Thermal Spray

1. Proceedings of the 22nd
National and 11th
International
ISHMT-ASME Heat and Mass Transfer Conference
December 28-31, 2013, IIT Kharagpur, India
HMTC1300290
SPLASHING MECHANISM DURING IMPACT OF CONTINUOUS AND
HOLLOW DROPLETS ON A SUBSTRATE
Rajesh Kumar Shukla
Indian institute of Technology Kanpur
Kanpur, Uttar Pradesh, 208016
India
shuklark@iitk.ac.in
Arvind Kumar
Indian Institute of Technology Kanpur
Kanpur, Uttar Pradesh, 208016
India
arvindkr@iitk.ac.in
ABSTRACT
In a thermal spray coating process the quality of the
coating depends on the impingement process of the feedstock
particles on the substrate in which the individual molten
particles flatten and solidify on the substrate forming the
individual splat. It has been reported that improved quality of
coating can be obtained using hollow particles in comparison
to the conventional continuous particles. In this paper the
splashing behaviour of continuous and hollow molten droplet
during its impact on a substrate has been numerically
investigated and compared. The spherical hollow droplet used
in this study consists of a liquid shell enclosing a gas (air)
cavity immediately prior to droplet-substrate collision.
Volume of fluid surface tracking method (VOF) coupled with
the solidification model within a one-domain continuum
formulation is used to model the transient flow during the
droplet impact, subsequent spreading and solidification. The
results show that splashing reduces significantly while using
the hollow droplets. On the other hand, an analogous
conventional continuous droplet shows significant splashing.
We highlight that how a new phenomenon, formation of
counter liquid jetting, with the hollow droplets is responsible
for less splashing.
NOMENCLATURE
c Specific heat capacity
C Constant related to Darcy source term
D0 Initial droplet diameter
d0 Initial void diameter
fl Weight fraction of liquid
fs Weight fraction of solid
F Volume of fluid function
Fvol Continuum surface tension force
g

Acceleration due to gravity vector
gl Volume fraction of liquid
gs Volume fraction of solid
k Thermal conductivity
L Latent heat of fusion
T Time
T Temperature
U0 Droplet's initial impact velocity
u

Continuum velocity vector
Greek symbols
μ Dynamic viscosity
ρ Density
Subscript
d Droplet
subs Substrate
air Air
eff Effective
l Liquid
0 Initial
s Solid
INTRODUCTION
In a thermal spray coating process molten particles are
projected towards the substrate where they flatten and solidify
on the substrate forming the coating layer. However, splashing
(break up into smaller satellite droplets known as impact
splashing, and break up during flattening known as spreading
splashing or fingering) occurs when molten droplets impact
with high velocity on a solid substrate. Droplet splashing is
undesirable since it reduces the deposition efficiency (the
fraction of sprayed material which adheres to the surface) of
the process. It not only results in wastage of material but also
create environmental pollution and reduces the strength of the
coating.
Due to its practical importance many studies have been
devoted to investigate the mechanism behind splashing of
molten metal droplet just after the impact to solid surface.
Fukumoto and Huang [1] observed that freezing along the
bottom of an impinging droplet causes splashing: liquid
flowing on top of the solid layer jets off and splashes.
Delaying solidification, either by raising surface temperature
or increasing thermal contact resistance at the droplet–
substrate interface, is expected to suppress splashing. Allen [2]
first put forward the hypothesis that splashing is caused by

