7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
Dynamics of twophase flows induced by drop collisions
I. V. Roisman*t, E. Berberovi6*, S. JakirliC and C. Tropea*tt
Institute of Fluid Mechanics and Aerodynamics, Technische Universitat Darmstadt, 64287 Darmstadt, Germany
t Center of Smart Interfaces, Technische Universitit Darmstadt, Petersenstr. 34, 64287 Darmstadt, Germany
eberberovic @sla.tudarmstadt.de, roisman@sla.tudarmstadt.de and ctropea@sla.tudarmstadt.de
Keywords: Drop impact, crater evolution, binary collision, asymptotic solutions
Twophase flows with free surfaces occurring during
impact of a drop onto a liquid wall film, onto a dry sub
strate and doublesymmetric binary drop collisions are an
alyzed in this study. Numerical simulations of the flow are
performed using an interface capturing model based on
the volumeoffluid (VOF) method. For a sharp interface
resolution an additional convective term is introduced into
the transport equation for phase fraction without explicit
reconstruction of the free surface.
In this paper the theoretical and numerical investiga
tions of the inertia dominated flow induced by drop col
lision with a rigid substrate and symmetric collision with
another drop are conducted. It is shown that, if the im
pact Reynolds and Weber numbers are high enough, the
lamella shape in the area near the axis of symmetry is self
similar and independent of the impact conditions, yielding
a universal velocity and pressure distributions. The exist
ing experimental data are compared to the numerical sim
ulations. The agreement is rather good.
Finally, the dynamics of drop impact onto a wall film
was determined numerically by varying impact parame
ters and liquid properties.
1 Introduction
Collision of a drop or droplet with a surface can be ob
served in everyday life and lies to the rots of numerous
technical applications. The phenomenon of a drop impact
is a problem rich in fluid dynamics, a deep insight into
which may enable to improve numerous technical appli
cations, such as highquality inkjet printing, perfect cov
erage of surfaces in paint spraying, spray cooling or a re
duction of exhaust gases in internal combustion engines.
Splashing of drops on liquid layers is encountered fre
quently in nature and leads to various phenomena like air
bubble formation during the rain, formation of a crown
like liquid sheet ejecting secondary droplets, or ejection
of the Worthington jet from the region of impact. Inves
tigations of drop impact onto liquid films have also im
portance in ecological fields, such as soil erosion and dis
persion of seed and microorganisms. The fluiddynamical
phenomena involved in drop impact onto various surfaces
were the subject of numerous studies, a comprehensive
review of which can be found in Rein (1993) and the se
quence of events occurring during the impact of single
drops onto films or pools of various depths has been de
scribed by Yarin (2006). Extensive research has been con
ducted to study the evolution of the maximum crater depth
and the formation of the crown or corona, the splashing,
the Worthington jet and bubble entrainment during drop
impact onto thin and deep liquid pools. Less investiga
tions were devoted to the phenomena occurring below the
impact surface, in particular the evolution of the crater
in shallow pools (Shin and McMahon 1990; Fedorchenko
and Wang 2004; Macklin and Hobbs 1969), which is im
portant for spray cooling.
Drop impact onto a dry substrate is a frequently inves
tigated phenomena in fluid mechanics because of the nu
merous industrial applications. Various outcomes of drop
impact, like splash, deposition or rebound (Levin 1971;
Rioboo et al. 2001) are determined by the impact param
eters and numerous substrate properties, such as the sub
strate roughness, shape, elasticity, porosity and wettabil
ity. These phenomena can be modeled if the main mech
anisms involved in drop spreading are identified and well
described. In contrast to an extensive knowledge about
the geometry of drop spreading on the wall (Rioboo et al.
(2002)), less data is available for the geometry of binary
drop collisions. The reason is in the relatively small, sub
millimeter diameter of the drops which are commonly
generated in such experiments. The experimental data for
the temporal evolution of the diameter of the liquid mass
formed after drop binary collision (Willis and Orme 2000,
2003) is available only for the relatively late stages after
impact. On the other hand, the phenomena related to ax
isymmetric binary drop collision can be much easier to
model than drop impact onto a dry substrate since com
plicating wall effects are not present.
Rapid advances in computer hardware and develop
ments of numerical algorithms have enabled a broader
use of computational methods for investigating the drop
impact phenomena. Numerical simulations provide a de
tailed database comprising not only the dynamics of the
drop surface with respect to its position and form but also
the temporal behavior of the complete velocity and pres
sure fields. The latter are beyond the reach of the existing
experimental methods where highspeed digital photogra
phy is still the main utility for extracting information. Be
cause of their importance, numerous computational stud
ies of these flows have been reported, some of the relevant
being Bussmann et al. (2000); Nikolopoulos et al. (2007);
Josserand and Zaleski (2003), etc.
