The droplet impact process on a solid surface is divided into a spreading phase where the droplet reaches the maximum deformation followed by a retracting phase. However, in the case of surfaces with high contact angle hysteresis, these two phases are connected by a relaxation phase where the contact angle changes from the advancing to the receding contact angle almost without motion of the contact line. Although the relaxation time can represent a significant part of the total droplet contact time, this relaxation regime has been less explored, especially for superhydrophobic surfaces due to the challenge of designing such surfaces with controlled wetting properties. Here, we show that for superhydrophobic surfaces with large contact angle hysteresis, the relaxation time can be comparable to the spreading and retracting time. Our results indicate that both the contact angle hysteresis and the capillary forces play a major role in defining the relaxation time and that relaxation time scales with the inertial–capillary time when using the droplet relative deformation as the characteristic length scale for this relaxation regime.

1.
A. L.
Yarin
, “
Drop impact dynamics: Splashing, spreading, receding, bouncing
,”
Annu. Rev. Fluid Mech.
38
,
159
192
(
2006
).
2.
M.
Cao
,
D.
Guo
,
C.
Yu
,
K.
Li
,
M.
Liu
, and
L.
Jiang
, “
Water-repellent properties of superhydrophobic and lubricant-infused ‘slippery’ surfaces: A brief study on the functions and applications
,”
ACS Appl. Mater. Interfaces
8
,
3615
3623
(
2016
).
3.
Y.
Liu
,
X.
Yan
, and
Z.
Wang
, “
Droplet dynamics on slippery surfaces: Small droplet, big impact
,”
Biosurf. Biotribol.
5
,
35
45
(
2019
).
4.
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
).
5.
C.
Josserand
and
S. T.
Thoroddsen
, “
Drop impact on a solid surface
,”
Annu. Rev. Fluid Mech.
48
,
365
391
(
2016
).
6.
L.
Mishchenko
,
B.
Hatton
,
V.
Bahadur
,
J. A.
Taylor
,
T.
Krupenkin
, and
J.
Aizenberg
, “
Design of ice-free nanostructured surfaces based on repulsion of impacting water droplets
,”
ACS Nano
4
,
7699
7707
(
2010
).
7.
X.
Wang
,
J.
Zeng
,
X.
Yu
, and
Y.
Zhang
, “
Superamphiphobic coatings with polymer-wrapped particles: Enhancing water harvesting
,”
J. Mater. Chem. A
7
,
5426
5433
(
2019
).
8.
V.
Bergeron
,
D.
Bonn
,
J. Y.
Martin
, and
L.
Vovelle
, “
Controlling droplet deposition with polymer additives
,”
Nature
405
,
772
775
(
2000
).
9.
P.
Galliker
,
J.
Schneider
,
H.
Eghlidi
,
S.
Kress
,
V.
Sandoghdar
, and
D.
Poulikakos
, “
Direct printing of nanostructures by electrostatic autofocussing of ink nanodroplets
,”
Nat. Commun.
3
,
890
(
2012
).
10.
B.-J. D.
Gans
,
P. C.
Duineveld
, and
U. S.
Schubert
, “
Inkjet printing of polymers: State of the art and future developments
,”
Adv. Mater.
16
,
203
213
(
2004
).
11.
D.
Richard
and
D.
Quéré
, “
Bouncing water drops
,”
Europhys. Lett.
50
,
769
775
(
2000
).
12.
J. C.
Bird
,
R.
Dhiman
,
H.-M.
Kwon
, and
K. K.
Varanasi
, “
Reducing the contact time of a bouncing drop
,”
Nature
503
,
385
388
(
2013
).
13.
F.
Chu
,
X.
Wu
,
Y.
Zhu
, and
Z.
Yuan
, “
Relationship between condensed droplet coalescence and surface wettability
,”
Int. J. Heat Mass Transfer
111
,
836
841
(
2017
).
14.
C.
Guo
,
L.
Liu
, and
C.
Liu
, “
Contact time of impacting droplets on a superhydrophobic surface with tunable curvature and groove orientation
,”
J. Phys.
34
,
095001
(
2022
).
15.
F.
Chu
,
S.
Li
,
Z.
Hu
, and
X.
Wu
, “
Regulation of droplet impacting on superhydrophobic surfaces: Coupled effects of macrostructures, wettability patterns, and surface motion
,”
Appl. Phys. Lett.
122
,
160503
(
2023
).
16.
F.
Boyer
,
E.
Sandoval-Nava
,
J. H.
Snoeijer
,
J. F.
Dijksman
, and
D.
Lohse
, “
Drop impact of shear thickening liquids
,”
Phys. Rev. Fluids
1
,
013901
(
2016
).
17.
M.
Aytouna
,
D.
Bartolo
,
G.
Wegdam
,
D.
Bonn
, and
S.
