7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
Binary Collisions of Immiscible Liquid Drops for Liquid Encapsulation
C. Planchette*, E. Lorenceau* and G. Brennt
University ParisEst, LPMDI UMR 8108 du CNRS, 5 bvd Descartes,
77454 Mamela Vall6e cedex 2, France
t Institute of Fluid Mechanics and Heat Transfer, Graz University of Technology
Inffeldgasse 25/F, 8010 Graz, Austria
carole.planchette@univmlv.fr and brenn@fluidmech.tugraz.ac.at.
Keywords: Binary drop collisions, immiscible liquids, crossing separation, instability onset, encapsulation efficiency
Abstract
This work is dedicated to a general description of collisions between two drops of immiscible liquids. Our approach
is mainly experimental and allows us to describe the outcomes of such collisions according to a set of relevant param
eters. Varying the relative velocity as well as the impact parameter we can build for each pair of investigated liquids a
nomogram X, U showing three possible regimes : coalescence, headon separation and offcenter separation. In this
paper, we also study the influence of the liquid properties i.e viscosity, density, surface and interfacial tensions using
a set of aqueous glycerol solutions together with a set of silicon and perfluorinated oils. We show that the coalescence
regime always leads to the full spreading of the oil on the aqueous drop in contrast to the separation regimes where
part of the oil is expelled from the encapsulated drop. For headon separation, two different mechanisms have been
identified : the reflexive separation and the crossing separation. Concerning the stability limits of such collisions, the
aqueous phase seems to be of little influence in the range of studied liquids. For offcenter collisions, the efficiency
of the encapsulation is measured via the amount of oil forming the encapsulating shell. We show that the thickness of
this coating can be tuned independently from the liquid properties and drop relative velocity by varying the impact
parameter. Finally, we briefly address the case of unequal sized drops and the regimes observed for headon separation.
Nomenclature
Roman symbols
D drop diameter (rnm)
M momentum (kg.m.s 1)
S spreading parameter (mN.m 1)
U drops relative velocity (m.s 1)
V volume (rn3)
We Weber number
x impact parameter (m)
X normalized impact parameter
Greek symbols
A drops diameter ratio
p liquid density (kg.m 3)
p viscosity (mPa.s)
a surface or interfacial tension (mN.m 1)
( merged drop aspect ratio
p encapsulation efficiency
Subscripts
oil phase
aqueous phase: glycerol in water solution
maximum
initial
final
Introduction
For already several decades, drop collisions have been
of high interest for understanding natural phenomena as
well as for improving technical processes. Meteorology
and, more precisely, the investigation of rainfall condi
tions have triggered part of the work, see BrazierSmith
et al. (1972). Spray studies which are essential for ap
plications such as spray combustion or spray drying have
also contributed to the development of this research field
especially with the focus of the possible collision out
comes with, for instance, Ashgriz & Poo (1990), Jiang
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
et al. (1992), Qian & Law (1992), Orme (1997), Brenn et
al. (2001), Gotaas et al. (2007). More recently, the case
of collisions between drops consisting of different, in
part immiscible, liquids has raised some interest and we
can cite Gao et al. (2005), Chen & Chen (2006), Chen
(2007), and Planchette et al. (2009). Indeed, such colli
sions occur in combustion engines, but can also be gen
erated in case of a nuclear reactor accident to collect and
neutralize dangerous droplets, or can be used as a pro
cess for the encapsulation of liquids in pharmacology or
food sciences. This last example, which is of great im
portance for drug delivery, appears as a very promising
application of our current work.
To fully describe binary collisions of drops of the
same liquid, the following parameters are needed : the
ambient air properties, the liquid properties density p,
surface tension a, and viscosity p, together with the drop
diameters D1, D2 and relative velocity U, plus a ge
ometrical factor called the impact parameter x, which
measures the eccentricity of the impact. An illustrating
sketch is given in Fig. 1.
Figure 1: Binary collision of drops. Definition of the
impact parameter x.