2. Rayleigh–Taylor instability on the edges of the spreading
liquid film. Liu et al. [3] numerically studied the impact of a
droplet onto substrates with wavy surfaces; however, their
two-dimensional axi-symmetric model did not include
solidification. They found that for wavelengths of the surface
larger than the droplet diameter, droplet spreading ended with
break up. Bussman et al. [4] used a three-dimensional
computational fluid dynamics code to model droplet impact
and splashing. They initiated the growth of fingers in their
simulations by introducing a sinusoidal perturbation into the
velocity field immediately after impact. They speculated that
in reality protrusions on the surface disturb liquid flow, with
the amplitude of the perturbation proportional to the
magnitude of surface roughness. Ahmed and Rangel [5]
numerically studied the impingement and solidification of an
aluminum droplet on uneven substrates, using a two-
dimensional axi-symmetric model. Their results show that
droplet impact onto an uneven substrate is almost always
accompanied by splashing. However, the degree of splashing
decreases with the increase in surface roughness height.
Recently Mandre and Brenner [6] suggested that one possible
mechanism of splashing just after the impact of droplet on a
wall is due to the ejection of a liquid sheet launched into air
immediately after contact. The overall mechanism occurs
through two steps, first step involves the ejection of a thin
liquid sheet before the droplet touches the surface, and the
second stage of splashing requires this sheet to be deflected
away from the solid surface. Lei et al. [7], observed that
splashing can be suppressed by decreasing the pressure of the
surrounding gas. It is worth to point out that most of the
studies reported for splashing mechanism during droplet
impact assume continuous shape of the droplets without any
voids inside.
New possibilities for thermal spraying of functional
coatings formed by deposition of hollow melt droplets are
discussed in the work by Solonenko et al. [8, 9]. The limited
studies reported in this field suggest that the resulting coating
from hollow melt droplets have improved coating
characteristics as compared to the conventional continuous
droplets. Recently, Kumar et al. [10, 11] reported that the
impact of a hollow droplet onto the substrate and its spreading
behaviour differ from an analogous continuous droplet.
Likewise, the splashing behaviour of continuous and hollow
droplets can also be different.
The objective of this study is to discuss the fundamental
difference between splashing mechanism of continuous and
hollow droplets. The impact, flattening and solidification
behaviour of the two droplets onto a solid substrate are
numerically studied. We discuss how the flattening and
solidification patterns in the two droplets govern the splashing
mechanism.
MODEL AND GOVERNING EQUATIONS
We simulate the high velocity impact of ZrO2 droplet onto
a solid surface with conditions typically found in a real
thermal spray coating process. We consider two-dimensional
axi-symmetric formulation (Figure 1), based on a previously
validated model of Kamnis and Gu [12] for a continuous
droplet. The impact of a spherical hollow droplet and an
analogous (same mass) spherical continuous droplet is
considered. The hollow droplet consists of a liquid shell
enclosing a gas (air) cavity immediately prior to droplet-
substrate collision (Fig. 1). The impact conditions are: the
droplets at an initial uniform temperature of 2970 K impinge
with a velocity U0 (150 m/s) onto the substrate kept at an
initial temperature of 300 K.
The thermophysical property data used in the simulations are
shown in Table 1 [10]. The model used in the current study
has been discussed in detail elsewhere [10]. Therefore, here
we would only mention specific features of the model.
In the droplet impingement model transient fluid flow
dynamics during the impact, droplet spreading onto the
substrate and solidification heat transfer are considered using
the volume of fluid surface tracking method (VOF) coupled
with a solidification model within a one-domain continuum
approach based on the classical mixture theory [10-12]. For
computational cells which are undergoing phase change
(solidification), the solid-liquid interaction in the momentum
conservation (Eq. 4) is considered using Darcy's model of
viscous flow through a porous medium using the source term
Su (Eq. 5) [12]. Momentum conservation equation (Eq. 4) also
accounts for surface tension effects at the free surface, which
is considered by a continuum surface force model [11]. The
momentum and the energy conservation equations (Eqs. 4 and
6) are coupled. The source term Sh (Eq. 7), for handling the
solidification phase change, appearing in the energy
conservation (Eq. 6) is active only for the computational cells
filled with molten droplet (F = 1). In the substrate only the
conduction heat transfer is solved (Eq. 9). For the substrate
thermal contact resistance a constant value of 1.8×10-6
m2
KW-
1
, corresponding to a stainless steel substrate roughness of 0.06
μm, is used [11].
VOF equation:
0=⋅∇+
∂
∂
Fu
t
F 
(1)
Mixture quantities definitions for a cell in the mushy state:
Void (air) cavity
Symmetry
axis
Atmosphere(air)
g
D0 = 50 µm, d0 = 25 µm
U0 = 150 m/s
Hollow droplet
Substrate
Symmetry
axis
Atmosphere(air)
g
D = 0.956.D0
U0 = 150 m/s
Continuousdroplet
Substrate
(a)
(b)
Figure 1. SCHEMATIC OF (a) CONTINUOUS AND
(b) HOLLOW DROPLET IMPACT ON A SUBSTRATE

