Abstract

The energy conversion is proposed to analyze the effects of liquid properties on the formation of an ejecta sheet, prompt splashing, and crown evolution. The incompressible laminar Navier–Stokes equations coupled with the volume-of-fluid (VOF) model are solved numerically in an axisymmetric frame to simulate the impact process. Based on the energy conversion curves and liquid–gas interface shapes, the Weber number is shown to be the main dimensionless quantity controlling the impact process, especially with regard to crown evolution. However, the Reynolds number does have some influence on the drop impact process, especially during the stage of ejecta sheet formation and prompt splashing. By studying energy conversion during the impact process, the crown evolution is shown to be accelerated significantly with decreasing Weber number, but is hardly affected by the Reynolds number. A linear relation is found between the time to the moment of crown stabilization (when the crown height reaches its maximum value) and the square root of the Weber number. The relationship between the Weber number and the energy distribution at the moment of crown stabilization is also studied.

References

References
1.
Yoon
,
S. S.
, and
Demosthenous
,
B.
,
2006
, “
Effects of Air on Splashing During a Large Droplet Impact: Experimental and Numerical Investigations
,”
Atomization Sprays
,
16
(
8
), pp. 981–996.10.1615/AtomizSpr.v16.i1.20
2.
Yarin
,
A.
,
2006
, “
Drop Impact Dynamics: Splashing, Spreading, Receding, Bouncing…
,”
Annu. Rev. Fluid Mech.
,
38
(
1
), pp.
159
192
.10.1146/annurev.fluid.38.050304.092144
3.
Rein
,
M.
,
1993
, “
Phenomena of Liquid Drop Impact on Solid and Liquid Surfaces
,”
Fluid Dyn. Res.
,
12
(
2
), pp.
61
93
.10.1016/0169-5983(93)90106-K
4.
Josserand
,
C.
, and
Thoroddsen
,
S. T.
,
2016
, “
Drop Impact on a Solid Surface
,”
Annu. Rev. Fluid Mech.
,
48
(
1
), pp.
365
391
.10.1146/annurev-fluid-122414-034401
5.
Liang
,
G.
, and
Mudawar
,
I.
,
2016
, “
Review of Mass and Momentum Interactions During Drop Impact on a Liquid Film
,”
Int. J. Heat Mass Transfer
,
101
, pp.
577
599
.10.1016/j.ijheatmasstransfer.2016.05.062
6.
Yarin
,
A. L.
,
Roisman
,
I. V.
, and
Tropea
,
C.
,
2017
,
Collision Phenomena in Liquids and Solids
,
Cambridge University Press
,
Cambridge, UK
.
7.
Liu
,
J.
,
Franco
,
W.
, and
Aguilar
,
G.
,
2008
, “
Effect of Surface Roughness on Single Cryogen Droplet Spreading
,”
ASME J. Fluids Eng.
,
130
(
4
), p.
041402
.10.1115/1.2903810
8.
Worthington
,
A.
,
1876
, “
On the Forms Assumed by Drops of Liquids Falling Vertically on a Horizontal Plate
,”
Proc. R. Soc. London
,
25
(
171–178
), pp.
261
272
.10.1098/rspl.1876.0048
9.
Worthington
,
A. M.
, and
Cole
,
R.
,
1897
, “
Impact With a Liquid Surface, Studied by the Aid of Instantaneous Photography
,”
Philos. Trans. R. Soc. London., Ser. A
,
189
, pp.
137
148
.10.1098/rsta.1897.0005
10.
Worthington
,
A.
, and
Cole
,
R.
,
1900
, “
Impact With a Liquid Surface Studied by the Aid of Instantaneous Photography. Paper II
,”
Philos. Trans. R. Soc. London., Ser. A
,
194
, pp.
175
199
.10.1098/rsta.1900.0016
11.
Roisman
,
I. V.
,
Berberović
,
E.
, and
Tropea
,
C.
,
2009
, “
Inertia Dominated Drop Collisions—I: On the Universal Flow in the Lamella
,”
Phys. Fluids
,
21
(
5
), p.
052103
.10.1063/1.3129282
12.
Roisman
,
I. V.
,
2009
, “
Inertia Dominated Drop Collisions—II: An Analytical Solution of the Navier–Stokes Equations for a Spreading Viscous Film
,”
Phys. Fluids
,
21
(
5
), p.
052104
.10.1063/1.3129283
13.
Roisman
,
I. V.
,
Horvat
,
K.
, and
Tropea
,
C.
,
2006
, “
Spray Impact: Rim Transverse Instability Initiating Fingering and Splash, and Description of a Secondary Spray
,”
Phys. Fluids
,
18
(
10
), p.
102104
.10.1063/1.2364187
14.
Tang
,
X.
,
Saha
,
A.
,
Law
,
C. K.
, and
Sun
,
C.
,
2016
, “
Nonmonotonic Response of Drop Impacting on Liquid Film: Mechanism and Scaling
,”
Soft Matter
,
12
(
20
), pp.
