Droplet transport on a cylindrical wire has applications in numerous fields such as fog collection, mist elimination, filtration, and oil/water separation. This work reports a droplet transport phenomenon on a superhydrophilic wire that shows a transient velocity powered not by the gradient of substrate geometry or wettability but primarily by the surface-to-kinetic energy transition that occurs along the axial direction upon coalescence. The transition efficiency is mainly limited by the viscous friction at the local liquid wedge, a relationship that a modified Ohnesorge number can capture.

1.
Y.
Jiang
,
S.
Savarirayan
,
Y.
Yao
, and
K.
Park
, “
Fog collection on a superhydrophilic wire
,”
Appl. Phys. Lett.
114
,
083701
(
2019
).
2.
C.
Shin
and
G.
Chase
, “
Water-in-oil coalescence in micro-nanofiber composite filters
,”
AIChE J.
50
,
343
350
(
2004
).
3.
T.
Frising
,
C.
Noïk
, and
C.
Dalmazzone
, “
The liquid/liquid sedimentation process: From droplet coalescence to technologically enhanced water/oil emulsion gravity separators: A review
,”
J. Dispersion Sci. Technol.
27
,
1035
1057
(
2006
).
4.
E.
Brunazzi
and
A.
Paglianti
, “
Design of complex wire-mesh mist eliminators
,”
AIChE J.
46
,
1131
1137
(
2000
).
5.
I.
Agranovski
and
R.
Braddock
, “
Filtration of liquid aerosols on wettable fibrous filters
,”
AIChE J.
44
,
2775
2783
(
1998
).
6.
E.
Lorenceau
and
D.
Quéré
, “
Drops on a conical wire
,”
J. Fluid Mech.
510
,
29
45
(
2004
).
7.
B.
Carroll
, “
Equilibrium conformations of liquid drops on thin cylinders under forces of capillarity. A theory for the roll-up process
,”
Langmuir
2
,
248
250
(
1986
).
8.
B.
Carroll
, “
The accurate measurement of contact angle, phase contact areas, drop volume, and laplace excess pressure in drop-on-fiber systems
,”
J. Colloid Interface Sci.
57
,
488
495
(
1976
).
9.
G.
McHale
,
N.
Käb
,
M.
Newton
, and
S.
Rowan
, “
Wetting of a high-energy fiber surface
,”
J. Colloid Interface Sci.
186
,
453
461
(
1997
).
10.
G.
McHale
and
M.
Newton
, “
Global geometry and the equilibrium shapes of liquid drops on fibers
,”
Colloids Surf. A: Physicochem. Eng. Aspects
206
,
79
86
(
2002
).
11.
A. L.
Yarin
,
W.
Liu
, and
D.
Reneker
, “
Motion of droplets along thin fibers with temperature gradient
,”
J. Appl. Phys.
91
,
4751
4760
(
2002
).
12.
T.
Gilet
,
D.
Terwagne
, and
N.
Vandewalle
, “
Droplets sliding on fibres
,”
Eur. Phys. J. E
31
,
253
262
(
2010
).
13.
C.
Duprat
,
S.
Protiere
,
A.
Beebe
, and
H.
Stone
, “
Wetting of flexible fibre arrays
,”
Nature
482
,
510
513
(
2012
).
14.
R.
Schulman
,
A.
Porat
,
K.
Charlesworth
,
A.
Fortais
,
T.
Salez
,
E.
Raphaël
, and
K.
Dalnoki-Veress
, “
Elastocapillary bending of microfibers around liquid droplets
,”
Soft Matter
13
,
720
724
(
2017
).
15.
J.
Boreyko
and
C.
Chen
, “
Self-propelled dropwise condensate on superhydrophobic surfaces
,”
Phys. Rev. Lett.
103
,
184501
(
2009
).
16.
K.
Zhang
,
F.
Liu
,
A.
Williams
,
X.
Qu
,
J.
Feng
, and
C.
Chen
, “
Self-propelled droplet removal from hydrophobic fiber-based coalescers
,”
Phys. Rev. Lett.
115
,
074502
(
2015
).
17.
R.
Enright
,
N.
Miljkovic
,
J.