3. sllld
d
ll
lslsl gg
g
fffgg ρρρ
ρ
ρ
)1(,,1,1 −+===+=+
aird FF ρρρ )1( −+= ,
airdeff cFcFc )1( −+=
airdeff kFkFk )1( −+= with
sllld kgkgk )1( −+=
(2)
Table 1. MATERIAL PROPERTIES DATA
Material properties Values
Impinging droplet material Zirconia (ZrO2)
Substrate material Stainless steel (SS)
Gas phase (the void and the droplet
surrounding medium)
Air (air)
Droplet initial temperature 2970 K
Substrate initial temperature 652 K
Solidus temperature (ZrO2) 2949 K
Liquidus temperature (ZrO2) 2951 K
Thermal conductivity (liquid ZrO2) 2.00 W ∙ m-1
/ K
Thermal conductivity (solid ZrO2) 2.32 W ∙ m-1
/ K
Thermal conductivity (SS) 14.9 W ∙ m-1
/ K
Thermal conductivity (air) 0.0242 W ∙ m-1
/ K
Density (liquid ZrO2) 5700 kg/m3
Density (solid ZrO2) 5700 kg/m3
Density (SS) 7900 kg/m3
Density (air) 1.225 kg/m3
Droplet surface tension 0.43 N/m
Contact angle 100°
Viscosity (liquid ZrO2) 0.021 kg ∙ m-1
/s
Viscosity (air) 1.7894×10-5
kg ∙ m-1
/s
Specific heat capacity
(solid and liquid ZrO2)
713 J ∙ kg-1
/ K
Specific heat capacity (SS) 477 J ∙ kg-1
/ K
Specific heat capacity (air) 1006.43 J ∙ kg-1
/ K
Latent heat of fusion 7.07x105
J/kg
Continuity:
0)()( =⋅∇+
∂
∂
u
t

ρρ
(3)
Momentum conservation:
(4)
2
3
(1 )
1
0 1
l
l
g
C u F
Su g
F
  −
=  =   

<


(5)
Energy conservation:
heffeffeff STkTcuTc
t
+∇⋅∇=⋅∇+
∂
∂
)()()(

ρρ
(6)







<
=





∇+
∂
∂
−
=
10
1).()(
F
Ffuf
t
L
S
ll
h

ρρ
(7)
liquidussolidus
liquidus
solidus
l
liquidusl
solidusl
TTTif
TT
TT
f
TTiff
TTiff
<<
−
−
=
≥=
≤=
1
0
(8)
Substrate heat transfer:
)()( TkTc
t
subssubssubs ∇⋅∇=
∂
∂
ρ
(9)
RESULTS AND DISCUSSION
Continuous Droplet
Flattening and spreading pattern of the continuous droplet at
different time is shown in Figure 2. Splashing at the advancing
edge of the spreading droplet can be noticed from the very
beginning. This results in break up at the edge and finally
creates a discontinuous splat. For better understanding of the
physical mechanism we subsequently show in Figs. 3-5 the
zoomed images in the rectangular portion marked in Fig. 2 for
spreading, solidification, velocity and temperature at different
time. It was noticed that just after the impact during the initial
stage of spreading droplet flattens with very high velocity (450
m/s). Such high velocity creates instability at the advancing
edge and some small satellite droplet get detached from the
main spreading droplet material [2]. These detached droplets
solidify at the substrate. This tendency can be seen from the
maps of VOF, solidification, velocity and temperature shown
in Fig. 3. Such behaviour leads to formation of discontinuous
solidified layer at the substrate.
From the spreading and solidification maps shown in Figs.
3-5 at different time a thin discontinuous layer of solidified
splat develop at the substrate surface. Further flattening of
droplet occurs over this thin discontinuous solidified layer
which lead to further instability of the advancing droplet and
its break up. This tendency is refer to as flattening splashing
[4]. This splashing is formed because of very high flattening
velocity and formation and solidification of detached satellite
droplets over the substrate during the early stage of the
spreading process. The solidified detached drops crates a
barrier in the path of the spreading liquid leading to further
instability and splashing in the spreading droplet known as
flattening splashing.

