. Update
12
,
23
37
(
2006
).
10.
S. M.
Ross
and
S.
Corrsin
, “
Results of an analytical model of mucociliary pumping
,”
J. Appl. Physiol.
37
,
333
340
(
1974
).
11.
T. K.
Chaudhury
, “
Swimming in a viscoelastic liquid
,”
J. Fluid Mech.
95
,
189
197
(
1979
).
12.
G. R.
Fulford
,
D. F.
Katz
, and
R. L.
Powell
, “
Swimming of spermatozoa in a linear viscoelastic fluid
,”
Biorheology
35
,
295
309
(
1998
).
13.
E.
Lauga
, “
Propulsion in a viscoelastic fluid
,”
Phys. Fluids
19
,
083104
(
2007
).
14.
H. C.
Fu
,
T. R.
Powers
, and
H. C.
Wolgemuth
, “
Theory of swimming filaments in viscoelastic media
,”
Phys. Rev. Lett.
99
,
258101
258105
(
2007
).
15.
H. C.
Fu
,
C. W.
Wolgemuth
, and
T. R.
Powers
, “
Beating patterns of filaments in viscoelastic fluids
,”
Phys. Rev. E
78
,
041913
1
(
2008
).
16.
H. C.
Fu
,
C. W.
Wolgemuth
, and
T. R.
Powers
, “
Swimming speeds of filaments in nonlinearly viscoelastic fluids
,”
Phys. Fluids
21
,
033102
(
2009
).
17.
E.
Lauga
, “
Life at high Deborah number
,”
Europhys. Lett.
86
,
64001
(
2009
).
18.
J.
Teran
,
L.
Fauci
, and
M.
Shelley
, “
Viscoelastic fluid response can increase the speed and efficiency of a free swimmer
,”
Phys. Rev. Lett.
104
,
038101
(
2010
).
19.
X. N.
Shen
and
P. E.
Arratia
, “
Undulatory swimming in viscoelastic fluids
,”
Phys. Rev. Lett.
106
,
208101
(
2011
).
20.
B.
Liu
,
T. R.
Powers
, and
K. S.
Breuer
, “
Force-free swimming of a model helical flagellum in viscoelastic fluids
,”
Proc. Natl. Acad. Sci. U.S.A.
108
,
19516
19520
(
2011
).
21.
M. W.
Harman
,
S. M.
Dunham-Ems
,
M. J.
Caimano
,
A. A.
Belperron
,
L. K.
Bockenstedt
,
H. C.
Fu
,
J. D.
Radolf
, and
C. W.
Wolgemuth
, “
The heterogeneous motility of the Lyme disease spirochete in gelatin mimics dissemination through tissue
,”
Proc. Natl. Acad. Sci. U.S.A.
109
,
3059
3064
(
2012
).
22.
D. V.
Boger
, “
A highly elastic constant-viscosity fluid
,”
J. Non-Newtonian Fluid Mech.
3
,
87
91
(
1977
).
23.
C. H.
Wiggins
and
R. E.
Goldstein
, “
Flexive and propulsive dynamics of elastica at low Reynolds number
,”
Phys. Rev. Lett.
80
,
3879
3882
(
1998
).
24.
See supplementary material at http://dx.doi.org/10.1063/1.4795166 for Videos 1–3. Video 1 shows a typical magnetic swimmer with a flexible tail, in a Boger fluid. Video 2 shows the swimmer with the rigid tail, in a Newtonian fluid. It was done to confirm that the lack of tail flexibility impedes locomotion. Video 3 shows a typical PIV experiment from which the velocity field around the swimmer was obtained. The case shown corresponds to the swimmer with a flat tail moving in a Boger fluid (B2).
25.
Y.
Kraftmakher
,
Experiments and Demonstrations in Physics
(
World Scientific
,
Singapore
,
2007
).
26.
M.
Baumgaertel
and
H. H.
Winter
, “
Determination of discrete relaxation and retardation time spectra from dynamic mechanical data
,”
Rheol. Acta
28
,
511
519
(
1989
).
27.
T. S.
Yu
,
E.
Lauga
, and
A. E.
Hosoi
, “
Experimental investigations of elastic tail propulsion at low Reynolds number
,”
Phys. Fluids
18
,
091701
(
2006
).
28.
H. A.
Barnes
,
J. F.
Hutton
, and
K.
Walters
,
An Introduction to Rheology
(
Elsevier
,
Amsterdam
,
1999
).

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