spontaneous liquid marble formation on packed porous beds
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Dynamic Article LinksC<Soft Matter
Cite this: DOI: 10.1039/c2sm26529j
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Spontaneous liquid marble formation on packed porous beds†
Catherine P. Whitby,* Xun Bian and Rossen Sedev
Received 2nd July 2012, Accepted 6th September 2012
DOI: 10.1039/c2sm26529j
The encapsulation of aqueous and organic solvents with particles used to form liquid marbles implies
there are attractive interactions between the particles and those different liquids. This is often masked,
however, by the impact of the droplet kinetic energy on marble formation. We investigated droplet
wetting and evaporation when drops were gently placed (without rolling or shaking) on beds of
silanised glass beads. Particle coating of the drop surface occurred within seconds of liquid contact with
the particle bed. This ruled out evaporation from causing the particles to appear to rise up the surface of
the drop as it was reduced in volume. Particles attach to the fresh liquid surface created during the
droplet oscillations immediately after contact. The further ordered advance of the particles over the
drop surface and the close-packed arrangement of the particles revealed the role of capillary forces in
the coating process. By minimising the kinetic energy of the droplet contact with the particles, we found
that maximum particle coating occurs at liquid surface tensions just above the critical wetting tension of
the beads.
Introduction
The wetting behaviour of fine particles at air–liquid surfaces1 is
important in powder and soil technologies where liquid droplets
are in contact with granular or powdery surfaces. These include
dispersion, granulation, filtration and water repellency. Liquid
cannot penetrate into powders that consist of poorly wetting
particles. The particles may encapsulate drops that are rolled
across the bed, forming liquid core–particle shell structures
(liquid marbles) that have large contact angles on any
substrate.2–4 Several studies have exploited ‘‘liquid marbles’’ for
transporting small volumes of high surface tension liquids,5
storing water in a powdered form6,7 and for the encapsulation
and delivery of active (water soluble) ingredients.8,9 Recently
Gao and McCarthy,10 Xue et al.11 and Matsukuma et al.12
reported encapsulating liquids with lower surface tensions (down
to 20 mN m�1) using fluorinated polymeric powders. All the
liquid marbles had large contact angles. On the other hand,
McHale et al.13 showed that simply depositing water drops onto
beds of hydrophobic particles causes the underside of the drops
to be coated with particles, but no liquid marble is formed. These
observations suggest that the particle surface energy influences
liquid marble formation. They are complicated, however, by the
contribution of the drop kinetic energy to the particle wetting
and attachment processes. In this paper, we study the attachment
and movement of particles over the surfaces of stationary drops
of ethanol–water solutions. The particle wettability (q) was
Ian Wark Research Institute, University of South Australia, MawsonLakes, SA 5095, Australia. E-mail: [email protected]
† Electronic supplementary information (ESI) available. See DOI:10.1039/c2sm26529j
This journal is ª The Royal Society of Chemistry 2012
varied systematically from hydrophobic (<90�) to hydrophilic
(>90�) by controlling the ethanol concentration and hence liquid
surface tension (gl).
A liquid droplet (of radius, R and viscosity, m) placed on the
surface of a bed of particles (of radius, r) may absorb into the bed
(Fig. 1a) or evaporate (Fig. 1b), depending on the particle
wettability. The average rate of imbibition of liquid into a porous
substrate is determined by the pore geometry and q.14 For steady
flow conditions and small pores, the Washburn equation relates
the capillary driving force of a liquid penetrating through a
compact bed of particles and the viscous drag as
d2
t¼ reffgl cos q
2m(1)
where d is the depth of liquid penetrating into the bed in time
t. reff is the effective pore radius. For the special case of powder
beds that can be treated as uniform arrays of cylindrical
pores,15,16 reff is calculated using
reff ¼ 2(1 � fp)/fprpAp (2)
where Ap is the specific surface area of the particles. fp, the
porosity parameter, is determined by the ratio mp/VTrp, where
mp is the mass of particles in the bed, VT is the bed volume and rpis the particle density. Assuming that the three phase contact line
remains stationary as liquid drains into the pores (the constant
drawing, or constant radius limiting case17), the penetration or
wicking time, s, is given by
s ¼ 1:35Vo
2=3
�1� fp
�2reff
m
gl cos q(3)
Soft Matter
Fig. 1 Behaviour of ethanol–water droplets (10 mL in volume) on
packed beds of hydrophobic glass spheres (98 mm in diameter). (a)
Ethanol-rich drops wet the particles and penetrate into the packed bed
within seconds, leaving a circular depression on the bed surface. (b)
Water-rich drops wet the particles only partially and remain trapped on
the packed beds; they evaporate over a few hours. (c) Water drops rolled
over the packed bed surface become encapsulated by a layer of particles,
i.e. form liquid marbles. The particle shell is robust and the liquid marble
can be rolled onto other surfaces without breaking or leaking. (d) A water
marble sitting on the packed bed. (e) Particles coat drops of intermediate
alcohol concentrations within a few seconds of drop impact on the bed.