4. Figure 2. SPREADING PATTERN OF CONTINUOUS
DROPLET DURING THE IMPACT PROCESS (SHOWN BY
CONTOUR OF VOF FOR LIQUID PHASE)
t = 0.19 µsTemperature (K)
Velocity (m/s)
(a)
(b)
(c)
(d)
Figure 3. ZOOMED IMAGES OF (A) SPREADING (VOF OF
LIQUID PHASE) (B) SOLIDIFICATION (LIQUID FRACTION)
(C) VELOCITY (MAGNITUDE) AND (D) TEMPERATURE AT
0.19 µs IN RECTANGULAR PORTION MARKED IN FIG. 1
t = 0.25 µsTemperature (K)
Velocity (m/s)
(a)
(b)
(d)
(c)
Figure 4. ZOOMED IMAGES OF (a) SPREADING (VOF OF
LIQUID PHASE) (b) SOLIDIFICATION (LIQUID FRACTION)
(c) VELOCITY (MAGNITUDE) AND (d) TEMPERATURE AT
0.25 µs IN RECTANGULAR PORTION MARKED IN FIG. 1
(a)
t = 0.43 µsTemperature (K) Velocity (m/s)
(b)
(c)
(d)
Figure 5. ZOOMED IMAGES OF (a) SPREADING (VOF OF
LIQUID PHASE) (b) SOLIDIFICATION (LIQUID FRACTION)
(c) VELOCITY (MAGNITUDE) AND (d) TEMPERATURE AT
0.43 µs IN RECTANGULAR PORTION MARKED IN FIG. 1
t = 0.14 µs
t = 0.19 µs
t = 0.25 µs
t = 0.43 µs
t = 0.51 µs
t = 0.83 µs
t = 2.19 µs

5. Figure 6. SPREADING PATTERN OF HOLLOW DROPLET
DURING THE IMPACT PROCESS (SHOWN BY CONTOUR
OF VOF FOR LIQUID PHASE)
t = 0.20 µs
Temperature (K) Velocity (m/s)
(a)
(c)
(d)
(b)
Figure 7. ZOOMED IMAGES OF (a) SPREADING (VOF OF
LIQUID PHASE) (b) SOLIDIFICATION (LIQUID FRACTION)
(c) VELOCITY (MAGNITUDE) AND (d) TEMPERATURE AT
0.20 µs IN RECTANGULAR PORTION MARKED IN FIG. 6
t = 0.35 µsTemperature (K) Velocity (m/s)
(a)
(b)
(c)
(c)
(d)
(a)
(b)
FIGURE 8. ZOOMED IMAGES OF (a) SPREADING (VOF OF
LIQUID PHASE) (b) SOLIDIFICATION (LIQUID FRACTION)
(c) VELOCITY (MAGNITUDE) AND (d) TEMPERATURE AT
0.35 µs IN RECTANGULAR PORTIONS MARKED IN FIG. 6
t = 0.55 µsTemperature (K) Velocity (m/s)
(a)
(b)
(c)
(d)
(c)
Figure 9. ZOOMED IMAGES OF (a) SPREADING (VOF OF
LIQUID PHASE) (b) SOLIDIFICATION (LIQUID FRACTION)
(c) VELOCITY (MAGNITUDE) AND (d) TEMPERATURE AT
0.55 µs IN RECTANGULAR PORTIONS MARKED IN FIG. 6
Hollow Droplet
Flattening and spreading pattern of the hollow droplet at
different time is shown in Figure 6. Unlike the continuous
droplet no splashing at the advancing edge of the spreading
droplet is noticed at the beginning of the Further, a final
continuous splat is observed [10]. However, in contrast to the
continuous droplet a new phenomenon of counter liquid
jetting can be clearly seen in this case. This formation of
phenomenon is reported in [10]. Because of the formation of
the upward moving counter jet large mass of liquid goes into
this jet and only some mass of liquid is horizontally spreading
along the substrate. This reduces the inertia of the horizontally
spreading liquid and hence its flattening velocity. For better
understanding of the physical mechanism we show in Figs. 7-
9 the zoomed images in the rectangular portion marked in Fig.
t = 0.06 µs
t = 0.12 µs
t = 0.20 µs
t = 0.23 µs
t = 0.35 µs
t = 0.55 µs
t = 0.91 µs