4521
4529
.10.1039/C6SM00397D
15.
Mundo
,
C.
,
Sommerfeld
,
M.
, and
Tropea
,
C.
,
1995
, “
Droplet-Wall Collisions: Experimental Studies of the Deformation and Breakup Process
,”
Int. J. Multiphase Flow
,
21
(
2
), pp.
151
173
.10.1016/0301-9322(94)00069-V
16.
Wang
,
A.-B.
, and
Chen
,
C.-C.
,
2000
, “
Splashing Impact of a Single Drop Onto Very Thin Liquid Films
,”
Phys. Fluids
,
12
(
9
), pp.
2155
2158
.10.1063/1.1287511
17.
Rioboo
,
R.
,
Bauthier
,
C.
,
Conti
,
J.
,
Voué
,
M.
, and
De Coninck
,
J.
,
2003
, “
Experimental Investigation of Splash and Crown Formation During Single Drop Impact on Wetted Surfaces
,”
Exp. Fluids
,
35
(
6
), pp.
648
652
.10.1007/s00348-003-0719-5
18.
Yarin
,
A.
, and
Weiss
,
D.
,
1995
, “
Impact of Drops on Solid Surfaces: Self-Similar Capillary Waves, and Splashing as a New Type of Kinematic Discontinuity
,”
J. Fluid Mech.
,
283
, pp.
141
173
.10.1017/S0022112095002266
19.
Cossali
,
G.
,
Coghe
,
A.
, and
Marengo
,
M.
,
1997
, “
The Impact of a Single Drop on a Wetted Solid Surface
,”
Exp. Fluids
,
22
(
6
), pp.
463
472
.10.1007/s003480050073
20.
Vander Wal
,
R. L.
,
Berger
,
G. M.
, and
Mozes
,
S. D.
,
2006
, “
The Splash/Non-Splash Boundary Upon a Dry Surface and Thin Fluid Film
,”
Exp. Fluids
,
40
(
1
), pp.
53
59
.10.1007/s00348-005-0045-1
21.
Motzkus
,
C.
,
Gensdarmes
,
F.
, and
Géhin
,
E.
,
2011
, “
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
(
2
), pp.
540
552
.10.1016/j.jcis.2011.06.031
22.
Zhang
,
L. V.
,
Toole
,
J.
,
Fezzaa
,
K.
, and
Deegan
,
R. D.
,
2012
, “
Evolution of the Ejecta Sheet From the Impact of a Drop With a Deep Pool
,”
J. Fluid Mech.
,
690
(
1
), pp.
5
15
.10.1017/jfm.2011.396
23.
Thoroddsen
,
S. T.
,
Thoraval
,
M. J.
,
Takehara
,
K.
, and
Etoh
,
T. G.
,
2011
, “
Droplet Splashing by a Slingshot Mechanism
,”
Phys. Rev. Lett.
,
106
(
3
), p.
034501
.10.1103/PhysRevLett.106.034501
24.
Krechetnikov
,
R.
, and
Homsy
,
G. M.
,
2009
, “
Crown-Forming Instability Phenomena in the Drop Splash Problem
,”
J. Colloid Interface Sci.
,
331
(
2
), pp.
555
559
.10.1016/j.jcis.2008.11.079
25.
Pan
,
K.-L.
, and
Hung
,
C.-Y.
,
2010
, “
Droplet Impact Upon a Wet Surface With Varied Fluid and Surface Properties
,”
J. Colloid Interface Sci.
,
352
(
1
), pp.
186
193
.10.1016/j.jcis.2010.08.033
26.
Rein
,
M.
,
1996
, “
The Transitional Regime Between Coalescing and Splashing Drops
,”
J. Fluid Mech.
,
306
, pp.
145
165
.10.1017/S0022112096001267
27.
Thoraval
,
M. J.
,
Takehara
,
K.
,
Etoh
,
T. G.
,
Popinet
,
S.
,
Ray
,
P.
,
Josserand
,
C.
,
Zaleski
,
S.
, and
Thoroddsen
,
S. T.
,
2012
, “
Von Kármán Vortex Street Within an Impacting Drop
,”
Phys. Rev. Lett.
,
108
(
26
), p.
264506
.10.1103/PhysRevLett.108.264506
28.
Agbaglah
,
G.
,
M.-J
,
T.
,
Thoroddsen
,
S. T.
,
Zhang
,
L. V.
,
Fezzaa
,
K.
, and
Deegan
,
R. D.
,
2015
, “
Drop Impact Into a Deep Pool: Vortex Shedding and Jet Formation
,”
J. Fluid Mech.
,
764
, p. R1.10.1017/jfm.2014.723
29.
Josserand
,
C.
, and
Zaleski
,
S.
,
2003
, “
Droplet Splashing on a Thin Liquid Film
,”
Phys. Fluids
,
15
(
6
), pp.
1650
1657
.10.1063/1.1572815
30.
