In order to advance the understanding of the process of droplet impact on wet surfaces, realized in various applications such as droplet-based coating methods (inkjet printing, aerosol-jet, and spray coating), we studied the impact of a dyed water droplet onto a clear water film. The color contrast in images allowed investigation of mixing process of the like liquids during the rapid dynamic stage and beyond. Four Weber numbers (We), in the range of 121–304, and four dimensionless film thickness to droplet diameter ratios (h*), in the range of 0.092–0.367, were considered. The aforementioned numbers correspond to the film thickness of 0.4–1.6 mm, droplet size of 4.36 mm, and impact velocity of 1.4–2.2 m/s. While the experimental database is rather comprehensive and can be used for further detailed analysis, here we focused on less-explored topics of capillary surface waves formed outside the crater and found the wave characteristics and their role in mixing. Within the range of parameters studied here, we found that the outer capillary surface waves were created as a result of perturbing the liquid film by droplet impact, but the wave characteristics such as frequency (400-500 Hz) were not a strong function of the impact We number. We also observed six mixing mechanisms of miscible liquids, including the expansion/compression waves and turbulence created upon impact, stable crown wall formation with an acute wall angle, which causes a tsunami-type of flow, unstable crown leading to fingering and splashing, capillary waves, and molecular diffusion.

1.
M.
Eslamian
, “
Spray-on thin film PV solar cells: Advances, potentials and challenges
,”
Coatings
4
,
60
84
(
2014
).
2.
M.
Eslamian
, “
Inorganic and organic solution-processed thin film devices
,”
Nano-Micro Lett.
9
,
3
(
2017
).
3.
M.
Rein
, “
Phenomena of liquid drop impact on solid and liquid surfaces
,”
Fluid Dyn. Res.
12
,
61
93
(
1993
).
4.
A. L.
Yarin
, “
Drop impact dynamics: Splashing, spreading, receding, bouncing
,”
Annu. Rev. Fluid. Mech.
38
,
159
192
(
2006
).
5.
C.
Josserand
and
S. T.
Thoroddsen
, “
Drop impact on a solid surface
,”
Annu. Rev. Fluid Mech.
48
,
365
391
(
2016
).
6.
A. G.
Bick
,
W. D.
Ristenpart
,
A.
van Nierop
, and
H. A.
Stone
, “
Bubble formation via multidrop impacts
,”
Phys. Fluids
22
,
042105
(
2010
).
7.
M.
Rein
, “
Wave phenomena during droplet impact
,” in
IUTAM Symposium on Waves in Liquid/Gas and Liquid/Vapour Two-Phase Systems
, Fluid Mechanics and its Applications Vol. 31 (
Springer, Dordrecht
,
1994
), pp.
171
190
.
8.
C.
Tropea
and
M.
Marengo
, “
The impact of drops on walls and films
,”
Multiphase Sci. Technol.
11
,
19
36
(
1999
).
9.
A. M.
Worthington
, “
On impact with a liquid surface
,”
Proc. R. Soc. London
34
,
217
230
(
1883
).
10.
H. E.
Edgerton
and
J. R.
Killian
,
Flash! Seeing the Unseen by Ultra-High-Speed Photography
(
Boston
,
Branford
,
1954
).
11.
O. G.
Engel
, “
Initial pressure, initial flow velocity, and the time dependence of crater depth in fluid impacts
,”
J. Appl. Phys.
38
,
3935
(
1967
).
12.
W. C.
Macklin
and
G. J.
Metaxas
, “
Splashing of drops on liquid layers
,”
J. Appl. Phys.
47
,
3963
3970
(
1976
).
13.
G. E.
Cossali
,
A.
Coghe
, and
M.
Marengo
, “
The impact of a single drop on a wetted solid surface
,”
Exp. Fluids
22
,
463
472
(
1997
).
14.
D.
Sivakumar
and
C.
Tropea
, “
Splashing impact of a spray onto a liquid film
,”
Phys. Fluids
14
,
L85
(
2002
).
15.
R.
Rioboo
,
C.
Bauthier
,
J.
Conti
,
M.
Voue
, and
J.