Rafaï
, “
Impact dynamics of surfactant laden drops: Dynamic surface tension effects
,”
Experiments Fluids
48
,
49
57
(
2010
).
18.
D.
Izbassarov
and
M.
Muradoglu
, “
Effects of viscoelasticity on drop impact and spreading on a solid surface
,”
Phys. Rev. Fluids
1
,
023302
(
2016
).
19.
M.
Song
,
H.
Zhao
,
T.
Wang
,
S.
Wang
,
J.
Wan
,
X.
Qin
, and
Z.
Wang
, “
A new scaling number reveals droplet dynamics on vibratory surfaces
,”
J. Colloid Interface Sci.
608
,
2414
2420
(
2022
).
20.
L.
Chen
,
E.
Bonaccurso
,
P.
Deng
, and
H.
Zhang
, “
Droplet impact on soft viscoelastic surfaces
,”
Phys. Rev. E
94
,
063117
(
2016
).
21.
S.
Shi
,
C.
Lv
, and
Q.
Zheng
, “
Temperature-regulated adhesion of impacting drops on nano/microtextured monostable superrepellent surfaces
,”
Soft Matter
16
,
5388
5397
(
2020
).
22.
A.
Gauthier
,
S.
Symon
,
C.
Clanet
, and
D.
Quéré
, “
Water impacting on superhydrophobic macrotextures
,”
Nat. Commun.
6
,
8001
(
2015
).
23.
S.
Lin
,
B.
Zhao
,
S.
Zou
,
J.
Guo
,
Z.
Wei
, and
L.
Chen
, “
Impact of viscous droplets on different wettable surfaces: Impact phenomena, the maximum spreading factor, spreading time and post-impact oscillation
,”
J. Colloid Interface Sci.
516
,
86
97
(
2018
).
24.
T. M.
Schutzius
,
S.
Jung
,
T.
Maitra
,
G.
Graeber
,
M.
Köhme
, and
D.
Poulikakos
, “
Spontaneous droplet trampolining on rigid superhydrophobic surfaces
,”
Nature
527
,
82
85
(
2015
).
25.
H.
Lambley
,
T. M.
Schutzius
, and
D.
Poulikakos
, “
Superhydrophobic surfaces for extreme environmental conditions
,”
Proc. Natl. Acad. Sci. U. S. A.
117
,
27188
27194
(
2020
).
26.
M.
Pasandideh-Fard
,
Y. M.
Qiao
,
S.
Chandra
, and
J.
Mostaghimi
, “
Capillary effects during droplet impact on a solid surface
,”
Phys. Fluids
8
,
650
659
(
1996
).
27.
C.
Clanet
,
C.
Béguin
,
D.
Ricahrd
, and
D.
Quéré
, “
Maximal deformation of an impacting drop
,”
J. Fluid Mech.
517
,
199
208
(
2004
).
28.
D.
Bartolo
,
C.
Josserand
, and
D.
Bonn
, “
Retraction dynamics of aqueous drops upon impact on non-wetting surfaces
,”
J. Fluid Mech.
545
,
329
338
(
2005
).
29.
C.
Antonini
,
A.
Amirfazli
, and
M.
Marengo
, “
Drop impact and wettability: From hydrophilic to superhydrophobic surfaces
,”
Phys. Fluids
24
,
102104
(
2012
).
30.
F.
Wang
and
T.
Fang
, “
Retraction dynamics of water droplets after impacting upon solid surfaces from hydrophilic to superhydrophobic
,”
Phys. Rev. Fluids
5
,
033604
(
2020
).
31.
C.
Antonini
,
F.
Villa
,
I.
Bernagozzi
,
A.
Amirfazli
, and
M.
Marengo
, “
Drop rebound after impact: The role of the receding contact angle
,”
Langmuir
29
,
16045
16050
(
2013
).
32.
H.-J.
Butt
,
J.
Liu
,
K.
Koynov
,
B.
Straub
,
C.
Hinduja
,
I.
Roismann
,
R.
Berger
,
X.
Li
,
D.
Vollmer
,
W.
Steffen
, and
M.
Kappl
, “
Contact angle hysteresis
,”
Curr. Opin. Colloid Interface Sci.
59
,
101574
(
2022
).
33.
M.
Abolghasemibizaki
and
R.
Mohammadi
, “
Droplet impact on superhydrophobic surfaces fully decorated with cylindrical macrotextures
,”
J. Colloid Interface Sci.
509
,
422
431
(
2018
).
34.
B.
Zhang
,
V.
Sanjay
,
S.
Shi
,
Y.
Zhao
,
C.
Lv
,
X.-Q.
Feng
, and
D.
Lohse
, “
Impact forces of water drops falling on superhydrophobic surfaces
,”
Phys. Rev. Lett.
129
,
104501
(
2022
).
You do not currently have access to this content.