Drop impact on superhydrophobic surfaces has gained great attention because of its physics and application in water repellency, drag reduction, and anti-icing. Spreading lengths and the contact time are the crucial parameters determining the extend of drop–surface interaction and effective heat transfer between the two and are, hence, trivial to many engineering applications. Post-collisional dynamics over cylindrical geometries are quite different from that of the flat surfaces due to the asymmetry in spreading and retraction dynamics. The dynamics are mainly governed by the impact Weber number and curvature ratio of impacting surface to drop. The spreading dynamics in axial direction is found to be fairly predicted by the governing laws coined for flat surfaces. However, the spreading dynamics in the azimuthal direction is quite complex. Herein, we propose a simple scaling analysis for the spreading dynamics in the azimuthal direction as well as for the contact time of the impacting drop with the surface. A modified capillary length is proposed accounting the curvature effect of the substrate by incorporating a centrifugal component of acceleration for the expanding lamella over the curved surface. With the proposed modified capillary length, a universal scaling relationship for azimuthal spreading length and contact time is developed. The proposed scaling laws are found to be in good agreement with the experimental results from the present study as well as with the existing literature for a wide range of Weber numbers and surface curvature.
REFERENCES
1.
C.
Antonini
,
A.
Amirfazli
, and
M.
Marengo
, “
Drop impact and wettability: From hydrophilic to superhydrophobic surfaces
,” Phys. Fluids
24
, 102104
(2012
).2.
C.
Josserand
and
S. T.
Thoroddsen
, “
Drop impact on a solid surface
,” Annu. Rev. Fluid Mech.
48
, 365
–391
(2016
).3.
H.
Zhao
,
D.
Orejon
,
C.
Mackenzie-Dover
,
P.
Valluri
,
M. E.
Shanahan
, and
K.
Sefiane
, “
Droplet motion on contrasting striated surfaces
,” Appl. Phys. Lett.
116
, 251604
(2020
).4.
P. T.
Naveen
,
K.
Ashish
,
A. S.
Hegde
, and
A. R.
Harikrishnan
, “
Confined evaporation-mediated enhanced residence time of levitated water drops over deep oil pools
,” Langmuir
37
, 14472
–14482
(2021
).5.
A.
Mohammad Karim
, “
Physics of droplet impact on various substrates and its current advancements in interfacial science: A review
,” J. Appl. Phys.
133
, 030701
(2023
).6.
C.
Clanet
,
C.
Béguin
,
D.
Richard
, and
D.
Quéré
, “
Maximal deformation of an impacting drop
,” J. Fluid Mech.
517
, 199
–208
(2004
).7.
Y.
Liu
,
M.
Andrew
,
J.
Li
,
J. M.
Yeomans
, and
Z.
Wang
, “
Symmetry breaking in drop bouncing on curved surfaces
,” Nat. Commun.
6
, 1
–8
(2015
).8.
K.
Chaudhury
and
S.
Chakraborty
, “
Spreading of a droplet over a nonisothermal substrate: Multiple scaling regimes
,” Langmuir
31
, 4169
–4175
(2015
).9.
R. S.
Rajesh
,
P. T.
Naveen
,
K.
Krishnakumar
, and
S. K.
Ranjith
, “
Dynamics of single droplet impact on cylindrically-curved superheated surfaces
,” Exp. Therm. Fluid Sci.
101
, 251
–262
(2019
).10.
D.
Khojasteh
,
A.
Bordbar
,
R.
Kamali
, and
M.
Marengo
, “
Curvature effect on droplet impacting onto hydrophobic and superhydrophobic spheres
,” Int. J. Comput. Fluid Dyn.
31
, 310
–323
(2017
).11.
H.
Zhang
,
X.
Yi
,
Y.
Du
,
R.
Zhang
,
X.
Zhang
,
F.
He
,
F.
Niu
, and
P.
Hao
, “
Dynamic behavior of water drops impacting on cylindrical superhydrophobic surfaces
,” Phys. Fluids
31
, 032104
(2019
).12.
P. T.
Naveen
,
R. R.
Simhadri
, and
S. K.
Ranjith
, “
Simultaneous effect of droplet temperature and surface wettability on single drop impact dynamics
,” Fluid Dyn.
55
, 640
–652
(2020
).13.
X.
Zhang
,
Z.
Zhu
,
C.
Zhang
, and
C.
Yang
, “
Reduced contact time of a droplet impacting on a moving superhydrophobic surface
,” Appl. Phys. Lett.
117
, 151602
(2020
).14.
N.
Sahoo
,
G.
Khurana
,
A.
Harikrishnan
,
D.
Samanta
, and
P.
Dhar
, “
Post impact droplet hydrodynamics on inclined planes of variant wettabilities
,” Eur. J. Mech. B
79
, 27
–37
(2020
).15.
S.
Nishimoto
and
B.
Bhushan
, “
Bioinspired self-cleaning surfaces with superhydrophobicity, superoleophobicity, and superhydrophilicity
,” RSC Adv.
3
, 671
–690
(2013
).16.
W.
Fang
,
K.
Zhang
,
Q.
Jiang
,
C.
Lv
,
C.
Sun
,
Q.
Li
,
Y.
Song
, and
X.-Q.
Feng
, “
Drop impact dynamics on solid surfaces
,” Appl. Phys. Lett.
