Seaweed and fish have slippery outer surfaces because of the secretion of a layer of mucus. The hydrodynamics over a three-dimensional lubricant-infused slip surface that mimics the mucus layers of seaweed and fish was numerically explored. The morphological features of the lubricant-infused surface were designed to mimic such biological mucus storage systems. The lubricant was assumed to fill the cavity and to be supplemented without limit from the bottom surface of the cavity. The slip motion at the interface between the lubricant and water was simulated by using the volume of fluid method. Simulations were performed for two cavity open area fractions, 40% and 60%, and for three lid thicknesses, 0.01D, 0.03D, and 0.06D, where D is the width of the cavity (D = 400 μm). The simulation was conducted by employing realistic material properties. The contact angle of the lubricant in deionized water was directly measured (θeq = 25.9°). This slippery lubricant layer contributes to drag reduction by lessening the velocity gradient of the surrounding fluid. The hydrodynamics of the slip surface was examined by scrutinizing the effects of varying the open area and the lid thickness on the slip velocity and length, the dispersion area, and the lubricant consumption. The maximum slip velocity and length were obtained in the center of the contact interface, which forms a paraboloid. The effects of varying the cavity open area fraction on the maximum slip velocity and length are significant. The lid thickness affects both the lubricant dispersion pattern and the height to which the lubricant builds up. The lubricant consumption for a cavity open area fraction of 60% is larger than that for 40%. The cavity with an open area fraction of 60% and a lid thickness of 0.06D provides the best drag reduction of the cavities we simulated.

1.
Arenas
,
I.
,
García
,
E.
,
Fu
,
M. K.
,
Orlandi
,
P.
,
Hultmark
,
M.
, and
Leonardi
,
S.
, “
Comparison between super-hydrophobic, liquid infused and rough surfaces: A direct numerical simulation study
,”
J. Fluid Mech.
869
,
500
525
(
2019
).
2.
Bernadsky
,
G.
,
Sar
,
N.
, and
Rosenberg
,
E.
, “
Drag reduction of fish skin mucus: Relationship to mode of swimming and size
,”
J. Fish Biol.
42
(
5
),
797
800
(
1993
).
3.
Bhushan
,
B.
and
Jung
,
Y. C.
, “
Natural and biomimetic artificial surfaces for superhydrophobicity, self-cleaning, low adhesion, and drag reduction
,”
Prog. Mater. Sci.
56
,
1
108
(
2011
).
4.
Bone
,
Q.
, “
Muscular and energetic aspects of fish swimming
,” in
Swimming and Flying in Nature
(
Springer
,
Boston, MA
,
1975
), pp.
439
582
.
5.
Brackbill
,
J. U.
,
Kothe
,
D. B.
, and
Zemach
,
C.
, “
A continuum method for modeling surface tension
,”
J. Comput. Phys.
100
,
335
354
(
1992
).
6.
Busse
,
A.
,
Sandham
,
N. D.
,
McHale
,
G.
, and
Newton
,
M. I.
, “
Change in drag, apparent slip and optimum air layer thickness for laminar flow over an idealised superhydrophobic surface
,”
J. Fluid Mech.
727
,
488
508
(
2013
).
7.
Chang
,
J.
,
Jung
,
T.
,
Choi
,
H.
, and
Kim
,
J.
, “
Predictions of the effective slip length and drag reduction with a lubricated micro-groove surface in a turbulent channel flow
,”
J. Fluid Mech.
874
,
797
820
(
2019
).
8.
Costantini
,
R.
,
Mollicone
,
J.-P.
, and
Battista
,
F.
, “
Drag reduction induced by superhydrophobic surfaces in turbulent pipe flow
,”
Phy. Fluids
30
,
025102
(
2018
).
9.
Daniel
,
T. L.
, “
Fish mucus: In situ measurements of polymer drag reduction
,”
Biol. Bull.
160
(
3
),
376
382
(
1981
).