A distinct area of investigation in fluid mechanics deals
with processes included in spray impact. Although the
flow generated by drop collisions is pertinent to spray im
pact, for practical reasons a direct numerical simulation
of spray impingement is still far beyond the capacity of
the present computer power. This is because spray im
pingement involves a large range of different time and
length scales. Spray consists of a large number of drops
of very different sizes and velocities impinging on a sur
face. The length scale of the wall film fluctuation may be
much larger than the diameter of a single drop diameter
and the time scale determining these fluctuations may be
quite different from the time scale of a single drop im
pact. The twophase flow of the underlying gas and the
falling droplets is rather complex and hard to model by
the existing turbulence models. Therefore a determinis
tic approach for spray impingement including individual
treatment of all droplets is still practically impossible.
This report presents results of theoretical and numerical
analyses of free surface flows generated during impact of
a single drop onto a liquid wall film, onto a dry substrate
and by doublesymmetric binary drop collisions. The ac
companied theoretical model for the crater penetration ac
counting for the liquid inertia, viscosity, gravity, and sur
face tension is presented. In addition the results of the the
oretical and numerical investigations of the inertia domi
nated flow induced by drop collision with a rigid substrate
and symmetric collision with another drop are presented.
The derived analytical solution for the selfsimilar flow in
the lamella at early times after the impact is outlined. The
theoretical and numerical results are compared to the ex
isting experimental database and a rather good agreement
is obtained.
Numerical simulations of drop impact are used to es
timate the time evolution of the spreading drop. The nu
merical method includes interface capturing methodology
based on the VOFmethod. The competitive effects in
fluencing the flow field during impact and the final out
come after the impact, i.e. gravity, viscous, inertial and
surface tension forces are taken in the account. Equations
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
of motion are extended to account for the surface tension
force acting on the free surface using the Continuum Sur
face Force model (CSF) of Brackbill et al. (1992). The
free surface position is determined from the solution of
the transport equation for volume fraction), which takes
values between zero and one, corresponding to regions
occupied by gas and liquid. Both phases are assumed to
be immiscible Newtonian fluids, thus equations of motion
are solved for a single effective fluid, the physical prop
erties of which are calculated as weighted averages be
tween the phases and equal to those of each phase in the
regions it occupies. Although the phase fraction is macro
scopically a discontinuous function (due to the very small
interface thickness), it is changing siii, nil\ over the in
terface in this model, producing a smooth change of fluid
properties and surface tension force, in accordance with
the CSF model. The smearing of steep gradients is sup
pressed by introducing an additional convective term in
the phase fraction equation counteracting numerical dif
fusion. The numerical procedure for keeping a sharply re
solved interface formulated by OpenCFD Ltd Ltd (2007)
is used, and the description of the algorithm is given in
BerberoviC et al. (2009), where the term "conventional
VOF" has been used merely to indicate the destroying ef
fects of the diffusion on the solution for the volume frac
tion. Basically, the algorithm avoids the use of special
compressive schemes for convection, such as CICSAM
of Ubbink and Issa (1999) and requires no explicit geo
metric interface reconstruction technique. The computa
tions were performed using the code OpenFOAM (Weller
et al. 1998), an open source CFD toolbox, utilizing a
cellcenterbased finite volume method on a fixed unstruc
tured numerical grid and employing the solution proce
dure based on the PISO algorithm for coupling between
pressure and velocity in transient flows (Issa 1986). The
computational domains have the form of a 2D axisym
metric slice with only one cell in the azimuthal direction.
The computational model incorporates a cellcenterbased
finite volume method with the finite volume approxima
tion of terms in the transport equations and an adjustable
time step. In simulations of impact onto a wall the no slip
boundary condition is set at the impacting plane. Since no
data on contact angle is provided, capillarity at the wall
is not accounted for. In cases of binary collisions, the
symmetry plane boundary condition is employed, thereby
simulating an axisymmetric drop binary collision.