De Coninck
, “
Experimental investigation of splash and crown formation during single drop impact on wetted surfaces
,”
Exp. Fluids
35
,
648
652
(
2003
).
16.
A.-B.
Wang
and
C.-C.
Chen
, “
Splashing impact of a single drop onto very thin liquid films
,”
Phys. Fluids
12
,
2155
(
2000
).
17.
A. I.
Fedorchenko
and
A.-B.
Wang
, “
On some common features of drop impact on liquid surfaces
,”
Phys. Fluids
16
,
1349
(
2004
).
18.
G. E.
Cossali
,
M.
Marengo
,
A.
Coghe
, and
S.
Zhdanov
, “
The role of time in single drop splash on thin film
,”
Exp. Fluids
36
,
888
900
(
2004
).
19.
T.
Okawa
,
T.
Shiraishi
, and
T.
Mori
, “
Production of secondary drops during the single water drop impact onto a plane water surface
,”
Exp. Fluids
41
,
965
974
(
2006
).
20.
H. N.
Oguz
and
A.
Prosperetti
, “
Bubble entrainment by the impact of drops on liquid surfaces
,”
J. Fluid Mech.
219
,
143
(
1990
).
21.
D. A.
Weiss
and
A. L.
Yarin
, “
Single drop impact onto liquid films: Neck distortion, jetting, tiny bubble entrainment, and crown formation
,”
J. Fluid Mech.
385
,
229
(
1999
).
22.
I. V.
Roisman
and
C.
Tropea
, “
Impact of a drop onto a wetted wall: Description of crown formation and propagation
,”
J. Fluid Mech.
472
,
373
397
(
2002
).
23.
M. R.
Davidson
, “
Spreading of an inviscid drop impacting on a liquid film
,”
Chem. Eng. Sci.
57
,
3639
3647
(
2002
).
24.
C.
Josserand
and
S.
Zaleski
, “
Droplet splashing on a thin liquid film
,”
Phys. Fluids
15
,
1650
(
2003
).
25.
E.
Berberović
,
N. P.
van Hinsberg
,
S.
Jakirlić
,
I. V.
Roisman
, and
C.
Tropea
, “
Drop impact onto a liquid layer of finite thickness: Dynamics of the cavity evolution
,”
Phys. Rev. E
79
,
036306
(
2009
).
26.
S. T.
Thoroddsen
,
T. G.
Etoh
, and
K.
Takehara
, “
Crown breakup by Marangoni instability
,”
J. Fluid Mech.
557
,
63
72
(
2006
).
27.
Z.
Che
and
O. K.
Matar
, “
Impact of droplets on liquid films in the presence of surfactant
,”
Langmuir
33
,
12140
12148
(
2017
).
28.
K.-L.
Pan
and
C.-Y.
Hung
, “
Droplet impact upon a wet surface with varied fluid and surface properties
,”
J. Colloid Interface Sci.
352
,
186
193
(
2010
).
29.
C.
Motzkus
,
F.
Gensdarmes
, and
E.
Géhin
, “
Study of the coalescence/splash threshold of droplet impact on liquid films and its relevance in assessing airborne particle release
,”
J. Colloid Interface Sci.
362
,
540
552
(
2011
).
30.
S.
Alghoul
,
C.
Eastwick
, and
D.
Hann
, “
Droplet impact on shear-driven liquid films
,”
Atomization Sprays
21
,
833
846
(
2011
).
31.
X.
Gao
and
R.
Li
, “
Impact of a single drop on a flowing liquid film
,”
Phys. Rev. E
92
,
053005
(
2015
).
32.
C.
Liu
,
M.
Shen
, and
J.
Wu
, “
Investigation of a single droplet impact onto a liquid film with given horizontal velocity
,”
Eur. J. Mech.: B/Fluids
67
,
269
279
(
2018
).
33.
M. V.
Gielen
,
P.
Sleutel
,
J.
Benschop
,
M.
Riepen
,
V.
Voronina
,
C. W.
Visser
,
D.
Lohse
,
J. H.
Snoeijer
,
M.
Versluis
, and
H.
Gelderblom
, “
Oblique drop impact onto a deep liquid pool
,”
Phys. Rev. Fluids
2
,
083602
(
2017
).
34.
Y.