If we neglect the variations of the gaseous ambient
medium, these parameters can be given in a dimension
less form with the following numbers : the diameter ra
tio of the drops A = D1/D2, the dimensionless im
pact parameter X = 2x/(D + D2), and the Weber
and Ohnesorge numbers, respectively defined as We
U2Dip/ac and Oh p= p/Dip. Considering equal
sized drops with a given Ohnesorge number, the binary
collision outcome can be represented by a (X, We)
nomogram. Several regimes appear corresponding to
one of the four possible outcomes: bouncing, coales
cence, and two mechanisms of separation the reflexive
separation for low impact parameters, and the stretch
ing separation for high impact parameters. This classical
and relatively well described result is shown in Fig. 2.
In this paper we develop similar nomograms for bi
nary collisions of immiscible liquid drops. Our exper
B
C
Str. S
C Ref. S
C: colescence
B: bouncing
Str. S: stretching
separation
Ref. S: reflexive
separation
We
Figure 2: Typical (X, We) nomogram obtained for bi
nary collisions of equalsized drops. A similar
scheme can be found in Qian & Law (1992).
mental work is focused in the survey of the outcomes
and their mechanisms, together with the modifications
of the stability limits by the liquid properties. A very
promising and reliable application of this study is shown
with the control of the shell thickness enabling a tunable
encapsulation of one droplet. Finally, collisions between
unequalsized drops are studied.
Experimental facility
Droplet generators and image processing
To achieve binary collisions of immiscible liquid
drops in a controlled way, we use two droplet genera
tors by Brenn et al. (1996). The drop generators con
sist of a tube with a nozzle of different possible sizes
producing a laminar jet. An integrated piezoceramic
excited by an electrical signal at a given frequency cre
ates a disturbance of the jet and leads to its breakup
with a given wave length (Rayleightype breakup). As
a result, we obtain continuous streams of monodisperse
drops of variable size and defined trajectories. Those tra
jectories are adjusted via the displacement of the gener
ators on microcontrol traverses. The accuracy of 2pm
and 2 allows us to vary accurately their relative im
pact velocity U, as well as the nondimensional impact
parameter X. The setup is shown in Fig. 3.
An ultrafast flash in the order of 10ns illuminates
the region of impact and a Sensicam video camera
produces movies of the collisions. By aliasing the
generator frequency with the flash frequency, we can
record the same collision at different phases. Pictures
are then extracted from the movies in order to determine
the sizes of the drops before and after the collision,
deduce the relative drop velocity U, and calculate the
normalized impact parameter X. In the first part of
our study, the drop sizes varied between 180 pm and
210 pm, and the size ratio A of the two colliding drops
equals unity, except for the final part of the study on
X"/rD,
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
Filters
LIQUID 1 LIQUID 2
Pressurized reservoirs
Drop generators
Computer Camera
on traverse
Signal
Figure 3: Experimental setup consisting of two droplet
generators connected to two immiscible liquid
reservoirs. The generator positions can be ad
justed with microcontrol traverses. The ultra
fast flash allows illumination of the collisions,
which are recorded by the camera.
collisions of unequalsized drops.
Immiscible liquids
In our experiments we use pairs of immiscible liq
uids consisting of one aqueous phase and one organic
phase. The pairs of liquids were selected according to
their surface and interfacial tensions with the aim to en
able a complete encapsulation of the aqueous phase by
the oil phase. As the aqueous phase, mixtures of glyc
erol with water were chosen (G), where the dynamic
viscosity may be varied by the composition of the mix
tures, while the surface tension against air as well as the
density remain fairly constant. The concentrations are
given in weight percent with the following range: from
20% to 55%, which correponds to a viscosity range of
1.76 mPas to 7.90 mPas. As the oil phase, we use four
different types of silicon oil (SO) plus two mixtures of
them. This set of oils allows us to investigate the influ
ence of the dynamic viscosity, keeping the density and
surface tension almost unchanged. Additionally, we also
Liquid Density Dynamic
viscosity
kg/m3 mPa.s
G 20% 1047.9 1.76
G 30% 1072.9 2.50
G 40% 1098.8 3.72
G 50% 1126.0 6.00
G 50% 1126.0 6.00
G 55% 1139.0 7.90
SOM3 892.2 2.79*
SOM5 913.4 4.57*
SOM5+10 925.3 6.6
SOM10 937.2 9.37*
SOM10+20 944.5 14.28
SOM20 951.8 19.0*
PERFLUO 1934.9 5.5*
Surface
tension
mN/m
70.7
70.3
69.5
68.6
68.6
68.1
19.5*
19.5
19.8
20.1
20.3
20.7
17.8
Interf.
tension
mN/m
37.71
36.71
34.91
34.81
34.32
33.81
34.93
36.53
Table 1: Physical properties of the investigated liquids
at 20C.