Sprittles
,
K.
Nolan
,
R.
Mitchell
, and
E.
Wang
, “
How coalescing droplets jump
,”
ACS Nano
8
,
10352
10362
(
2014
).
18.
F.
Liu
,
G.
Ghigliotti
,
J.
Feng
, and
C.
Chen
, “
Numerical simulations of self-propelled jumping upon drop coalescence on non-wetting surfaces
,”
J. Fluid Mech.
752
,
39
65
(
2014
).
19.
F.
Liu
,
G.
Ghigliotti
,
J.
Feng
, and
C.
Chen
, “
Self-propelled jumping upon drop coalescence on leidenfrost surfaces
,”
J. Fluid Mech.
752
,
22
38
(
2014
).
20.
H.
Cha
,
C.
Xu
,
J.
Sotelo
,
J.
Chun
,
Y.
Yokoyama
,
R.
Enright
, and
N.
Miljkovic
, “
Coalescence-induced nanodroplet jumping
,”
Phys. Rev. Fluids
1
,
064102
(
2016
).
21.
S.
Daniel
,
M.
Chaudhury
, and
J.
Chen
, “
Fast drop movements resulting from the phase change on a gradient surface
,”
Science
291
,
633
636
(
2001
).
22.
M.
Garimella
,
S.
Koppu
,
S.
Kadlaskar
,
V.
Pillutla
, and
W.
Choi
, “
Difference in growth and coalescing patterns of droplets on bi-philic surfaces with varying spatial distribution
,”
J. Colloid Interface Sci.
505
,
1065
1073
(
2017
).
23.
A.
Ghosh
,
S.
Beaini
,
B.
Zhang
,
R.
Ganguly
, and
C.
Megaridis
, “
Enhancing dropwise condensation through bioinspired wettability patterning
,”
Langmuir
30
,
13103
13115
(
2014
).
24.
S.
Chandra
and
C.
Avedisian
, “
On the collision of a droplet with a solid surface
,”
Proc. Royal Soc. London. Ser. A: Math. Phys. Sci.
432
,
13
41
(
1991
).
25.
F. C.
Wang
,
F.
Yang
, and
Y. P.
Zhao
, “
Size effect on the coalescence-induced self-propelled droplet
,”
Appl. Phys. Lett.
98
,
053112
(
2011
).
26.
C.
Lv
,
P.
Hao
,
Z.
Yao
,
Y.
Song
,
X.
Zhang
, and
F.
He
, “
Condensation and jumping relay of droplets on lotus leaf
,”
Appl. Phys. Lett.
103
,
021601
(
2013
).
27.
B.
Peng
,
S.
Wang
,
Z.
Lan
,
W.
Xu
,
R.
Wen
, and
X.
Ma
, “
Analysis of droplet jumping phenomenon with lattice Boltzmann simulation of droplet coalescence
,”
Appl. Phys. Lett.
102
,
151601
(
2013
).
28.
S. T.
Thoroddsen
,
K.
Takehara
, and
T. G.
Etoh
, “
The coalescence speed of a pendent and a sessile drop
,”
J. Fluid Mech.
527
,
85
114
(
2005
).
29.
T.
Mouterde
,
T.
Nguyen
,
H.
Takahashi
,
C.
Clanet
,
I.
Shimoyama
, and
D.
Quéré
, “
How merging droplets jump off a superhydrophobic surface: Measurements and model
,”
Phys. Rev. Fluids
2
,
112001
(
2017
).
30.
J. D.
Paulsen
,
J. C.
Burton
, and
S. R.
Nagel
, “
Viscous to inertial crossover in liquid drop coalescence
,”
Phys. Rev. Lett.
106
,
114501
(
2011
).
31.
P. D.
Gennes
, “
Wetting: Statics and dynamics
,”
Rev. Mod. Phys.
57
,
827
863
(
1985
).
32.
S.
Haefner
,
O.
Bäumchen
, and
K.
Jacobs
, “
Capillary droplet propulsion on a fibre
,”
Soft Matter
11
,
6921
6926
(
2015
).
33.
P.
Brunet
,
J.