Li
,
Y.
Zheng
,
Z.
Lan
,
W.
Xu
, and
X.
Ma
, “
The evolution of droplet impacting on thin liquid film at superhydrophilic surface
,”
Appl. Phys. Lett.
111
,
231601
(
2017
).
35.
H.
Lhuissier
,
C.
Sun
,
A.
Prosperetti
, and
D.
Lohse
, “
Drop fragmentation at impact onto a bath of an immiscible liquid
,”
Phys. Rev. Lett.
110
,
264503
(
2013
).
36.
S.
Shaikh
,
G.
Toyofuku
,
R.
Hoang
, and
J. O.
Marston
, “
Immiscible impact dynamics of droplets onto millimetric films
,”
Exp. Fluids
59
,
7
(
2018
).
37.
W. J.
Doak
,
D. M.
Laiacona
,
G. K.
German
, and
P. R.
Chiarot
, “
Rebound of continuous droplet streams from an immiscible liquid pool
,”
Phys. Fluids
28
,
057104
(
2016
).
38.
H.
Shetabivash
,
F.
Ommi
, and
G.
Heidarinejad
, “
Numerical analysis of droplet impact onto liquid film
,”
Phys. Fluids
26
,
012102
(
2014
).
39.
Y.
Guo
,
Y.
Lian
, and
M.
Sussman
, “
Investigation of drop impact on dry and wet surfaces with consideration of surrounding air
,”
Phys. Fluids
28
,
073303
(
2016
).
40.
Z.
Zhang
,
H.
Liu
,
F.
Zhang
, and
M.
Yao
, “
Numerical study of spray micro-droplet impinging on dry/wet wall
,”
Appl. Therm. Eng.
95
,
1
9
(
2016
).
41.
C.
Josserand
,
P.
Ray
, and
S.
Zaleski
, “
Droplet impact on a thin liquid film: Anatomy of the splash
,”
J. Fluid Mech.
802
,
775
805
(
2016
).
42.
G.
Liang
and
I.
Mudawar
, “
Review of mass and momentum interactions during drop impact on a liquid film
,”
Int. J. Heat Mass Transfer
101
,
577
599
(
2016
).
43.
A. L.
Yarin
and
D. A.
Weiss
, “
Impact of drops on solid surfaces: Self-similar capillary waves, and splashing as a new type of kinematic discontinuity
,”
J. Fluid Mech.
283
,
141
173
(
1995
).
44.
B. L.
Scheller
and
D. W.
Bousfield
, “
Newtonian drop impact with a solid surface
,”
AIChE J.
41
,
1357
1367
(
1995
).
45.
J. H.
Wang
, “
Self-diffusion coefficients of water
,”
J. Phys. Chem.
69
,
4412
(
1965
).
46.
K. L.
Kostka
,
M. D.
Radcliffe
, and
E.
Von Meerwall
, “
Diffusion coefficients of methylene blue and thioflavin T dyes in methanol solution
,”
J. Phys. Chem.
96
,
2289
2292
(
1992
).
47.
I. G.
Currie
,
Fundamental Mechanics of Fluids
(
Marcel Dekker, Inc.
,
New York
,
2003
).
48.
A.
Rahimzadeh
,
M. R.
Ahmadian-Yazdi
, and
M.
Eslamian
, “
Experimental study on the characteristics of capillary surface waves on a liquid film on an ultrasonically vibrated substrate
,”
Fluid Dyn. Res.
50
,
065510
(
2018
).
49.
F.
Behroozi
and
A.
Perkins
, “
Direct measurement of the dispersion relation of capillary waves by laser interferometry
,”
Am. J. Phys.
74
,
957
961
(
2006
).
50.
D.
Nikolic
and
L.
Nesic
, “
Determination of surface tension coefficient of liquids by diffraction of light on capillary waves
,”
Eur. J. Phys.
33
,
1677
1685
(
2012
).
51.
T. R.
Larson
and
J. W.
Right
, “
Wind-generated gravity-capillary waves: Laboratory measurements of temporal growth rates using microwave backscatter
,”
J. Fluid Mech.
70
,
417
436
(
1975
).

Supplementary Material

You do not currently have access to this content.