The needle shown in the top image is 1.7 mm wide.
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where Vo is the initial liquid volume. Although suited to a large
volume of liquid, Marmur17 showed that this theory describes the
kinetics of liquid penetration from a single large drop (R/r >
�30).
Above a critical q, s/N and the droplet is effectively trapped
on the bed surface. For water drops on solid surfaces, q ¼ 90� isthe boundary between hydrophilic and hydrophobic solids.
Providing that porous solids behave like bundles of capillary
tubes, the 90� threshold will also apply. Ban et al.18 observed a
lower threshold, however, for powders of spherical particles wet
by ethanol–water solutions. The shape of a liquid surface inside a
cylindrical capillary does not change during imbibition. In
contrast, capillaries formed by the voids between close-packed
spherical particles do not possess parallel sides and the curvature
of the liquid surface keeps changing. Assuming that the radius of
the droplet is much larger than the size of the voids, Ban et al.18
Soft Matter
predicted that highest contact angle at which wetting occurs (qc)
is qc is 50.7�. Ban et al.18 found qc ¼ 50–58� for polymeric,
silanised glass and sulphur powders of various sizes. Compacted
powder beds were prepared by centrifuging polyethylene tubes
filled with powder. Shirtcliffe et al.19 measured critical contact
angles of 52–61� for fluorinated glass beads and 61–65� for
fluorinated sand. These analyses neglected the effect of the
hydrostatic pressure. Recently Extrand and Moon14 showed that
imbibition may be prevented even at very low q for drops
comparable in size to the pores between spherical particles.
A small drop of fluid trapped on a surface will adopt a
spherical cap shape, of contact radius, rd, and height, hd and
evaporate over time. Assuming that evaporation is due to
diffusion through the liquid vapour interface and that the vapour
concentration gradient is radially outwards, McHale et al.20
showed that the evaporation rate can be expressed as
dV/dt ¼ �lhd (4)
where l ¼ 2pD(cN � c0)/r. D is the vapour diffusion coefficient
and c0 and cN are the vapour concentrations at the drop surface
and far removed from the surface, respectively. For non-wetting,
pure liquids (q > 90�), the contact radius decreases while the
contact angle remains constant during evaporation.20 Under
these conditions20
rd2 ¼ C � 2lt sin2
q
pð1� cos qÞð2þ cos qÞ (5)
where C is a constant. The evaporation of binary liquid mixtures
has been examined experimentally. Sefiane et al.21 and Cheng
et al.22 observed that the more volatile ethanol evaporates before
the water from ethanol–water drops. A kind of ‘‘stick–slip’’
behaviour or transition regime is observed in between, as the
contact area de-pins and q increases to reflect the higher water
content of the drop. Comparison between roughened and
smooth substrates suggests that droplet pinning on textured
surfaces can slow evaporation.23
Solid particles strongly adhere to liquid surfaces. The depth to
which a particle immerses into the liquid (H) is given by
H ¼ r(1 + cos q) (6)
Thus as q/ 180� particles attached to droplet surfaces form a
barrier that prevents the liquid from contacting other surfaces.
