Impacts of liquid droplets with another stationary droplet resting on a surface are important basic processes in many applications such as agricultural sprays, spray cooling, and inkjet printing. We investigated the head-on collision of unequal-size droplets of the same liquid on wetting surfaces both experimentally and theoretically at different size ratios and low-impact Weber numbers (We). A series of high-speed camera images showing representative sequences of collision processes for greatly different size ratios are analyzed. Different collision outcomes such as coalescence, bouncing, and partial coalescence–partial bouncing are analyzed thoroughly. Four different stages are identified for characterizing the complete bouncing process during the impact of unequal-size droplets on a solid surface. Subsequently, an analytical model based on energy balance is developed to calculate the maximum spread diameter and restitution coefficient of falling droplets, and compared with experimental data, satisfactory qualitative agreements are obtained. Results show that the dimensionless maximum spread diameter of falling droplets depends weakly on We and it is small for a higher size ratio. The restitution coefficient does not change significantly at a higher size ratio at a fixed We despite more viscous dissipation in bigger sessile droplets and it scales with We−1/2.

1.
V.
Bergeron
,
D.
Bonn
,
J. Y.
Martin
, and
L.
Vovelle
, “
Controlling droplet deposition with polymer additives
,”
Nature
405
,
772
(
2000
).
2.
R. J.
Gilliom
,
J. E.
Barbash
,
C. G.
Crawford
,
P. A.
Hamilton
,
J. D.
Martin
,
N.
Nakagaki
,
L. H.
Nowell
,
J. C.
Scott
,
P. E.
Stackelberg
, and
G. P.
Thelin
, “
Pesticides in the nation's streams and ground water 1992–2001
,”
Circular Report No. 1291
, The Quality of Our Nation's Waters (
U.S. Geological Survey
,
2006
), p.
184
.
3.
M.
Massinon
and
F.
Lebeau
, “
Comparison of spray retention on synthetic superhydrophobic surface with retention on outdoor grown wheat leaves
,” in
Proceedings of the Aspects 114 International Advances in Pesticide Application
(
Association of Applied Biologists
,
Warwick, United Kingdom
,
2012
).
4.
H.
Wijshoff
, “
The dynamics of the piezo inkjet printhead operation
,”
Phys. Rep.
491
(
4–5
),
77
(
2010
).
5.
J. Z.
Wang
,
Z. H.
Zheng
,
H. W.
Li
,
W. T. S.
Huck
, and
H.
Sirringhaus
, “
Dewetting of conducting polymer inkjet droplets on patterned surfaces
,”
Nat. Mater.
3
(
3
),
171
(
2004
).
6.
D.
Soltman
and
D. V.
Subramanian
, “
Inkjet-printed line morphologies and temperature control of the coffee ring effect
,”
Langmuir
24
(
5
),
2224
(
2008
).
7.
J.
Adam
,
N.
Lindblad
, and
C.
Hendricks
, “
The collision, coalescence, and disruption of water droplets
,”
J. Appl. Phys.
39
(
11
),
5173
(
1968
).
8.
N.
Ashgriz
and
J.
Poo
, “
Coalescence and separation in binary collisions of liquid drops
,”
J. Fluid Mech.
221
,
183
(
1990
).
9.
Y. J.
Jiang
,
A.
Umemura
, and
C. K.
Law
, “
An experimental investigation on the collision behavior of hydrocarbon droplets
,”
J. Fluid Mech.
234
,
171
(
1992
).
10.
J.
Qian
and
C. K.
Law
, “
Regimes of coalescence and separation in droplet collision
,”
J. Fluid Mech.
331
,
59
(
1997
).
11.
K. L.
Pan
,
P. C.
Chou
, and
Y. J.
Tseng
, “
Binary droplet collision at high Weber number
,”
Phys. Rev. E
80
(
3
),
036301
(
2009
).
12.
R. H.
Chen
, “
Diesel–diesel and diesel–ethanol drop collisions
,”
Appl. Therm. Eng.
27
(
2–3
),
604
(
2007
).
13.
C.
Tang
,
P.
Zhang
, and
C. K.
Law
, “
Bouncing, coalescence, and separation in head-on collision of unequal-size droplets
,”
Phys. Fluids
24
(
2
),
022101
(
2012
).
14.
H.
Deka
,
G.
Biswas
,
S.
Chakraborty
, and
A.
Dalal
, “
Coalescence dynamics of unequal sized drops
,”
Phys. Fluids
31
(
1
),
012105
(
2019
).
15.
G. S.
Chaitanya
,
K. C.
Sahu
, and
G.
Biswas
, “
A study of two unequal-sized droplets undergoing oblique collision
,”
Phys. Fluids
33
(
2
),
022110
(
2021
).
16.
R.
Rioboo
,
C.
Tropea
, and
M.
Marengo
, “
Outcomes from a drop impact on solid surfaces
,”
Atomization Sprays
11
(
2
),
155
(
2001
).
17.
A. L.
Yarin
, “
Drop impact dynamics: Splashing, spreading, receding, bouncing
,”
Annu. Rev. Fluid Mech.
38
(
1
),
159
(
2006
).
18.
Y.
Renardy
,
S.
Popinet
,
L.
Duchemin
,
M.
Renardy
,
S.
Zaleski
,
C.
Josserand
,
M. A.
Drumright-Clarke
,
D.
Richard
,
C.
Clanet
, and
D.
Quéré
, “
Pyramidal and toroidal water drops after impact on a solid surface
,”
J. Fluid Mech.
484
,
69
(
2003
).
19.
C.