(*) Values from data sheet of dealer Carl Roth;
(1) /SO M3; (2) /SO M5; (3) G 50%.
used a fluorinated oil called perfluorodecaline (perfluo)
which has similar properties as the silicon oils, except
for its density. Table 1 puts together the physical data of
the liquids relevant to the collisional interaction.
From those thermodynamic data we can calculate a
spreading parameter S. S = Ia oI cow. As S > 0,
the oil is going to spread onto the aqueous phase until
full encapsulation is achieved.
Results and discussion
Survey of regimes and mechanisms
In order to validate our experimental setup, we first
realized binary collisions of drops of a glycerol solution
at 40%. For such collisions of drops of the same liquid,
the four expected regimes could be observed: bouncing,
permanent coalescence, reflexive separation for headon
collisions, and stretching separation for the offcenter
cases. Replacing one of the two glycerol drops by the
silicon oil M3, we observed very similar outcomes :
permanent coalescence plus two separation regimes for
headon and offcenter collisions. Note that the bounc
ing regime has not been observed within our range of
impact velocities but its occurrence has been proven by
Chen & Chen (2006). To keep the comparison with dif
ferent liquid pairs as clear as possible, we replaced the
(X, We) nomogram used for drops of the same liquid
by (X, U) nomograms. As it is shown in Fig. 6, the
nomogram obtained for immiscible liquids looks very
similar to the one for drops of the same liquid. Despite
such similarities, it is important to note that the mech
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
a
a,
C,
won a
eel It
'e 8 0
* coalescence
c stretching separation
* reflexive separation
x bouncing
0 4 8 U, m/s 12
Figure 5: Coalescence between a drop of G 50% and a
drop of SO M3. D = 199pm, U = 2.19m/s
and X = 0. The dark drops consist of the
glycerol solution, which has been dyed.
1.8 U, m/s 2.2 2.6
Figure 4: Top: (X, U) nomogram obtained for binary
collisions of two drops of G 40%. Bottom:
(X, U) nomogram obtained for binary colli
sions of a drop of G 40% with a drop of
SO M3. In both cases, the drop diameter is
200pm 11,'. Considering the respective
range of investigated velocities, the nomo
grams present important similarities.
anisms leading to the separation of the drops are com
pletely different with immiscible liquids.
Coalescence occurs for relatively low impact parame
ters and velocities. Typically X < 0.3 and U < 2 rn/s.
The two drops enter into contact, get strongly distorted,
and lead to an encapsulated drop (aqueous core with an
oil shell) which slowly relaxes to a spherical shape due
to surface tension and viscous loss during its distortion.
A picture of this regime is given in Fig. 5.
Offcenter separation takes place when increasing the
impact parameter independently from the relative veloc
ity (X > 0.6). The oil which starts to spread on the
aqueous phase forms a filament between the two drops.
Because of their opposite trajectories, the drops stretch
this liquid bridge, leading to its breakup. In contrast to
binary collisions of drops of the same liquid, the com
plex formed after impact is not symmetric. This obser
vation was expected, since the two liquids do not play a
symmetric role any more, see Fig. 6.
The most complex case is seen with headon separa
tion. For binary collisions of drops of the same liquid,
Figure 6: Stretching separation of a G 50% with a SO
M10 drop. Top: D 204pm, U 4.00m/s
and X 0.41. Bottom: D = 206pm,
U = 3.99m/s and X = 0.62. The dark drops
consist of the dyed glycerol solution.
the socalled reflexive separation occurs. The drops are
first compressed together. The disclike complex relaxes
under the excess of surface energy and the internal flows.
A cylinder is generated, which stretches and breaks up,
leading to two main drops (at the ends of the cylinder)
plus eventually some additional satellites (central part of
the cylinder). The name of this process comes from the
fact that the liquid of the drop coming from the right side
before impact is mainly found on the right drop born by
the separation. The impact plane acts as a mirror and
redistributes the liquid equally on both sides.