6. 6 for spreading, solidification, velocity and temperature at
different time.
From the velocity contour shown in Figure 7c we can
observe that the velocity of the advancing liquid during the
initial spreading stage in the case of hollow droplet is very less
(250 m/s) in comparison to that in the continuous droplet.
Comparing Figs. 3-5 and Figs. 7-9 we can notice the same
tendency in the magnitude of the advancing velocity. The
lower advancing velocity reduces the instability at the
advancing front and hence any formation of initial detached
drops. The further spreading of the hollow droplet material
does not experience any barrier, as observed for continuous
droplet. This causes smooth flattening of the droplet along the
substrate without any instability. We can clearly see in Figs.
7-9 that the solidification layer along the substrate is smooth
and continuous (no break up) and the advancing velocity is
also much lower.
Since a 2D approach is used in the current study, more
detailed 3D simulations and some quantitative comparison
with the experiments on the hollow droplets are needed in
order to develop further insights of the splashing phenomenon.
Our future work will undertake a 3D simulation of hollow
droplet impact.
CONCLUSIONS
This study contributes to the development of new
techniques to increase the material deposition efficiency
during thermal spray coating process. In the spraying using
hollow particles it is likely that the impacting droplets will
less break up after the impact, and hence splashing can be
reduced which will enhance the efficiency. We studied the
splashing behaviour of continuous and hollow droplets during
their impact onto a solid substrate. The main conclusions are:
• A new phenomenon, formation of counter liquid jetting,
leads to less splashing in case of the hollow droplets. On
the other hand, flattening mainly governed by inertia in
case of the continuous droplet leads to significant
splashing.
• Continuous splats (no break up) obtained in case of the
hollow droplet with absence of any flattening splashing
imply improved efficiency and good bonding of the
coating with the substrate. In this way, coating of
precious metal using hollow particles can be a better
substitute for dense particles.
REFERENCES
[1] Fukumoto, M., and Huang, Y., 1999. “Flattening
Mechanism in Thermal Sprayed Ni Particles Impinging
on Flat Substrate Surface”. Journal of Thermal Spray
Technology, 8(3), pp. 427–432
[2] Allen, R.F., 1988. “The Mechanics of Splashing”.
Journal of Colloid and Interface Science , 124(1), pp.
309–316.
[3] Liu, H., Lavernia, E.J., and Rangel, R.H., 1995.
“Modeling of Molten Droplet Impingement on a Non-
Flat Surface”. Acta Metallurgica et Materialia, 43(5),
pp-2053–2072.
[4] Bussmann, M., Chandra, S., and Mostaghimi, J., 2000.
“Modeling the Splash of a Droplet Impacting a Solid
Surface”. Physics of Fluids, 12, pp. 3121–3132.
[5] Ahmed, A.M., and Rangel, R.H., 2002. “Metal Droplet
Deposition on Non-flat Surfaces: Effect of Substrate
Morphology”. International Journal of Heat and Mass
Transfer, 45, pp. 1077–1091.
[6] Mandre, S., and Brenner, M.P., 2012. “The Mechanism
of a Splash on a Dry Solid Surface”. Journal of Fluid
Mechanics, 690, 148–172.
[7] Xu, L., Zhang, W.W., and Nagel, S. R., 2005. “Drop
Splashing on a Dry Smooth Surface”. Physical Review
Letters, 94(18), pp. 505–516.
[8] Solonenko, O.P., Smirnov, A.V., and Gulyaev, I.P.,
2008. “Spreading and Solidification of Hollow Molten
Droplet under its Impact onto Substrate: Computer
Simulation and Experiment” in Tokuyama, M.,
Oppenheim, I., Nishiyama, H. (Eds.), AIP Conference
Proceedings, Vol. 982. pp. 561–568.
[9] Solonenko, O.P., Gulyaev, I.P., and Smirnov, and A.V.,
2008. “Plasma Processing and Deposition of Powdered
Metal Oxides consisting of Hollow Spherical Particles”.
Technical Physics Letters, 34, pp. 1050–1052
[10] Kumar, A., Gu, S., Tabbara, H., and Kamnis, S., 2012.
“Study of Impingement of Hollow ZrO2 Droplets onto a
Substrate”. Surface and Coatings Technology, 220, pp.
164–169.
[11]Kumar, A., Gu, S. and Kamnis, S., 2012. “Simulation of
Impact of a Hollow Droplet on a Flat Surface”. Applied
Physics A: Materials Science & Processing, 109, pp.
101–109.
[12] Kamnis, S., and Gu, S., 2005. “Numerical Modelling of
Droplet Impingement”. Journal of Physics D: Applied
Physics, 38, pp. 3664–3673.