Weiss
,
D. A.
, and
Yarin
,
A. L.
,
1999
, “
Single Drop Impact Onto Liquid Films: Neck Distortion, Jetting, Tiny Bubble Entrainment, and Crown Formation
,”
J. Fluid Mech.
,
385
, pp.
229
254
.10.1017/S002211209800411X
31.
Nikolopoulos
,
N.
,
Theodorakakos
,
A.
, and
Bergeles
,
G.
,
2005
, “
Normal Impingement of a Droplet Onto a Wall Film: A Numerical Investigation
,”
Int. J. Heat Fluid Flow
,
26
(
1
), pp.
119
132
.10.1016/j.ijheatfluidflow.2004.06.002
32.
Morton
,
D.
,
Rudman
,
M.
, and
Jong-Leng
,
L.
,
2000
, “
An Investigation of the Flow Regimes Resulting From Splashing Drops
,”
Phys. Fluids
,
12
(
4
), pp.
747
763
.10.1063/1.870332
33.
Engel
,
O. G.
,
1966
, “
Crater Depth in Fluid Impacts
,”
J. Appl. Phys.
,
37
(
4
), pp.
1798
1808
.10.1063/1.1708605
34.
Engel
,
O. G.
,
1967
, “
Initial Pressure, Initial Flow Velocity, and the Time Dependence of Crater Depth in Fluid Impacts
,”
J. Appl. Phys.
,
38
(
10
), pp.
3935
3940
.10.1063/1.1709044
35.
Macklin
,
W.
, and
Metaxas
,
G.
,
1976
, “
Splashing of Drops on Liquid Layers
,”
J. Appl. Phys.
,
47
(
9
), pp.
3963
3970
.10.1063/1.323218
36.
Thoroddsen
,
S.
,
Etoh
,
T. G.
, and
Takehara
,
K.
,
2006
, “
Crown Breakup by Marangoni Instability
,”
J. Fluid Mech.
,
557
, pp.
63
72
.10.1017/S002211200600975X
37.
Oguz
,
H. N.
, and
Prosperetti
,
A.
,
1990
, “
Bubble Entrainment by the Impact of Drops on Liquid Surfaces
,”
J. Fluid Mech.
,
219
(
1
), pp.
143
179
.10.1017/S0022112090002890
38.
Li
,
R.
,
Ashgriz
,
N.
, and
Chandra
,
S.
,
2010
, “
Maximum Spread of Droplet on Solid Surface: Low Reynolds and Weber Numbers
,”
ASME J. Fluids Eng.
,
132
(
6
), p.
061302
.10.1115/1.4001695
39.
Xu
,
L.
,
Zhang
,
W. W.
, and
Nagel
,
S. R.
,
2005
, “
Drop Splashing on a Dry Smooth Surface
,”
Phys. Rev. Lett.
,
94
(
18
), p.
184505
.10.1103/PhysRevLett.94.184505
40.
Guo
,
Y.
,
Lian
,
Y.
, and
Sussman
,
M.
,
2016
, “
Investigation of Drop Impact on Dry and Wet Surfaces With Consideration of Surrounding Air
,”
Phys. Fluids
,
28
(
7
), p.
073303
.10.1063/1.4958694
41.
Shetabivash
,
H.
,
Ommi
,
F.
, and
Heidarinejad
,
G.
,
2014
, “
Numerical Analysis of Droplet Impact Onto Liquid Film
,”
Phys. Fluids
,
26
(
1
), p.
012102
.10.1063/1.4861761
42.
Berberović
,
E.
,
van Hinsberg
,
N. P.
,
Jakirlić
,
S.
,
Roisman
,
I. V.
, and
Tropea
,
C.
,
2009
, “
Drop Impact Onto a Liquid Layer of Finite Thickness: Dynamics of the Cavity Evolution
,”
Phys. Rev. E
,
79
(
3
), p.
036306
.10.1103/PhysRevE.79.036306
43.
Diaz
,
A. J.
, and
Ortega
,
A.
,
2016
, “
Gas-Assisted Droplet Impact on a Solid Surface
,”
ASME J. Fluids Eng.
,
138
(
8
), p.
081104
.10.1115/1.4033025
44.
ANSYS Inc.,
2012
, “
ANSYS FLUENT 14.0 Documentation
,” ANSYS, Canonsburg, PA.
45.
Eggers
,
J.
,
Fontelos
,
M. A.
,
Josserand
,
C.
, and
Zaleski
,
S.
,
2010
, “
Drop Dynamics After Impact on a Solid Wall: Theory and Simulations
,”
Phys. Fluids
,
22
(
6
), p.
062101
.10.1063/1.3432498
46.
Thoroddsen
,
S. T.
,
2002
, “
The Ejecta Sheet Generated by the Impact of a Drop
,”
J. Fluid Mech.
,
451
(
451
), pp.
373
381
.10.1017/S0022112001007030
47.
Zhang
,
H.
,
2008
, “
A Study of Different Fluid Droplets Impacting on a Liquid Film
,”
Petrol. Sci.
,
5
(
1
), pp.
62
66
.10.1007/s12182-008-0010-8
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