For immiscible liquids, within our combinations of
liquids, different mechanisms have been seen. The full
description of those processes and their domains of oc
currence are still under investigation. In the limit of rel
atively small velocities (in the order of the threshold ve
locity Uo), and with our current knowledge, it seems that
when the liquid densities are of the same order, the vis
cosity ratio pilots the separation. If the encapsulating
0.8
It
* E
6***
64
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
a V
I
I
Figure 7: Crossing separation between G 50% and SO
M3 drops. Left: DG = 210pm, Do
210pm, U = 2.76m/s and X = 0.04. Right:
DG = 192pm Do = 206pm, U = 3.68m/s
and X = 0.09. In both cases, the oil (not
died) can be identified on the right side up
stream from the contact point. Downstream,
an encapsulted drop is seen on the right side,
the left drop is pure oil.
phase is not much more viscous than the encapsulated
one, it can easily flow around it and find itself on the
opposite side of the contact point. This excrescence is
getting stretched by the non dissipated kinetic energy
and breaks up, leading to an aqueous drop fully encap
sulated by an oil shell plus a second drop of pure oil
coming from the
excrescence break up. This crossing separation has
first been described by us in Planchette et al. (2009) and
can be seen in Fig. 7. If the viscosity of the encapsu
lating phase becomes too high as compared to the en
capsulated one, it will stretch the aqueous drop while
flowing around. The resulting twophase cylinder gets
thiner and breaks. Two encapsulated drops are then gen
erated. In the work of Chen & Chen (2006) this pro
cess is called singlereflex separation. One drop mainly
consists of the aqueous phase (and would correspond to
the encapsulated drop of a crossing separation), while
the other one contains much more oil (and would cor
respond to the expelled oil of a crossing separation). In
our work it is currently very difficult to identify the two
phases in the separated drops. Because the encapsulated
drop is smaller than the pure aqueous one before impact,
the same kind of liquid distribution must result, see Fig.
8 and pictures from Chen & Chen (2006). Finally, if the
liquid densities are not of the same order, the distribu
tion of the encapsulated phase is changed: part of it stays
on the contact side, while the rest flows to the opposite
side. The bigger excrescence breaks up under the effect
Figure 8: Headon separation between a drop of G ".i' .
and a drop of SO M10. Do = 202pm,
DG = 200pm, U = 6.08m/s and X = 0.03.
The glycerol (darker) comes from the right
side upstream from the impact. Downstream,
it is difficult to identify the two phases.
of surface tension. This can happen on the impact side,
creating a reflexive separation, see Fig. 9. The occur
rence of these three mechanisms of headon separation
is given, for our current experimental combinations with
equalsized drops, in Table 2.
Influence of the encapsulated liquid viscosity in the
crossing separation domain
In this part of the paper we try to estimate the influ
ence of the encapsulated phase viscosity on the stability
limits of the collisions. For this purpose we used only
the Silicon Oil M3 for the oil phase and varied the vis
cosity of the glycerol solution. For each glycerol con
centration we obtain a (X, U) nomogram where both co
alescence and separation can be observed, see Fig. 10.
It is important to note that, with these combinations of
liquids, the mechanism of headon separation is always
the crossing separation.
These results clearly show that the influence of the en
capsulated phase viscosity on the stability limits of the
binary collisions is extremely low when staying in the
crossing separation domain. This was to be expected.
As the separation is due to break up of the oil phase
excrescence, the aqueous phase is not directly involved
and its influence can be neglected. To predict the thresh
old velocity of the crossing separation Uo, we decided
to measure the aspect ratio of the oil/glycerol complex
Cp b/a at a typical stage after the collision. See Fig.
11 for a definition of (p.
We varied the glycerol concentration and noted the
value of Cp at the stability limit. After a validation of this
measurement by checking that for a given collision Cp
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
 .4
Figure 9: Reflexive separation between a G ".i' drop
(right upstream) with a perfluorodecaline
drop. Do = 182pm, DG = 180pm, U =
3.42m/s and X = 0.06. The oil is expelled
from the left side.