10.
Daniello
,
R. J.
,
Waterhouse
,
N. E.
, and
Rothstein
,
J. P.
, “
Drag reduction in turbulent flows over superhydrophobic surfaces
,”
Phys. Fluids
21
,
085103
(
2009
).
11.
Davenport
,
J.
,
Hughes
,
R.
,
Shorten
,
M.
, and
Larsen
,
P.
, “
Drag reduction by air release promotes fast ascent in jumping emperor penguins—A novel hypothesis
,”
Mar. Ecol. Prog. Ser.
430
,
171
182
(
2011
).
12.
Fudge
,
D. S.
,
Levy
,
N.
,
Chiu
,
S.
, and
Gosline
,
J. M.
, “
Composition, morphology and mechanics of hagfish slime
,”
J. Exp. Biol.
208
,
4613
4625
(
2005
).
13.
Fu
,
M. K.
,
Arenas
,
I.
,
Leonardi
,
S.
, and
Hultmark
,
M.
, “
Liquid-infused surfaces as a passive method of turbulent drag reduction
,”
J. Fluid Mech.
824
,
688
700
(
2017
).
14.
Golovin
,
K. B.
,
Gose
,
J. W.
,
Perlin
,
M.
,
Ceccio
,
S. L.
, and
Tuteja
,
A.
, “
Bioinspired surfaces for turbulent drag reduction
,”
Philos. Trans. R. Soc., A
374
,
20160189
(
2016
).
15.
Huang
,
W.-X.
,
Chang
,
C. B.
, and
Sung
,
H. J.
, “
Three-dimensional simulation of elastic capsules in shear flow by the penalty immersed boundary method
,”
J. Comput. Phys.
231
,
3340
3364
(
2012
).
16.
Jacobi
,
I.
,
Wexler
,
J. S.
, and
Stone
,
H. A.
, “
Overflow cascades in liquid-infused substrates
,”
Phys. Fluids
27
,
082101
(
2015
).
17.
Jang
,
J.
,
Choi
,
S. H.
,
Ahn
,
S.
,
Kim
,
B.
, and
Seo
,
J. S.
, “
Experimental investigation of frictional resistance reduction with air layer on the hull bottom of a ship
,”
Int. J. Nav. Archit. Ocean Eng.
6
,
363
379
(
2014
).
18.
Kim
,
K.
,
Baek
,
S. J.
, and
Sung
,
H. J.
, “
An implicit velocity decoupling procedure for the incompressible Navier-Stokes equations
,”
Int. J. Numer. Methods Fluids
38
,
125
138
(
2002
).
19.
Kwon
,
B. H.
,
Kim
,
H. H.
,
Jeon
,
H. J.
,
Kim
,
M. C.
,
Lee
,
I.
,
Chun
,
S.
, and
Go
,
J. S.
, “
Experimental study on the reduction of skin frictional drag in pipe flow by using convex air bubbles
,”
Exp. Fluids
55
,
1722
(
2014
).
20.
Lee
,
S. J.
,
Kim
,
H. N.
,
Choi
,
W.
,
Yoon
,
G. Y.
, and
Seo
,
E.
, “
A nature-inspired lubricant-infused surface for sustainable drag reduction
,”
Soft Matter
15
,
8459
(
2019
).
21.
Mäkiharju
,
S. A.
,
Perlin
,
M.
, and
Ceccio
,
S. L.
, “
On the energy economics of air lubrication drag reduction
,”
Int. J. Nav. Archit. Ocean Eng.
4
,
412
422
(
2012
).
22.
Martell
,
M. B.
,
Rhothstein
,
J. P.
, and
Perot
,
B.
, “
An analysis of superhydrophobic turbulent drag reduction mechanisms using direct numerical simulation
,”
Phys. Fluids
22
,
065102
(
2010
).
23.
Maynes
,
D.
,
Jeffs
,
K.