Hence Aussillous and Quere24,25 showed that weak forces can
actuate motion of water and glycerol drops encapsulated by
silanised, naturally textured grains (lycopodium spores) with q �160 to 165�. Liquid marbles are formed by agitating drops on
very hydrophobic powders (hydrophobised silica, fluoropoly-
mers and graphite, Fig. 1c). Coatings formed by perfluoroalkyl
particles (q � 177�, up to 35 mm in size) are unusually robust and
long-lived.10 Water marbles move reversibly under electrowetting
conditions due to the high water surface tension and conform-
ability of the particle coating (silanised lycopodium spores).26
The rate of water evaporation from marbles (graphite micro-
powder) is substantially slower than from uncoated droplets.27
The drop profile remains spherical as the liquid volume
decreases, until the maximum surface packing density is reached
and the coating crumples into a compressed residue.27
This journal is ª The Royal Society of Chemistry 2012
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Liquid drops may be partially coated by hydrophobic parti-
cles. McEleney et al.28 observed that the mass of PMMA beads
(q� 120�, dp ¼ 42 mm) or copper powder (q� 157�, dp ¼ 9, 15 or
320 mm) collected by a water drop rolled on the powder bed was
proportional to the drop surface area. The ratio of the powder
mass to surface area varied with the particle density, size and
contact angle. Hapgood and Khanmohammadi29 observed liquid
marbles form prior to penetration of drops into beds of particles
(tens of micrometres in size) with q < 90�. The rate of penetrationby liquid sprayed onto a bed is delayed when particles adhere to
the drops.30 Eshtiaghi et al.31 observed that the impact of a drop
(of aqueous glycerol) on a bed of polytetrafluoroethylene spheres
(diameter, dp ¼ 100 mm) could cause liquid marble formation.
They found that the coated surface area depends on the drop
kinetic energy and m, but is less sensitive to gl.31 McHale et al.13
found that drops of alkanes of short chain lengths were partially
coated by coarse fluorinated silica beads under saturated vapour
conditions. Crucially, the mechanism of particle coating and the
roles of particle wettability and liquid absorption or evaporation
in the coating process remain unclear.
Here we present the results of a systematic study of particle
coating of alcohol–water drops placed onto porous beds of
silanised coarse glass spheres (98 mm in diameter). The kinetic
energy of the droplet impact and hence entrainment of the glass
spheres by liquid flow or oscillations was minimised. The kinetics
of the penetration and evaporation of alcohol–water drops
placed onto the porous beds were investigated to determine their
roles in the coating process. We show that the spheres coat the
drops within minutes. The attached particles form a hexagonally
close packed layer. Maximum coating is achieved when q is just
above the threshold for wetting of the powder bed.
Experimental section
Spherical glass beads (Potters Industries) of three different sizes:
(42 � 4) mm, (98 � 8) mm and (165 � 15) mm in diameter (as
measured from SEM images) were hydrophobised using tri-
chloro(1H,1H,2H,2H-perfluorooctyl)silane (97%, Sigma-
Aldrich). The particles were mixed with a solution of the silane
dissolved in 4 : 1 (v/v) mixture of hexadecane (99+%, Sigma-
Aldrich) and chloroform (99.8%, Chem-Supply) in a dry
nitrogen environment. Planar glass slides treated in the same
fashion exhibited a water contact angle of 108�.Particle beds were prepared by packing hydrophobised glass
beads into cylindrical containers, 25 mm in diameter and 11 mm
in height. The particles were packed gradually while tapping the
container to remove air pockets. A clean glass microscope slide
was used to smooth the surface of the bed. The effective pore
radius in the beds was derived frommeasurements of the pressure
required to prevent capillary flow of cylcohexane (a perfectly
wetting liquid) in beds of the particles (capillary pressure
technique).
Liquid drops (10 mL in volume) were gently placed on the
surfaces of the packed beds. The ratio of the drop volume to the
volumes of the pores in the beds was about 105, ensuring that
the penetration kinetics could be described by the Lucas–
Washburn theory.17 The liquids used were mixtures of ethanol
(99%, Chem-Supply) and ultrapure water, toluene (99%, Merck),
cyclopentanol (98%, Ajax), ethylene glycol (99%, Sigma
This journal is ª The Royal Society of Chemistry 2012
Aldrich), glycerol (99%, Chem-Supply) and methyl-
trioctylammonium trifluoroacetate (Merck). The evolution of
the drop shape during penetration or evaporation was recorded
using the video camera of a sessile drop setup (OCA20, Data-
Physics). The drop height, hd, drop radius, rd, and the height of
the particle coating, hp, were measured at different times from
images extracted from the video recording using ImageJ soft-
ware. The time for a drop to fully penetrate into the dry bed, s,was taken as the time from drop deposition to the moment when
no liquid remained on the porous surface, i.e. when hd ¼ 0.
Results
The possible behaviour of a liquid droplet deposited on a packed
bed is shown in Fig. 1. If the liquid wets the particles it will pene-
trate into the capillary channels under the contact area rather
quickly (Fig. 1a). If the particles are hydrophobic enough, the top
layer of particles behaves like a superhydrophobic surface. The
droplet sits on the particles but microscopically, a major portion of
the nominal contact area consists of separate liquid–air interfaces.