Oil phase Aqueous phase
SO M3
SO M3
SO M3
SO M3
SO M3
SO M5
SO M5 + M10
SO M10
SO M10 + M20
SO M20
PERFLUO
Glycerol 20%
Glycerol 30%
Glycerol 40%
Glycerol 50%
Glycerol 55%
Glycerol 50%
Glycerol 50%
Glycerol 50%
Glycerol 50%
Glycerol 50%
Glycerol 50%
Headon separation
mechanism
Crossing separation
Crossing separation
Crossing separation
Crossing separation
Crossing separation
Crossing separation
Single Reflex sep.
Single Reflex sep.
Single Reflex sep.
Single Reflex sep.
Reflexive separation
Table 2: Occurrence of the different mechanisms of
headon separation for the investigated pairs of
liquids. Drop diameters are 200 pm 20%.
remains almost constant with time, we built a modified
Rayleigh criteria.
For SO M3, in the crossing separation domain, the
stability limit is found for 2.7 < (p < 3.2 and is not
changed by varying the encapsulated liquid viscosity
by a factor 4 (see Table 3 for details). This is our so
called modified Rayleigh criterion. Surprisingly, not
only the value of the critical Cp remains constant for
various glycerol concentrations, but the behavior of this
complex also remains similar: we observe a quasi linear
growth of (p with U, without any difference before and
after the separation. See the results presented in Fig
12. At the present stage of our experiments, it is not
possible to say if this influence remains small also for
the reflexive separation and the singlereflex separation
domains. This question is currently under investigation.
1.6 1.8 2 U, mIs 2.4 2.6 2.8
1.6 1.8 2 U, m/s 2.4 2.6 2.8
1.6 1.8 2 U, m/s 2.2 2.4 2.6 2.8
Figure 10: Nomograms of SO M3 / glycerol binary drop
collisions. The black symbols in the four
nomograms correspond to G 50% and allow
a direct comparison with the other concen
trations.
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
a a a
Figure 11: Collisions between G 50% and SO M3
drops. D z 200pm. From left to right
U 1.81m/s, U 2.53m/s, U
2.60m/s, U 3.25m/s. The aspect ratio
is defined as (p b/a.
zX
*t8 L
.+; r
7Cft
0:
a
*50% SO M3
A 40% SO M3
+ 30% SO M3
* 20% SO M3
x 55% SO M3
1.5 1.7 1.9 U, m/s 2.3 2.5 2.7 2.9
Figure 12: Time evolution of (C for different glycerol
concentrations and velocities >Uo and
Oil phase
SO M3
SO M3
SO M3
SO M3
SO M3
Aqueous phase
Glycerol 20%
Glycerol 30%
Glycerol 40%
Glycerol 50%
Glycerol 55%
Critical value of Cp
2.9 < (p < 3.3
3.0 < (p < 3.3
2.8 < (p < 3.1
2.7 < (p < 3.0
2.7 < C( < 2.9
Table 3: Critical value of Cp for different glycerol con
centrations. The oil phase is SO M3.
1.8 2 2.2 2.4 2.6 2.8
U, m/s
3 3.2 3.4 3.6 3.8
Figure 13: (X, U) nomogram obtained for binary col
lisions of 50% glycerol solution drops with
drops of silicon oil M5. The black symbols
correspond to a similar nomogram where the
oil phase is SO M3. In both cases the drop
diameter is 200pm 11' The influence of
the encapsulating phase viscosity is clearly
seen for the headon collisions.
Influence of the encapsulating liquid
In this part of the paper we focused our analysis on
the influence of the encapsulating phase on the stabil
ity limits. For this purpose, we use drops of a glycerol
solution at 50% and compare the (X, U) nomograms ob
tained for collisions with drops of SO M3 and SO M5,
see Fig. 13. Note that both pairs of liquids lead to cross
ing separation. In contrast to the encapsulated phase, the
oil phase has a strong influence on the stability limits of
the collisions.
