The impact dynamics of a water droplet on a flexible substrate is useful for designing pesticide sprays and understanding insects flying in rainfall. We experimentally analyze the impact dynamics of a microliter water droplet on a superhydrophobic cantilever beam for Weber number in the range of 30–76. A thin copper sheet was coated with a commercial coating to render it superhydrophobic and high-speed imaging was used for visualization. During the impact, the spreading droplet converts its inertial energy into surface energy and elastic energy of the substrate. While retraction of the contact line, the latter energies convert to the kinetic energy of the droplet, and the droplet could bounce off the deforming cantilever beam. The characteristics timescales of droplet and cantilever beams are varied by changing the droplet diameter and impact velocity, and beam length, respectively. We show that the overall system dynamics, i.e., bouncing of the droplet and oscillations of the cantilever, is dependent on the interplay of these two timescales. A spring-mass system has been used to model this coupling and to explain the experimental observations. These findings can help to design systems to achieve desirable contact time, droplet rebound kinetic energy, energy transfer to the cantilever beam, and the droplet spreading diameter.
References
1.
S. D.
Hoath
, Fundamentals of Inkjet Printing: The Science of Inkjet and Droplets
(John Wiley & Sons
, 2016
).2.
3.
R.
Andrade
, O.
Skurtys
, and F.
Osorio
, “Drop impact behavior on food using spray coating: Fundamentals and applications
,” Food Res. Int.
54
(1
), 397
–405
(2013
).4.
M.
Ma
and R. M.
Hill
, “Superhydrophobic surfaces
,” Curr. Opin. Colloid Interface Sci.
11
(4
), 193
–202
(2006
).5.
S.
Nishimoto
and B.
Bhushan
, “Bioinspired self-cleaning surfaces with superhydrophobicity, superoleophobicity, and superhydrophilicity
,” RSC Adv.
3
(3
), 671
–690
(2013
).6.
K.
Liu
and L.
Jiang
, “Bio-inspired self-cleaning surfaces
,” Annu. Rev. Mater. Res.
42
, 231
–263
(2012
).7.
L.
Cao
, A. K.
Jones
, V. K.
Sikka
, J.
Wu
, and D.
Gao
, “Anti-icing superhydrophobic coatings
,” Langmuir
25
(21
), 12444
–12448
(2009
).8.
S.
Farhadi
, M.
Farzaneh
, and S. A.
Kulinich
, “Anti-icing performance of superhydrophobic surfaces
,” Appl. Surf. Sci.
257
(14
), 6264
–6269
(2011
).9.
P. G.
Bange
and R.
Bhardwaj
, “Computational study of bouncing and non-bouncing droplets impacting on superhydrophobic surfaces
,” Theor. Comput. Fluid Dyn.
30
(3
), 211
–235
(2016
).10.
D.
Richard
, C.
Clanet
, and D.
Quéré
, “Contact time of a bouncing drop
,” Nature
417
(6891
), 811
(2002
).11.
Y.
Liu
, L.
Moevius
, X.
Xu
, T.
Qian
, J. M.
Yeomans
, and Z.
Wang
, “Pancake bouncing on superhydrophobic surfaces
,” Nat. Phys.
10
(7
), 515
–519
(2014
).12.
J. C.
Bird
, R.
Dhiman
, H.-M.
Kwon
, and K. K.
Varanasi
, “Reducing the contact time of a bouncing drop
,” Nature
503
(7476
), 385
–388
(2013
).13.
A. L.
Yarin
, “Drop impact dynamics: Splashing, spreading, receding, bouncing…
,” Annu. Rev. Fluid Mech.
38
, 159
–192
(2006
).14.
C.
Josserand
and S. T.
Thoroddsen
, “Drop impact on a solid surface
,” Annu. Rev. Fluid Mech.
48
, 365
–391
(2016
).15.
N. D.
Patil
, R.
Bhardwaj
, and A.
Sharma
, “Droplet impact dynamics on micropillared hydrophobic surfaces
,” Exp. Therm. Fluid Sci.
74
, 195
–206
(2016
).16.
L. K.
Malla
, N. D.
Patil
, R.
Bhardwaj
, and A.
Neild
, “Droplet bouncing and breakup during impact on a microgrooved surface
,” Langmuir
33
(38
), 9620
–9631
(2017
).17.
M.
Kumar
and R.
Bhardwaj
, “Wetting characteristics of colocasia esculenta (taro) leaf and a bioinspired surface thereof
,” Sci. Rep.
10
(1
), 1
–15
(2020
).18.
A. A.
Alhareth
and S. T.
Thoroddsen
, “Partial coalescence of a drop on a larger-viscosity pool
,” Phys. Fluids
32
(12
), 122115
(2020
).19.
M.
Kumar
, R.
Bhardwaj
, and K. C.
Sahu
, “Coalescence dynamics of a droplet on a sessile droplet
,” Phys. Fluids
32
(1
), 012104
(2020
).20.
P.
Zhu
, W.
Wang
, X.
Chen
, F.
Lin
, X.
Wei
, C.
Ji
, and J.
Zou
, “Experimental study of drop impact on a thin fiber
,” Phys. Fluids
31
(10
), 107102
(2019
).21.
M.
Damak
, S. R.
Mahmoudi
, M. N.
Hyder
, and K. K.
Varanasi
, “Enhancing droplet deposition through in-situ precipitation
,” Nat. Commun.
7
(1
), 1
–9
(2016
).22.
M.
Massinon
and F.