2 Drop collision with a rigid wall and with
another drop
Universal shape of the lamella The phenomena
of normal drop impact onto a dry substrate and double
symmetric drop binary collision are very similar. Colli
sion of two equal drops can be represented as a drop im
Drop impact onto a Axisymmetric impact of
dry substrate two equal drops
lamella /dro rim lamella drop ri
I substrate I
symmetry plane\
Figure 1: Sketch of the normal drop impact onto a dry
substrate and the axisymmetric binary collision
of two equal drops.
pact onto a symmetry plane (Fig. 1). It is obvious that
the modeling approaches to these two kindred problems
should also be similar.
The dimensionless parameters governing the dynamics
of spreading of drop on a dry wall are the impact We
ber number, We pDoUo/cr, Reynolds number, Re
DoUo/v, and the dynamic contact angle 0.
In Yarin and Weiss (1995) the remote asymptotic solu
tion for the flow in the thin axisymmetric fast spreading
sheet is obtained in the form:
Vr V
t+ T
2z
t+ T
where v, is the radial velocity, vz is the axial velocity
component, T is a constant. Expression (1) is relevant
only in the central part of the sheet far from the sheet edge
where the capillary effects lead to the formation of a rim.
Equation (1) can be easily written in the Lagrangian
form
r = ro + vrot, vo = ro/T, (2)
where ro and vo are the radial coordinate and the radial
velocity of a material point at the time instant t = The
mass balance in the lagrangian form yields:
h roho(ro) Or 1(3)
(3)
r 9ro)
where ho (ro) is the initial distribution of the sheet thick
ness.
Equation (3) allows to write a general expression for
the sheet thickness in the Eulerian form
h (t 2 ho0 (4)
which yields the evolution of the film thickness at the axis,
hc, obtained in Yarin and Weiss (1995)
hce= (5)
(t + (5))2
If the impact Weber and Reynolds numbers are high,
the flow far from the wall (where the velocity gradients
are not negligibly small) is determined mainly by iner
tia. Therefore, the dimensionless velocity of the lamella
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
and its dimensionless shape in the central region of the
deforming drop should not depend on the impact param
eters. In Fig. 2 left the experimental data (Bakshi et al.
2007) and the results of numerical predictions (Fukai et al.
1995; S. Sikalo et al. 2005; Mukherjee 2007) for the evo
lution of the drop height he at the symmetry center are
shown as a function of time for various impact parame
ters. All the values are scaled using the initial drop diam
eter Do as the length scale and impact velocity Uo as the
velocity scale.
The corresponding results of our numerical simulations
of drop impact onto a symmetry plane are shown in Fig. 2
right. During the first two regimes all the results lie ap
proximately on a single curve for all the impact param
eters. In the first and second nonviscous regimes, the
height of the drop at the symmetry axis is approximated
by the curves also shown in Fig. 2. It is obvious that the
development of the nearwall boundary layer is not rele
vant in the case for drop impact onto a symmetry plane.
In Fig. 3 the results of the numerical simulations of
the average radial velocity at t 1 in the lamella gen
erated by drop impact onto a symmetry plane are shown
as a function of the radius for various impact parameters.
Surprisingly, the velocity is linear over a relatively wide
range of the radius. Moreover, the velocity distribution
almost doesn't depend on the impact parameters except at
the edge region, where the lamella is deformed due to the
viscous and capillary forces.
As shown in Fig. 4, the shape of the central part of the
lamella also almost doesn't depend on the impact parame
ters except of the edge region associated with the rim for
mation. Therefore, it can be assumed that the thickness of
the lamella and its velocity distribution at very high Weber
and Reynolds numbers are selfsimilar.
The universal dimensionless thickness of the lamella
(4) is determined by approximating of the numerically
predicted shape by a Gaussian function at dimensionless
time instant t 1 and estimating the value of 7 0.25 in
(1) from the numerically predicted velocity gradient:
S0.39 2.34T2
L (t+ 0.25)2 exp (t +0.25)2
Here all the overbared symbols are dimensionless.
In Fig. 5 the approximate shape (6) is compared with
the numerical simulations (Fukai et al. 1995) of drop im
pact with Re 1565 and We 32. At t 1 and
t 2 the agreement is rather good far from the lamella
edge where the lamella is thicker than predicted (indicat
ing that the velocity gradient here is smaller then near the
axis r = 0) and where the rim formation becomes visible.