Actually, the mean flows generated by the collisions
are located in the thin film coming from the encapsulat
ing drop spreading around the aqueous drop. Observ
ing headon collisions at different relative velocities, we
notice that the time needed for the oil to arrive on the
other side of the glycerol and generate a closed shell
is almost constant when the impact velocity is varied:
for U 2.23m/s, t 813ps; for U 2.463m/s,
t 806ps; for U 2.60m/s, t 844ps; and for
U 2.76m/s, t 833ps. Assuming that the spread
ing velocity of the oil Uspread (in the direction of a
spherical coordinate system) is not affected by the rel
ative velocity of the drops, the dissipation associated to
this flow is independent of U and can be written as :
Evise ftdtfvotpo (r9' ) dV oc Apo, where A
is a constant, po the oil viscosity, r oc Uspread/h,
and h is the thickness of the coating layer. This view
is in good agreement with the experimental results:
2.3 .
1.9 +
+ +
Uo(SOM3) = 2.55m/s, Uo(SOM5) = 3.25m/s,
which leads to a kinetic energy ratio of 0.61. The vis
cosity ratio is 2.677/4.567 0.59.
A 1.5
E
1
0.5
0
75 85 95 t 1,05
t(Dmax), uS
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
3.9
3.5 ^
3.1 
2.7 X/ A slope 1.51
2.3 slope 1.17 S
1.9 A A glycerol 50% SO M5
1.7 2.1 2.5 2.
U,m/s
Figure 14: Evolutionof D,,,/Do witht(Dmax). Ives
tigated oil phases: SOM5 + SOM10;
SOM10; SOM10 + SOM20 and SOM20.
2.3m/s < U < 7.0m/s involving full coa
lescence and separation. Its linear evolution
allows us to consider the spreading velocity
of the oil constant.
y = 2.6297x .355
84 mPa.s12
Figure 16: Top: Evolution of (p with U SOM5/G 50%
and for perfluo/G 50%. The drops have a
7 diameter of approximately 200/pm. Down:
6 growth rate of (, as a function of the oil vis
cosity.
Sy=1.5034x050'1
15
S4 A ing velocity of the oil, we record the collisions at differ
ent instants. This procedure is possible by aliasing the
3 Asicon oils frequency of drop formation and the frequency of illu
Xperfluo mination, which produces moving pictures of the drops
2 with continuously varying phase. From those movies
S 4 8 mPa.s 12 16 20 we extract both the maximum diameter of the merged
drop, D,,,, and the time needed to reach this maxi
Figure 15: Evolution of the threshold velocity of head mum t(D,,,). The time t 0 is taken at the contact
on collisions Uo with o,. The encapsulated time. It appears (Fig. 14) that the evolution of D,,,
phase is G 50%. The data include six sili with t(D,,,,,) is linear and quasi similar for all further
con oils (SOM3; SOM5; SOM5 + SOM10; investigated oils : SO M10, SO M20, and the two mix
SOM10; SOM10 + SOM20 and SOM20) tures 1:1 SO M5+SO M10 and SO M10+SO M20. Now,
plus the perfluorodecaline. The scaling law looking at the stability limit of the headon collisions, we
Uo oc J ,1/2 is in good agreement with the plot in Fig. 15 the threshold velocity vs the oil viscosity
experimental values. (the glycerol concentration is kept constant at 50%). De
spite the fact that all different mechanisms can be seen
By further increasing the oil viscosity, while keeping for the headon separation, the agreement with the scal
the same glycerol concentration, we change the headon ing law Uo cx p, 1/2 is very good, see Fig. 15. Note that
separation mechanism (see Table 2). But if the main dis this evolution of Uo with p was already found by Jiang
sipation occurs at the early stage of the encapsulation, et al. (1992) for drops of equal liquids.
and if the oil spreading velocity is really constant, the To extend our study to the influence of the encapsu
previous description still holds, and the same behavior lating phase, experiments with perfluorodecaline have
should be seen for the other oils. To estimate the spread been carried out. As shown in Table 1, this allows
o X
x SO M5+10 Glycerol 50%
*SO M 10 Glycerol 50%
+ SO M 10+20 Glycerol 50%
o SO M 20 Glycerol 50%
125 135
x glycerol 50% Perfluoro
S 3.3 3.7
A silicon oils
Xperfluo
16 20
5,
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
* U=2.61 m/s
A U=2.10 m/s
x U=2.89 m/s
 pure geometric capture
modified geometric capture
0 0.1 0.2 0.3 0.4 X 0.6 0.7 0.8 0.9 1
Figure 17: Evolution of p with X at different impact
velocities. Aqueous phase: G 50%; oil
phase: SO M3.
us to vary the oil density, keeping the viscosity and
surface/interfacial tensions in the range of the one of
SO M5. Here again, we observe that the stability limit
for headon collisions is well described by Uo oc /o1/2
The difference in momentum prevents a regular dis
tribution of the oil around the glycerol solution. This
can be directly seen in Figs. 8 and 9. This twoheaded
distribution of the oil modifies the growth rate or Cp
(Fig. 16) but does not strongly change Uo (Fig. 15).