The droplet evaporates after a longer period of time (Fig. 1b). If the
droplet is rolled rather than deposited carefully on the surface, it
will collect many hydrophobic particles and form a liquid marble
(Fig. 1d). However, even a carefully deposited droplet may be
covered spontaneously with a particle layer, as shown in Fig. 1e.
When the drop impacts on the bed, it advances over the surface
to some extent. Hydrophobic particles attach on contact with the
freshly created liquid surface. Droplet spreading is opposed by
the poor wettability of the particles, causing the droplet to
retract. So the attached particles will be carried away from the
bed. If spherical, as in Fig. 1e, they form a hexagonal arrange-
ment; irregularly shaped particles form disordered arrays.
Particle coating during drop shape oscillations has been
described by Eshtiaghi et al.31 In the experiments described here,
however, the kinetic energy of the impact was minimised by
gentle deposition. The oscillations only last about 100 ms.
During this time the particle coating rises to about 66% of its
final height. Over the next few hundred milliseconds, the particle
array slowly advances to its final height over the now steady
surface. After 1 s there are only particle rearrangements within
the layer. In time, the liquid will evaporate from the armoured
droplet. The particle shell will sink back into the bed or remain
trapped on the bed surface, forming a crumpled residue.
For particles of a given size and shape, the area of the drop
that is coated by particles and the subsequent behaviour of the
drops (penetration into the bed, evaporation, or both) depends
on the surface tension of the liquid. Alcohol-rich drops (gl < 27
mN m�1) penetrate the packed bed within seconds. The kinetics
of penetration of a 10 mL drop is shown in Fig. 2. The drop
height, hd (solid line), decreases as liquid is quickly sucked into
the capillary space formed between the packed particles. As the
drop height decreases, particles coat the drop surface up to a
height hp (open symbols; hp# hd). The particle coating sinks with
the liquid as it is drawn into the bed. The time, s, taken for the
drop to penetrate completely into the porous substrate (with no
liquid remaining on the surface) is just over 1 s. During pene-
tration, the drop radius, rd (dashed line), increases very little as
particles on the surface of the bed pin the contact line quite
efficiently.
Soft Matter
Fig. 2 Droplet penetration. (a) Characteristic parameters of a sessile
water–ethanol drop (V ¼ 10 mL, gl ¼ 26.8 mN m�1) on a packed bed of
hydrophobic particles (98 mm in diameter). (b) Kinetic behaviour of the
drop: drop height, hd (solid line), drop radius, rd (dashed line) and height
of the particle coating, hp (open points) as functions of time. The drop
quickly penetrates the porous bed of hydrophobic glass spheres. The
penetration time, s, is the time taken for the whole droplet to disappear.
Fig. 3 Droplet evaporation. Kinetic behaviour of partially wetting
droplets (V ¼ 10 mL, gl ¼ 28.8 mN m�1) and slowly evaporate on (a) a
hydrophobic glass slide and (b) a packed bed (glass spheres, 98 mm in
diameter) of identical wettability. Parameters defined as in Fig. 2a: drop
height, hd (solid line), drop radius, rd (dashed line) and height of the
particle coating, hp (open points). (c) Profiles of an encapsulated drop
during evaporation. The droplet diameter in the upper image is 2.4 mm.
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For surface tensions lower than 26 mN m�1, the particle
coating does not appear to slow down liquid penetration. The
coating particles readily sink back into the bed as the liquid
drains out. However, at 26 <gl # 27 mN m�1, drops are rapidly
and fully coated by particles. This slows down penetration and sis now several seconds long. After penetration is complete, a
shallow depression is observed in the flattened packed bed.
The drop penetration time, s, was used to estimate the contact
angle of the ethanol–water solutions on the particles through eqn
(2). The derived angles were compared with those measured with
the same liquids on a flat glass plate silanised in the same manner
as the particles (Fig. S1 in ESI†). Except in the case of very short
penetration times (<0.2 s), the derived contact angles were
consistent with advancing contact angles on the flat surfaces.
The lowest contact angle at which a liquid drop sits on the
particle bed without any penetration is close to 84�. The criticalsurface tension of the particles was 15 mN m�1 as obtained from
linear plots of the cosine of the contact angle, cos q, against the
surface tension of the wetting liquid, gl (Zisman plot). The crit-
ical wetting angle is achieved by drops with gl > 27 mN m�1;
these poorly wet the particles, do not penetrate into the packed
bed, and evaporate.