At t = 0.5 the approximated solution overpredicts the
results of numerical simulations. At this relatively early
stage the velocity field is still two dimensional and cannot
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
1.2
Numerical, drop impact
1.0 t onto a substrate:
/ Re=210, We=30
o Re=450, We=137
0 8 Re = 4010,We= 90
v Re =6020, We =117
0.60..39 O Re = 6260, We = 128
(t + 0.25)2 Experimental, drop impact
0.4 onto a rigid sphere
4 / Re=1068,We 144
0.2
0 1 2 3 4 5 6
o We =397, Re =61
1.0 1t We=761, Re=83
/ We =1165, Re =104
0.6
0.4 T 0.39
(t + 0.25)2
0.2
0.0 2 4 8
0 14 5 6 7 8
t
Figure 2: Drop impact onto a dry substrate (left); the ex
perimental data (Bakshi et al. 2007) and the re
sults of existing numerical predictions (Fukai
et al. 1995; S. Sikalo et al. 2005; Mukherjee
2007) for the evolution of the lamella thickness
at the impact axis as a function of the dimen
sionless time. Drop impact onto a symmetry
plane (right); the results of our numerical pre
dictions for the evolution of the lamella thick
ness at the impact axis as a function of the di
mensionless time.
1.4
1.2
1.0
I 0.8 
0.6
O We =397, Re=61
S We=761, Re=83
0.2 We =1165, Re =104
0.0 .
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
r
Figure 3: Drop impact onto a symmetry plane. The re
sults of numerical predictions of the dimension
less average radial velocity at the time instant
t 1 as a function of the dimensionless radius.
0.25 Impact onto a symmetry plane:
We =397, Re =61
0.20 We=761, Re=83
We=1165,Re=104
Impact onto a solid wall
0.15 Fukai et a. (1995):
We =117,Re =6020
0.10 We=128, Re=6260
0.10
0.05
0.00 . .
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Figure 4: Drop impact onto a symmetry plane. The re
sults of numerical predictions for the dimen
sionless lamella thickness at the time instant
t 1 as a function of the dimensionless ra
dius compared with the numerical simulations
of drop impact onto a flat rigid substrate from
Fukai et al. (1995).
be described by the remote asymptotic solution. The re
sults of the numerical predictions of the pressure pc at the
impact point are shown in Fig. 6. The pressure pc decays
nearly exponentially in time. The best fit of the data is
Pc 1.7exp(3.11).
The universal, selfsimilar flow in the lamella generated
by drop collision corresponds to high Reynolds and We
ber numbers. It is shown Roisman et al. (2009) that the
validity range of the universal solution is determined by
Re > 14 and We > 2.5.
In Fig. 7 the numerical predictions for the dimension
less drop height hcl at the axis at the dimensionless time
instant t = 1 are shown for various Reynolds numbers. At
Reynolds numbers Re > 60 the characteristic drop height
at t = 1 reaches the constant magnitude hc0 = 0.245. In
this range of Reynolds numbers the universal solution is
applicable to the description of the flow in the lamella.
Residual film thickness Expression (6) is valid only
if the thickness of the lamella is much larger than the
thickness of the viscous boundary layer generated at the
wall. An analytical selfsimilar solution of the full Navier
Stokes equations for the flow in the lamella is obtained in
Roisman (2009).
The velocity field is expressed in the form
o[ 5ti
2g ] 
where g is a dimensionless streamfunction which is cal
culated by the numerical integration of the ordinary dif
ferential equation
g'" + 2gg" + g" + g g'2 = 0, (8)
2
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
0.7
Numerical, Fukai et al (1995)
0.6 6 t=0.5
o t=l
05" '.. A t=2
 Approximated
0.4 i ..... t=0.5
b _t=1
02 1
0.3 ,2
0.0 0.2 0.4 0 B 0.8 1.0 1.2 14 16 1.8 2.0 22
Figure 5: Drop impact onto a dry substrate with Re =
1565 and We 32. The numerical predictions
of Fukai et al. (1995) of the shape of the lamella
at various time instants are compared with the
approximate shape (6).
subject the boundary conditions
g = g' 0,
/' 1,
at 0, (9)
at * oo, (10)
with = z/ vt being the similarity variable.
The thickness of the boundary layer is estimated in Ro
isman (2009) from the solution of (8) as
6 1.88 v, (11)
which can be rewritten in the dimensionless form
S1.88 l L/Re. (12)
The thickness of the lamella, hb at the time instant t
tb at which the viscous boundary layer reaches the upper
free surface of the lamella can be estimated using (6) and
(12)
hb e2/5. (13)
At longer times, t > tb the flow in the lamella is gov
erned by the balance of the inertial and viscous forces
leading to its quick deceleration. The expression for the
residual film thickness is obtained in Roisman (2009) in
the following form:
hres 0.79Re2/5. (14)
3 Drop collision with a shallow pool
The dynamics of drop impact on liquid surface, the shape
of the formed crater, the formation and propagation of a
capillary wave in the crater and the residual film thickness
on the rigid wall are determined and analyzed. The shape
o Numerical imulations
Fitting curve
1.53 exp( 2.90
0.0 0.2 .4 .