121
, 210501
(2022
).17.
T.
Deng
,
K. K.
Varanasi
,
M.
Hsu
,
N.
Bhate
,
C.
Keimel
,
J.
Stein
, and
M.
Blohm
, “
Nonwetting of impinging droplets on textured surfaces
,” Appl. Phys. Lett.
94
, 133109
(2009
).18.
M.
Abolghasemibizaki
,
R. L.
McMasters
, and
R.
Mohammadi
, “
Towards the shortest possible contact time: Droplet impact on cylindrical superhydrophobic surfaces structured with macro-scale features
,” J. Colloid Interface Sci.
521
, 17
–23
(2018
).19.
M. A.
Samaha
and
M.
Gad-el Hak
, “
Slippery surfaces: A decade of progress
,” Phys. Fluids
33
, 071301
(2021
).20.
P. T.
Naveen
,
K.
Ashish
, and
A. R.
Harikrishnan
, “
Adverse impact of macro-textured superhydrophobicity on contact time reduction at high weber numbers
,” Colloids Surf. A
653
, 129948
(2022
).21.
I. V.
Roisman
,
R.
Rioboo
, and
C.
Tropea
, “
Normal impact of a liquid drop on a dry surface: Model for spreading and receding
,” Proc. R. Soc. London, Ser. A
458
, 1411
–1430
(2002
).22.
T.
Srivastava
and
S.
Kondaraju
, “
Analytical model for predicting maximum spread of droplet impinging on solid surfaces
,” Phys. Fluids
32
, 092103
(2020
).23.
Y. T.
Aksoy
,
P.
Eneren
,
E.
Koos
, and
M. R.
Vetrano
, “
Spreading of a droplet impacting on a smooth flat surface: How liquid viscosity influences the maximum spreading time and spreading ratio
,” Phys. Fluids
34
, 042106
(2022
).24.
D.
Richard
,
C.
Clanet
, and
D.
Quéré
, “
Contact time of a bouncing drop
,” Nature
417
, 811
–811
(2002
).25.
M.
Pasandideh-Fard
,
Y.
Qiao
,
S.
Chandra
, and
J.
Mostaghimi
, “
Capillary effects during droplet impact on a solid surface
,” Phys. Fluids
8
, 650
–659
(1996
).26.
H.
Zhang
,
X.
Zhang
,
X.
Yi
,
F.
He
,
F.
Niu
, and
P.
Hao
, “
Asymmetric splash and breakup of drops impacting on cylindrical superhydrophobic surfaces
,” Phys. Fluids
32
, 122108
(2020
).27.
S.
Khanzadeh Borjak
,
R.
Rafee
, and
M. S.
Valipour
, “
Experimental investigation of water droplet impact on the electrospun superhydrophobic cylindrical glass: Contact time, maximum spreading factor, and splash threshold
,” Langmuir
36
, 13498
–13508
(2020
).28.
J.
Han
,
W.
Kim
,
C.
Bae
,
D.
Lee
,
S.
Shin
,
Y.
Nam
, and
C.
Lee
, “
Contact time on curved superhydrophobic surfaces
,” Phys. Rev. E
101
, 043108
(2020
).29.
W.
Choi
and
S.
Yun
, “
Symmetry-breaking drop bouncing on superhydrophobic surfaces with continuously changing curvatures
,” Polymers
13
, 2940
(2021
).30.
C.
Guo
,
J.
Sun
,
Y.
Sun
,
M.
Wang
, and
D.
Zhao
, “
Droplet impact on cross-scale cylindrical superhydrophobic surfaces
,” Appl. Phys. Lett.
112
, 263702
(2018
).31.
G.
Khurana
,
N.
Sahoo
, and
P.
Dhar
, “
Post-collision hydrodynamics of droplets on cylindrical bodies of variant convexity and wettability
,” Phys. Fluids
31
, 022008
(2019
).32.
J.
Luo
,
S.-Y.
Wu
,
L.
Xiao
, and
Z.-L.
Chen
, “
The maximum spreading lengths in circumferential and axial directions when droplets impact on cylindrical surfaces
,” Int. J. Multiphase Flow
143
, 103774
(2021
).33.
G. I.
Taylor
, “
The dynamics of thin sheets of fluid. III. Disintegration of fluid sheets
,” Proc. R. Soc. London, Ser. A
253
, 313
–321
(1959
).34.
I. V.
Roisman
,
E.
Berberović
, and
C.
Tropea
, “
Inertia dominated drop collisions. I. On the universal flow in the lamella
,” Phys. Fluids
21
, 052103
(2009
).35.
S.
Kistler
and
L.
Scriven
, “
The teapot effect: Sheet-forming flows with deflection, wetting and hysteresis
,” J. Fluid Mech.
263
, 19
–62
(1994
).36.
C.
Duez
,
C.
Ybert
,
C.
Clanet
, and
L.
Bocquet
, “
Wetting controls separation of inertial flows from solid surfaces
,” Phys. Rev. Lett.
104
, 084503
(2010
).37.
E.
Jambon-Puillet
,
W.
Bouwhuis
,
J.
Snoeijer
, and
D.
Bonn
, “
Liquid helix: How capillary jets adhere to vertical cylinders
,” Phys. Rev. Lett.
122
, 184501
(2019
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
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