,
Woolford
,
B.
, and
Webb
,
B. W.
, “
Laminar flow in a microchannel with hydrophobic surface patterned microribs oriented parallel to the flow direction
,”
Phys. Fluids
19
,
093603
(
2007
).
24.
Park
,
H.
,
Park
,
H.
, and
Kim
,
J.
, “
A numerical study of the effects of superhydrophobic surface on skin-friction drag in turbulent channel flow
,”
Phys. Fluids
25
,
110815
(
2013
).
25.
Paschkewitz
,
J. S.
,
Dimitropoulos
,
C. D.
,
Hou
,
Y. X.
,
Somandepalli
,
V. S. R.
,
Mungal
,
M. C.
,
Shaqfeh
,
E. S. G.
, and
Moin
,
P.
, “
An experimental and numerical investigation of drag reduction in a turbulent boundary layer using a rigid rodlike polymer
,”
Phys. Fluids
17
,
085101
(
2005
).
26.
Piao
,
L.
and
Park
,
H.
, “
Two-dimensional analysis of air–water interface on superhydrophobic grooves under fluctuating water pressure
,”
Langmuir
31
,
8022
8032
(
2015
).
27.
Poetes
,
R.
,
Holtzmann
,
K.
,
Franze
,
K.
, and
Steiner
,
U.
, “
Metastable underwater superhydrophobicity
,”
Phys. Rev. Lett.
105
,
166104
(
2010
).
28.
Rastegari
,
A.
and
Akhavan
,
R.
, “
On the mechanism of turbulent drag reduction with super-hydrophobic surfaces
,”
J. Fluid Mech.
773
,
R4
(
2015
).
29.
Rosen
,
M. W.
and
Cornford
,
N. E.
, “
Fluid friction of fish slimes
,”
Nature
234
,
49
51
(
1971
).
30.
Ryu
,
J.
,
Byun
,
H.
,
Lee
,
S. J.
, and
Sung
,
H. J.
, “
Flapping dynamics of a flexible plate with Navier slip
,”
Phys. Fluids
31
,
091901
(
2019
).
31.
Ryu
,
J.
,
Park
,
S. G.
,
Kim
,
B.
, and
Sung
,
H. J.
, “
Flapping dynamics of an inverted flag in a uniform flow
,”
J. Fluids Struct.
57
,
159
169
(
2015
).
32.
Seo
,
J.
,
García-Mayoral
,
R.
, and
Mani
,
A.
, “
Turbulent flows over superhydrophobic surfaces: Flow-induced capillary waves, and robustness of air–water interfaces
,”
J. Fluid Mech.
835
,
45
85
(
2018
).
33.
Wexler
,
J. S.
,
Jacobi
,
I.
, and
Stone
,
H. A.
, “
Shear-driven failure of liquid-infused surfaces
,”
Phys. Rev. Lett.
114
,
168301
(
2015
).
34.
Wong
,
T.-S.
,
Kang
,
S. H.
,
Tang
,
S. K. Y.
,
Smythe
,
E. J.
,
Hatton
,
B. D.
,
Grinthal
,
A.
, and
Aizenberg
,
J.
, “
Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity
,”
Nature
477
,
443
447
(
2011
).
35.
Yao
,
X.
,
Hu
,
Y.
,
Grinthal
,
A.
,
Wong
,
T.-S.
,
Mahadevan
,
L.
, and
Aizenberg
,
J.
, “
Adaptive fluid-infused porous films with tunable transparency and wettability
,”
Nat. Mater.
12
,
529
534
(
2013
).
36.
Yeganehdoust
,
F.
,
Attarzadeh
,
R.
,
Karimfazli
,
I.
, and
Dolatabadi
,
A.
, “
A numerical analysis of air entrapment during droplet impact on an immiscible liquid film
,”
Int. J. Multiphase Flow
124
,
103175
(
2020
).
You do not currently have access to this content.