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Figure 6: Drop impact onto a symmetry plane. Numerical
predictions of the dimensionless pressure pc at
the impact point as a function of the dimension
less time. The impact parameters are We 761,
Re 83, and We 1165, Re 104.
of the crater within the film and the uprising liquid sheet
formed upon the impact are observed using a highspeed
video system. The numerical simulations of the phenom
ena are performed using a freesurface capturing model
based on the volumeoffluid (VOF) model in the frame
work of a 2D axisymmetric numerical method. The fluid
of the drop and the film is the same in all experiments and
three liquids with different properties were used: distilled
water, isopropanol and a glycerin/water mixture consist
ing of 70% glycerin and 30% water.
The governing impact parameters are the Weber num
ber We pUo2Do/a and Reynolds number Re
UoDo/v. The film thickness and time are normalized with
H Ho/Do and t tUo/Do, respectively. In the above
expressions p, a and p are dynamic viscosity, surface ten
sion coefficient and density of the liquids used, Do and Uo
are the diameter and the impact velocity of the drop, and
Ho is the initial film thickness. The initial drop diame
ter is 2.9 mm for distilled water, 2.14 mm for isopropanol
and 2.67 mm for glycerin/water mixture. The drop impact
velocity (velocity just before the drop reaches the film sur
face) is calculated from a distance measurement and a pre
set time delay between subsequent exposures. Thus, for
distilled water the impact velocity varied from 1.68 m/s to
2.91 m/s, for isopropanol from 1.7 m/s to 2.83 m/s and for
glycerin/water mixture from 1.81 m/s to 3.25 m/s. The
liquid film thickness was varied for all liquids, yielding
the nondimensional film thickness of 0.5 to 2.
Fig. 8 shows the crater shape at different time instants
for the flow configuration corresponding to H 2 for
isopropanol. The experimental data are from BerberoviC
et al. (2009). A small circumferential free liquid jet and
the formation of the penetrating and radially expanding
crater inside the liquid film observed in the experiments
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
0.7
0.6 O We 2.75
0.5
0.4
We= 17
0.3 We 761
 O 0
0.2 We=68 We=397 We=1165
0.1
0.0
0 20 40 60 80 100 121
Re
Figure 7: Numerical simulations of drop impact onto a
symmetry plane. The dimensionless drop height
hc1 at the time instant t 1 as a function of the
impact Reynolds number. The dashed line is a
fitting curve of the numerical results.
are shown. After reaching the maximum diameter, the
crater begins a receding motion driven by capillary forces.
It can be seen that the crater shape changes from a nearly
spherical form in the advancing motion to a conical one
during the receding phase.
For the purpose of a quantitative analysis, the predicted
dimensionless crater depth and diameter are compared to
measured ones. The depth is measured at the lowest point
of the crater, and the diameter is determined at a half film
thickness (y/Ho = 0.5), where y is the vertical distance
measured from the free surface of the film.
Plots of dimensionless crater diameter and depth
against dimensionless time are shown in Fig. 9 for iso
propanol, being similar in other cases. The agreement
between the numerical simulations and the experimental
data is rather good.
When the crater approaches the bottom the penetration
velocity decreases due to the wall effects. When the in
ertia of the liquid flow is strong enough, the thickness of
the film below the cavity follows the remote asymptotic
solution Yarin and Weiss (1995) and decreases as the in
verse of the time squared. At some time instant the film
thickness becomes comparable with the thickness of the
viscous boundary layer and the flow in the film is damped
by viscosity. The value of the residual film thickness is
rather important for the modeling of heat transfer associ
ated with drop or spray impact and prediction of the film
breakup. Since its experimental evaluation is not an easy
task, this value is determined from the numerical simula
tions.
It is obvious that the phenomena leading to the appear
ance of the residual film in the cases of drop impact onto
a dry wall and onto a wetted wall are similar. Therefore
expression in the form (14) can be used also for the de
Figure 8: Time evolution of the crater shape for the im
pact of an isopropanol drop, H 2, We = 392,
Re 1730: (a) experiment and (b) simulations.
The time sequences from top to bottom corre
spond tot 0, 1.08, 2.71, 10.84, 21.68, 31.44.