7. 6 for spreading, solidification, velocity and temperature at
different time.
From the velocity contour shown in Figure 7c we can
observe that the velocity of the advancing liquid during the
initial spreading stage in the case of hollow droplet is very less
(250 m/s) in comparison to that in the continuous droplet.
Comparing Figs. 3-5 and Figs. 7-9 we can notice the same
tendency in the magnitude of the advancing velocity. The
lower advancing velocity reduces the instability at the
advancing front and hence any formation of initial detached
drops. The further spreading of the hollow droplet material
does not experience any barrier, as observed for continuous
droplet. This causes smooth flattening of the droplet along the
substrate without any instability. We can clearly see in Figs.
7-9 that the solidification layer along the substrate is smooth
and continuous (no break up) and the advancing velocity is
also much lower.
Since a 2D approach is used in the current study, more
detailed 3D simulations and some quantitative comparison
with the experiments on the hollow droplets are needed in
order to develop further insights of the splashing phenomenon.
Our future work will undertake a 3D simulation of hollow
droplet impact.
CONCLUSIONS
This study contributes to the development of new
techniques to increase the material deposition efficiency
during thermal spray coating process. In the spraying using
hollow particles it is likely that the impacting droplets will
less break up after the impact, and hence splashing can be
reduced which will enhance the efficiency. We studied the
splashing behaviour of continuous and hollow droplets during
their impact onto a solid substrate. The main conclusions are:
• A new phenomenon, formation of counter liquid jetting,
leads to less splashing in case of the hollow droplets. On
the other hand, flattening mainly governed by inertia in
case of the continuous droplet leads to significant
splashing.
• Continuous splats (no break up) obtained in case of the
hollow droplet with absence of any flattening splashing
imply improved efficiency and good bonding of the
coating with the substrate. In this way, coating of
precious metal using hollow particles can be a better
substitute for dense particles.
REFERENCES
[1] Fukumoto, M., and Huang, Y., 1999. “Flattening
Mechanism in Thermal Sprayed Ni Particles Impinging
on Flat Substrate Surface”. Journal of Thermal Spray
Technology, 8(3), pp. 427–432
[2] Allen, R.F., 1988. “The Mechanics of Splashing”.
Journal of Colloid and Interface Science , 124(1), pp.
309–316.
[3] Liu, H., Lavernia, E.J., and Rangel, R.H., 1995.
“Modeling of Molten Droplet Impingement on a Non-
Flat Surface”. Acta Metallurgica et Materialia, 43(5),
pp-2053–2072.
[4] Bussmann, M., Chandra, S., and Mostaghimi, J., 2000.
“Modeling the Splash of a Droplet Impacting a Solid
Surface”. Physics of Fluids, 12, pp. 3121–3132.
[5] Ahmed, A.M., and Rangel, R.H., 2002. “Metal Droplet
Deposition on Non-flat Surfaces: Effect of Substrate
Morphology”. International Journal of Heat and Mass
Transfer, 45, pp. 1077–1091.
[6] Mandre, S., and Brenner, M.P., 2012. “The Mechanism
of a Splash on a Dry Solid Surface”. Journal of Fluid
Mechanics, 690, 148–172.
[7] Xu, L., Zhang, W.W., and Nagel, S. R., 2005. “Drop
Splashing on a Dry Smooth Surface”. Physical Review
Letters, 94(18), pp. 505–516.
[8] Solonenko, O.P., Smirnov, A.V., and Gulyaev, I.P.,
2008. “Spreading and Solidification of Hollow Molten
Droplet under its Impact onto Substrate: Computer
Simulation and Experiment” in Tokuyama, M.,
Oppenheim, I., Nishiyama, H. (Eds.), AIP Conference
Proceedings, Vol. 982. pp. 561–568.
[9] Solonenko, O.P., Gulyaev, I.P., and Smirnov, and A.V.,
2008. “Plasma Processing and Deposition of Powdered
Metal Oxides consisting of Hollow Spherical Particles”.
Technical Physics Letters, 34, pp. 1050–1052
[10] Kumar, A., Gu, S., Tabbara, H., and Kamnis, S., 2012.
“Study of Impingement of Hollow ZrO2 Droplets onto a
Substrate”. Surface and Coatings Technology, 220, pp.
164–169.
[11]Kumar, A., Gu, S. and Kamnis, S., 2012. “Simulation of
Impact of a Hollow Droplet on a Flat Surface”. Applied
Physics A: Materials Science & Processing, 109, pp.
101–109.
[12] Kamnis, S., and Gu, S., 2005. “Numerical Modelling of
Droplet Impingement”. Journal of Physics D: Applied
Physics, 38, pp. 3664–3673.