Encapsulation efficiency
With the aim to use such binary collisions for liquid
encapsulation of one liquid in an immiscible other one,
it is important to control the thickness of the shell. In
the case of stretching separation, the outcome always
consists of the full aqueous drop encapsulated by an oil
film and a smaller pure oil drop with some potential
satellites, all of pure oil. In contrast to headon colli
sions, such a configuration ensures the encapsulation of
the full aqueous drop. Measuring the difference between
the volumes of the drops of the coated liquid upstream
(Vw,,) and downstream from the impact point(Vwj), it
is possible to calculate the volume AVc V,,f V,,,i
of the oil forming the shell. Its nondimensional form
is defined as AVc/Vo,i, where Vo,i is the initial oil
drop volume (volume of the coating drop upstream from
the impact point). In cases of permanent coalescence of
the two drops, p 1. We first vary, for a given pair
of liquids (SO M3 and Glycerol at 50%), the impact
velocity and measure p (see Fig. 17 ) for different
impact parameters. The amount of oil left around the
aqueous core diminishes with X but is not modified by
U. Changing the concentration of the glycerol solution
or the organic phase (see Fig 18) shows the same
behavior : the only parameter from which p depends is
X. In other words, the thickness of the shell can easily
be tuned by changing X without taking into account
0.2 0.4 X 0.6
0.3 0.4 0.5 0.6 X 0.7
0.8 0.9 1
Figure 18: Top: Evolution of p with X for different
oils, the aqueous phase is G 50%. Bottom:
Evolution of p with X for different glycerol
concentrations. The oil phase is SO M3.
the relative velocity or the pair of liquids processed.
This phenomena is of course of a great advantage for
industrial applications. Comparing the results of Figs.
18 and 18 we see that, if we take into account the error
bars (not represented in Fig. 18 for clarity), all points
collapse on one line. The dashed lines of Figs. 18 and
18 ("pure geometric capture") assume that the quantity
of oil coating on the aqueous drop corresponds to the
interacting volume defined in Fig.19. For X > 0.5,
the nondimensional interacting volume can be written
as a function of X : (1 X)2 (1 + 2X). The
2R
Figure 19: Interacting volume for offcenter collisions
with X > 0.5. Its non dimensional form is
p (1 X)2. (1 + 2X).
1 A& asM ma an &
0.8
U=2.28 m/s[glyc]=20%
o U=2.26 m/s[glyc]=30%
A U=2.20 m/s[glyc]=40%
X U=2.25 m/s[glyc]=50%
 pure geometric capture
modified geometric capture
AA^*^
><<^^x
experimental volumes, however, are slightly smaller.
This may be due to the fact that, while the drops come
into contact, they are distorted and may slightly rotate.
Considering this possible explanation, our geometrical
argument agrees quite well with the experimental data.
Unequalsized drops
rI
a^
a
Figure 20: Collisions of G 50% and SO M3 drops.
Left: Do 155pm, DG 185pm, U
3.43m/s and X 0 Right: Do = 180pm,
Do 150pm, U = 3.14m/s and X
0.02. The oil is expelled due to crossing sep
aration.
(S
ft"
Figure 21: Collisions of G 50% and SO M3 drops.
Do 358pm, Do 202pm, U
5.23m/s and X 0.05. The oil is expelled
due to reflexive separation.