Lebeau
, “Experimental method for the assessment of agricultural spray retention based on high-speed imaging of drop impact on a synthetic superhydrophobic surface
,” Biosyst. Eng.
112
(1
), 56
–64
(2012
).23.
M.
Song
, J.
Ju
, S.
Luo
, Y.
Han
, Z.
Dong
, Y.
Wang
, Z.
Gu
, L.
Zhang
, R.
Hao
, and L.
Jiang
, “Controlling liquid splash on superhydrophobic surfaces by a vesicle surfactant
,” Sci. Adv.
3
(3
), e1602188
(2017
).24.
X.
Zhang
and O. A.
Basaran
, “Dynamic surface tension effects in impact of a drop with a solid surface
,” J. Colloid Interface Sci.
187
(1
), 166
–178
(1997
).25.
H.
Jafernika
, “The safety of unmanned aerial vehicle (uav) missions in storm and precipitation areas
,” Saf. Fire Technol.
54
(2
), 194
–204
(2019
).26.
D.
Soto
, A. B.
De Lariviere
, X.
Boutillon
, C.
Clanet
, and D.
Quéré
, “The force of impacting rain
,” Soft Matter
10
(27
), 4929
–4934
(2014
).27.
S.
Gart
, J. E.
Mates
, C. M.
Megaridis
, and S.
Jung
, “Droplet impacting a cantilever: A leaf-raindrop system
,” Phys. Rev. Appl.
3
(4
), 044019
(2015
).28.
X.
Huang
, X.
Dong
, J.
Li
, and J.
Liu
, “Droplet impact induced large deflection of a cantilever
,” Phys. Fluids
31
(6
), 062106
(2019
).29.
S.
Mangili
, C.
Antonini
, M.
Marengo
, and A.
Amirfazli
, “Understanding the drop impact phenomenon on soft pdms substrates
,” Soft Matter
8
(39
), 10045
–10054
(2012
).30.
J.
Bico
, É.
Reyssat
, and B.
Roman
, “Elastocapillarity: When surface tension deforms elastic solids
,” Annu. Rev. Fluid Mech.
50
, 629
–659
(2018
).31.
S.
Chen
and V.
Bertola
, “Drop impact on spherical soft surfaces
,” Phys. Fluids
29
(8
), 082106
(2017
).32.
H.
Chen
, X.
Zhang
, B. D.
Garcia
, A.
Georgoulas
, M.
Deflorin
, Q.
Liu
, M.
Marengo
, Z.
Xu
, and A.
Amirfazli
, “Drop impact onto a cantilever beam: Behavior of the lamella and force measurement
,” Interfacial Phenom. Heat Transfer
7
(1
), 85
(2019
).33.
T.
Vasileiou
, J.
Gerber
, J.
Prautzsch
, T. M.
Schutzius
, and D.
Poulikakos
, “Superhydrophobicity enhancement through substrate flexibility
,” Proc. Natl. Acad. Sci. U. S. A.
113
(47
), 13307
–13312
(2016
).34.
T.
Vasileiou
, T. M.
Schutzius
, and D.
Poulikakos
, “Imparting icephobicity with substrate flexibility
,” Langmuir
33
(27
), 6708
–6718
(2017
).35.
R. E.
Pepper
, L.
Courbin
, and H. A.
Stone
, “Splashing on elastic membranes: The importance of early-time dynamics
,” Phys. Fluids
20
(8
), 082103
(2008
).36.
M.
Pegg
, R.
Purvis
, and A.
Korobkin
, “Droplet impact onto an elastic plate: A new mechanism for splashing
,” J. Fluid Mech.
839
, 561
–593
(2018
).37.
T. I.
Khabakhpasheva
and A. A.
Korobkin
, “Splashing of liquid droplet on a vibrating substrate
,” Phys. Fluids
32
(12
), 122109
(2020
).38.
P. B.
Weisensee
, J.
Tian
, N.
Miljkovic
, and W. P.
King
, “Water droplet impact on elastic superhydrophobic surfaces
,” Sci. Rep.
6
, 30328
(2016
).39.
J.-H.
Kim
, J. P.
Rothstein
, and J. K.
Shang
, “Dynamics of a flexible superhydrophobic surface during a drop impact
,” Phys. Fluids
30
(7
), 072102
(2018
).40.
P.
Chantelot
, M.
Coux
, C.
Clanet
, and D.
Quéré
, “Drop trampoline
,” EPL
124
(2
), 24003
(2018
).41.
M.
Shoji
and X.
Zhang Yi
, “Study of contact angle hysteresis: In relation to boiling surface wettability
,” JSME Int. J., Ser. B
37
(3
), 560
–567
(1994
).42.
L.
Rayleigh
, “On the stability, or instability, of certain fluid motions
,” Proc. London Math. Soc.
s1-11
(1
), 57
–72
(1879
).43.
A.
Jha
, P.
Chantelot
, C.
Clanet
, and D.
Quéré
, “Viscous bouncing
,” Soft Matter
16
(31
), 7270
–7273
(2020
).44.
W.
Thomson
, Theory of Vibration with Applications
(CRC Press
, 2018
).45.
C.
Clanet
, C.
Béguin
, D.
Richard
, and D.
Quéré
, “Maximal deformation of an impacting drop
,” J. Fluid Mech.
517
, 199
(2004
).46.
X.
Dong
, X.
Huang
, and J.
Liu
, “Modeling and simulation of droplet impact on elastic beams based on sph
,” Eur. J. Mech.-A/Solids
75
, 237
–257
(2019
).© 2021 Author(s).
2021
Author(s)
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