Josserand
and
S. T.
Thoroddsen
, “
Drop impact on a solid surface
,”
Annu. Rev. Fluid Mech.
48
(
1
),
365
(
2016
).
20.
C.
Clanet
,
C.
Béguin
,
D.
Richard
, and
D.
Quéré
, “
Maximal deformation of an impacting drop
,”
J. Fluid Mech.
517
,
199
(
2004
).
21.
S.
Wildeman
,
C. W.
Visser
,
C.
Sun
, and
D.
Lohse
, “
On the spreading of impacting drops
,”
J. Fluid Mech.
805
,
636
(
2016
).
22.
D.
Richard
and
D.
Quéré
, “
Bouncing water drops
,”
Europhys. Lett.
50
(
6
),
769
(
2000
).
23.
F. C.
Wang
,
J. T.
Feng
, and
Y. P.
Zhao
, “
The head-on colliding process of binary liquid droplets at low velocity: High-speed photography experiments and modeling
,”
J. Colloid Interface Sci.
326
(
1
),
196
(
2008
).
24.
J.
Wakefield
,
C. F.
Tilger
, and
M. A.
Oehlschlaeger
, “
The interaction of falling and sessile drops on a hydrophobic surface
,”
Exp. Therm. Fluid Sci.
79
,
36
(
2016
).
25.
M.
Damak
and
K.
Varanasi
, “
Expansion and retraction dynamics in drop-on-drop impacts on nonwetting surfaces
,”
Phys. Rev. Fluids
3
(
9
),
093602
(
2018
).
26.
O.
Ramírez-Soto
,
V.
Sanjay
,
D.
Lohse
,
J. T.
Pham
, and
D.
Vollmer
, “
Lifting a sessile oil drop from a superamphiphobic surface with an impacting one
,”
Sci. Adv.
6
(
34
),
eaba4330
(
2020
).
27.
M.
Kumar
,
R.
Bhardwaj
, and
K. C.
Sahu
, “
Coalescence dynamics of a droplet on a sessile droplet
,”
Phys. Fluids
32
(
1
),
012104
(
2020
).
28.
A. K.
Jaiswal
and
S.
Khandekar
, “
Drop-on-drop impact dynamics on a superhydrophobic surface
,”
Langmuir
37
(
43
),
12629
(
2021
).
29.
W.
Yu
,
D.
Zhu
,
W.
Wang
,
Z.
Yu
,
S.
Chen
, and
J.
Zhao
, “
The rebounding-coalescing behaviors in drop-on-drop impact on a superhydrophobic surface
,”
Appl. Phys. Lett.
121
(
6
),
061602
(
2022
).
30.
A. L.
Xing
,
B. J.
Li
,
C. M.
Jiang
, and
D. L.
Zhao
, “
Simulation of coalescence dynamics of droplets on surfaces with different wettabilities
,”
Phys. Fluids
34
(
7
),
072114
(
2022
).
31.
D.
Chen
,
T.
Wang
,
L.
Ming
,
M.
Qiu
, and
Z.
Lin
, “
Dynamic characteristics of moving droplets impacting sessile droplets with different Reynolds numbers
,”
Phys. Fluids
34
(
11
),
117120
(
2022
).
32.
G.
Guggilla
,
A.
Pattamatta
, and
R.
Narayanaswamy
, “
Numerical investigation into the evaporation dynamics of drop-on-drop collisions over heated wetting surfaces
,”
Int. J. Heat Mass Transfer
123
,
1050
(
2018
).
33.
G.
Guggilla
,
R.
Narayanaswamy
,
P.
Stephan
, and
A.
Pattamatta
, “
Influence of flow rate and surface thickness on heat transfer characteristics of two consecutively impinging droplets on a heated surface
,”
Int. J. Heat Mass Transfer
165
,
120688
(
2021
).
34.
M.
Abouelsoud
and
B.
Bai
, “
Bouncing and coalescence dynamics during the impact of a falling drop with a sessile drop on different solid surfaces
,”
Phys. Fluids
33
(
6
),
063309
(
2021
).
35.
M.
Abouelsoud
,
V. A.
Thale
,
A. N.
Shmroukh
, and
B.
Bai
, “
Spreading and retraction of the concentric impact of a drop with a sessile drop of the same liquid: Effect of surface wettability
,”
Phys. Fluids
34
(
11
),
112108
(
2022
).
36.
P. G.
De Gennes
,
F.
Brochard-Wyart
, and
D.
Quéré
,
Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves
(
Springer
,
New York
,
2004
).
37.
A. L.
Biance
,
F.
Chevy
,
C.
Clanet
,
G.
Lagubeau
, and
D.
Quéré
, “
On the elasticity of an inertial liquid shock
,”
J. Fluid Mech.
554
,
47
(
2006
).
38.
C.
Hao
,
J.
Li
,
Y.
Liu
,
X.
Zhou
,
Y.
Liu
,
R.
Liu
,
R.
Che
,
W.
Zhou
,
D.
Sun
,
L.
Li
,
L.
Xu
, and
Z.
Wang
, “
Superhydrophobic-like tunable droplet bouncing on slippery liquid interfaces
,”
Nat. Commun.
6
(
1
),
7986
(
2015
).
39.
D.
Richard
,
C.
Clanet
, and
D.
Quéré
, “
Contact time of a bouncing drop
,”
Nature
417
(
6891
),
811
(
2002
).
40.
A.
Gauthier
,
S.
Symon
,
C.
Clanet
, and
D.
Quéré
, “
Water impacting on superhydrophobic macrotextures
,”
Nat. Commun.
6
(
1
),
8001
(
2015
).
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