The case of unequalsized drops is briefly touched in
this section. Our motivations are to better understand
these collisions, but also to generalize the encapsulation
application by broadening the stability of full coales
cence orby developing the possibility to have a shell vol
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
ume bigger than the core. Because the generation of our
droplets is based on the Rayleigh instability, their pro
duction at a given frequency limits their size ratio Brenn
(2000). For this reason, we worked with the following
combinations:
drops of SO M3 with Do 155pm plus drops of a
glycerol solution at 50% with Do z 185/m. This
size ratio corresponds for these two liquids to a mo
mentum ratio oil/glycerol (Mo/Mo) of 0.46.
drops of SO M3 with Do 180pm plus drops of
a glycerol solution at 50% with DoG 150pm for
Mo/M0 = 1.37.
drops of SO M3 with Do 350pm plus drops of
a glycerol solution at 50% with DG o 200pm for
Mo/MG 4.24.
Note that the momentum ratio given by perfluorodeca
line / glycerol at 50% with equal sized drops of 200pm
diameter (as in Fig. 9) is 1.72.
For M0/M = 0.46, i.e. when the oil phase has to
spread around an aqueous drop with a higher momen
tum, we observe that the stability limit for headon col
lisions is moved to 3.19 < Uo < 3.28m/s. In com
parison, for equal sized drops (D, Do 195pm
5%), we have : 2.52m/s < Uo < 2.56m/s. A sim
ilar stabilization is also seen for M,/MG 1.37 with
2.97m/s < Uo < 3.14m/s. In both cases, the pic
tures of the collisions indicate that crossing separation
occurs, compare Fig. 20 with Fig. 7. This means that,
in the case of an oil drop smaller than the aqueous one
(here Mo/Moof 0.46), less oil is available in the ex
crescence. As a result, more kinetic energy is needed to
stretch it until the modified Rayleigh criterion is reached
and leads to its breakup. Note that (, is found to be
3.05, which is in very good agreement with the values
found for equal sized drops and tends to validate our
point of view on crossing separation breakup. In con
trast, when the oil drop is bigger than the aqueous one
(here Mo/Mo = 1.37), a bigger volume of oil has to
flow, leading to higher viscous losses. For this reason,
the growth of the excrescence is limited, and the stabil
ity increases. The measurement of the critical ,p gives
a value between 2.85 and 2.95, which corroborates our
statement about the limited growth of the excrescence
while staying in the range of our modified Rayleigh cri
terion.
When increasing further Mo/M0 to 4.24, the sta
bility of the headon collisions is further increased :
4.14 < Uo < 5.22m/s. The broad range of Uo is due to
the difficulty to identify the transition with the recorded
frames. It is also interesting to point out that the mecha
nism for the headon separation is not the crossing sepa
ration any more. As for the perfluorodecaline, reflexive
VE+
separation takes place, see Figs. 21 and 9. At the mo
ment we may simply identify that, for a given viscosity
ratio of the two liquids, the momentum ratio of the two
drops determines the mechanism of the headon separa
tion. We hope that our ongoing work will bring a good
theoretical explanation of this observation.
Conclusions
We presented experimental investigations on immisci
ble liquid droplet collisions for encapsulation. Aque
ous glycerol solutions were tested with several silicon
oils and a fluorinated oil. We survey the different out
comes of such collisions and compare them to the more
classical case of collisions between drops of the same
liquid. Even if the regimes are very similar, we show
that the process leading to headon separation are com
pletely different. For immiscible liquids we could iden
tify three mechanisms: crossing separation, singlereflex
separation, and reflexive separation. The viscosity ra
tio plus the momentum ratio control the process of sep
aration. The threshold velocity for headon separation
scales as the square root of the encapsulating liquid. In
the crossing separation domain, this threshold velocity
is not modified by changing the encapsulated phase vis
cosity of a factor 4. For unequalsized drops, the full
encapsulation can be achieved for higher velocities, re
gardless which drop is the bigger one. Another way to
vary the shell thickness is to work with offcenter colli
sions. In the domain where X > 0.5, the coating thick
ness can be tuned by varying the impact parameter, in
dependently of both the pair of liquids and the relative
velocity of the drops. As a result, binary collisions of
immiscible liquids drops appear as a very promising and
reliable way to encapsulate a liquid.
Acknowledgements
We acknowledge financial support from the Hubert
Curien Program AMADEUS 2009 from the French Min
istry of Foreign Affairs and the Austrian OAD. Financial
support from the Steiermnirkische Landesregierung for
C.P is gratefully acknowledged. We wish to thank the
institute TVTUT of Graz University of Technology for
support in the measurements of intercafial tensions.
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
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