Eggers
, and
R. D.
Deegan
, “
Vibration-induced climbing of drops
,”
Phys. Rev. Lett.
99
,
144501
(
2007
).
34.
P.
Sartori
,
E.
Guglielmin
,
D.
Ferraro
,
D.
Filippi
,
A.
Zaltron
,
M.
Pierno
, and
G.
Mistura
, “
Motion of Newtonian drops deposited on liquid-impregnated surfaces induced by vertical vibrations
,”
J. Fluid Mech.
876
,
R4
(
2019
).
35.
J.
Ju
,
H.
Bai
,
Y.
Zheng
,
T.
Zhao
,
R.
Fang
, and
L.
Jiang
, “
A multi-structural and multi-functional integrated fog collection system in cactus
,”
Nat. Commun.
3
,
1247
(
2012
).
36.
Y.
Xue
,
Y.
Chen
,
T.
Wang
,
L.
Jiang
, and
Y.
Zheng
, “
Directional size-triggered microdroplet target transport on gradient-step fibers
,”
J. Mater. Chem. A
2
,
7156
7160
(
2014
).
37.
T.
Xu
,
Y.
Lin
,
M.
Zhang
,
W.
Shi
, and
Y.
Zheng
, “
High-efficiency fog collector: Water unidirectional transport on heterogeneous rough conical wires
,”
ACS Nano
10
,
10681
10688
(
2016
).
38.
H.
Chen
,
T.
Ran
,
Y.
Gan
,
J.
Zhou
,
Y.
Zhang
,
L.
Zhang
,
D.
Zhang
, and
L.
Jiang
, “
Ultrafast water harvesting and transport in hierarchical microchannels
,”
Nat. Mater.
17
,
935
942
(
2018
).
39.
H.
Zhou
,
M.
Zhang
,
C.
Li
,
C.
Gao
, and
Y.
Zheng
, “
Excellent fog-droplets collector via integrative janus membrane and conical spine with micro/nanostructures
,”
Small
14
,
1801335
(
2018
).
40.
B. E.
Pinchasik
,
M.
Kappl
, and
H. J.
Butt
, “
Small structures, big droplets: The role of nanoscience in fog harvesting
,”
ACS Nano
10
,
10627
10630
(
2016
).
41.
C.
Luo
and
X.
Wang
, “
Conditions for barrel and clam-shell liquid drops to move on bio-inspired conical wires
,”
Sci. Rep.
7
,
9717
(
2017
).
42.
K.
Park
,
S.
Chhatre
,
S.
Srinivasan
,
R.
Cohen
, and
G.
McKinley
, “
Optimal design of permeable fiber network structures for fog harvesting
,”
Langmuir
29
,
13269
13277
(
2013
).
43.
Y.
Jiang
,
C.
Machado
,
S.
Savarirayan
,
N.
Patankar
, and
K.
Park
, “
Onset time of fog collection
,”
Soft Matter
15
,
6779
6783
(
2019
).
44.
L.
Tanner
, “
The spreading of silicone oil drops on horizontal surfaces
,”
J. Phys. D: Appl. Phys.
12
,
1473
(
1979
).
45.
R.
Hoffman
, “
A study of the advancing interface
,”
J. Colloid Interface Sci.
50
,
228
241
(
1975
).
46.
S.
Daniel
and
M.
Chaudhury
, “
Rectified motion of liquid drops on gradient surfaces induced by vibration
,”
Langmuir
18
,
3404
3407
(
2002
).
47.
X.
Noblin
,
R.
Kofman
, and
F.
Celestini
, “
Ratchetlike motion of a shaken drop
,”
Phys. Rev. Lett.
102
,
194504
(
2009
).
48.
P.
Sartori
,
D.
Quagliati
,
S.
Varagnolo
,
M.
Pierno
,
G.
Mistura
,
F.
Magaletti
, and
C.
Casciola
, “
Drop motion induced by vertical vibrations
,”
New J. Phys.
17
,
113017
(
2015
).
49.
R.
Deegan
, “
Climbing a slippery slope
,”
J. Fluid Mech.
882
,
F1
(
2020
).

Supplementary Material

You do not currently have access to this content.