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
Experiments symbols
o H=1,We=384,Re=1700
SH=2,We=189,Re=1200
2,Re=1730
I,1 lines
/ 
10 20 30 40
4 
IQ 3
2 
1 
0
0
30
25
20
1 15
10
05
008
s 005 
0 79Re2'5
003
S021 Re2'5
000
0 2000 4000 6000 8000
Re
Figure 10: Computationally obtained residual film thick
ness under the cavity as a function of the im
pact Reynolds number compared to theoretical
estimations (15).
4 Conclusions
10 '20 30 40 50 In this paper the results of studies of flow occurring dur
10 20 30 40 50
t ing impact of a drop onto a liquid wall film, onto a dry
substrate and doublesymmetric binary drop collisions are
Figure 9: Experimentally and computationally obtained
dimensionless crater diameter (left) and crater
depth (right) for the impact of an isopropanol
drop
scription of the residual film thickness after impact onto a
liquid film:
h, e ARe 2/5 (15)
Fig. 10 displays the comparison of the numerically pre
dicted residual film thickness with the present experimen
tal data in terms of the impact Reynolds number. The
scaling relation (15) describes well the tendency of the
obtained results.
A spectacular phenomenon related to drop impact onto
a liquid film is the generation of a sharp capillary wave on
the crater sidewall. This wave propagates along the cavity
surface downwards, merging at the bottom of the crater
and finally leads to the creation of a central jet Zhang and
Thoroddsen (2008). Similar waves have been observed
in many experiments on drop impact onto a liquid layer
or liquid pool (Leng 2001; Morton et al. 2000). Such a
capillary wave is observed at the surface of the crater in
Fig. 8. It is created inside the uprising sheet and trav
els downwards along the crater surface. This behavior is
well resolved in the simulations. The capillary wave is
observed here only when isopropanol is used, whereas it
could not clearly be seen in impacts of distilled water and
glycerin/water mixture. This is explained by the much
lower surface tension of isopropanol.
presented.
The dynamics of drop impact on liquid surfaces was
focused on the evolution of the crater formed beneath the
surface upon the impact. A theoretical model is presented
for the penetration of the crater at the initial stage, ap
proximating the crater shape by a spherical cavity and the
velocity field in its vicinity by the potential flow. The
asymptotic solution was obtained by neglecting capillary,
viscous and gravity effects, showing a good agreement
with the experimental data. Details of flow including
crater penetration and the capillary wave were resolved
well in the numerical simulations. It is confirmed that in
creasing the impact velocity at a constant film thickness
has little to no effect on the crater evolution in depth and
on the time to reach maximum depth. The numerical sim
ulations demonstrate not only high level of the predictive
capabilities of the advanced model resolving the free sur
face, they also help to better understand the mechanisms
of crater evolution. Moreover, the results of numerical
predictions eventually help to understand the flow in the
liquid during the impact, since no detailed experimental
data for the distributions of pressure and velocity is avail
able. Scaling relations for the residual film thickness have
been proposed based on the description of the film evolu
tion and development of the viscous boundary layer. This
data can be valuable in the modeling of spray cooling.
For drop collisions with the rigid wall and the binary
drop collisions the study revealed that if the impact Weber
and Reynolds numbers are high enough, the flow in the
lamella far from its edge is selfsimilar. Its thickness, ve
locity distribution and pressure distribution are universal
Expenments symbols
o H=1,We=384,Re=1700
SH=2,We=189,Re=1200
H=2,We=392,Re=1730
Predictions lines
  k
Y
and almost don't depend on the impact parameters. The
spreading diameter is determined exclusively by the edge
effects, formation of the capillary rim and viscous com
pression of the lamella in a relatively thin region. The
evolution of the lamella thickness is determined by the
inviscid flow and viscosity. Theoretical modeling of the
spreading of the drop requires new alternative approaches
since the existing models, based on the energy balance or
based on the assumption that the drop spreading diameter
correlates with the lamella thickness, do not correctly de
scribe the mechanisms of drop collision. The results for
the selfsimilar distribution of the thickness of the lamella,
velocity distribution and pressure distribution obtained in
this study can be useful for future modeling of the phe
nomena related to the inertia dominated drop collisions,
including drop impact onto a rigid, porous or elastic sur
faces, impact of solidifying drops and drop binary colli
sions.
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Ilia V. Roisman, and Cameron Tropea. Drop impact onto
a liquid layer of finite thickness: Dynamics of the cavity
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