Water-rich droplets evaporate within about 100 minutes of
being deposited on the particle bed, in a similar fashion to drop
evaporation on flat plates. Drops are slowly coated by particles
in the late stages of evaporation, when the droplet contact area
de-pins. In contrast, drops of intermediate alcohol concentra-
tions (27 mN m�1 < gl < 45 mN m�1) are coated by particles
within seconds after deposition (Fig. 1d). The average rate of
coating increases as the surface tension decreases. Coated
droplets evaporate at slower rates than drops placed on a smooth
hydrophobic surface.
Soft Matter
The kinetics of drop evaporation (at 27 mN m�1 < gl < 45
mN m�1) on flat hydrophobic surfaces and on porous bed of
hydrophobic spheres is shown in Fig. 3a and b, respectively.
During the first 100 seconds, the radius and height of drops on
the flat surface decrease very slightly. In the next stage (�400 s),
the radius decreases dramatically as the drop contact angle
increases. The drop height and radius then decrease simulta-
neously as evaporation proceeds (at t > 500 s). In contrast, the
radius of drops on the porous bed increases slightly while the
height of the drop decreases, during the first 100 seconds.
Particles coat the drop up to a height hp (<hd) during the first few
seconds of this period. Further coating of the drops is driven by
the subsequent reduction in the drop radius, apparently trapping
the drop at a relatively low contact angle. After about 200 s, the
drop height decreases while the drop radius remains roughly
constant. Fig. 3c shows that the encapsulated drop collapses in
the centre. After 100 min, there are no apparent further changes,
so that a crumpled shell remains on top of the packed bed
(Fig. 3c).
Comparisons of the height of the particle coating, hp, on
droplet surfaces were made one second after placing the drops on
the powder bed. This characteristic time, sc, was selected so that
the coating is fully formed but evaporation is rather insignificant
(Fig. 3b). The hp (t ¼ sc) increases dramatically as the particle
wettability approaches the angle corresponding to the surface
tension below which penetration occurs (Fig. 4a). Particle
coating was also observed with a variety of other liquids such as
alkanes, aromatics, esters and their mixtures. For low viscosity
solvents, the relation between hp and gl is essentially the same
(Fig. 4, solid line). For highly viscous solvents, such as glycerol
This journal is ª The Royal Society of Chemistry 2012
Fig. 4 Dependence of (a) the height of the particle coating, hp, nor-
malised with the droplet height, hd, and (b) droplet penetration time, s, onthe particle wettability, q, for drops placed on packed beds of hydro-
phobic glass spheres: 98 mm (circular points) and 42 mm (triangular
points). Drops (V ¼ 10 mL) consisted of aqueous ethanol solutions and
pure solvents (solvent type indicated in the graph). qc is the contact angle
of the particles that corresponds to their critical wetting tension. sc is thecharacteristic time for particle coating of the drops. The lines are guides
to the eye.
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(gl ¼ 64 mN m�1, m ¼ 1490 mPa s) or ionic liquids (e.g. meth-
yltrioctylammonium nitrate, gl ¼ 27 mN m�1, m ¼ 2316 mPa s)
the rate of particle coating is substantially slower.
Similar relations between drop penetration, evaporation and
particle coating and the liquid surface tension were observed with
hydrophobic particles between 90 and 180 mm in size. Longer
penetration times, s, was observed for alcohol-rich drops (gl < 25
mN m�1) on beds of 44 mm particles. Particles that coat drops
during penetration readily sink back into the bed and do not slow
down penetration. The complete coating of the drops occurs,
however, at slightly lower contact angle values for 44 mm sized
particles (Fig. 4a). Drops are coated within seconds of deposi-
tion. This slows down penetration and s ranges between 1 and
100 seconds (Fig. 4b).
Discussion
We have manipulated the behaviour of small droplets (10 mL)
gently deposited on packed beds of hydrophobic glass particles
This journal is ª The Royal Society of Chemistry 2012
(from 38 to 180 mm in size) by varying the liquid surface tension.
At low surface tension the liquid wets the particles well. Capillary
suction into the porous space formed between the packed
particles quickly drains the liquid from the droplet. At larger
surface tensions, the wettability is worse, i.e. the contact angle is
larger. Liquid penetration into the packed bed is slowed down or
even completely prevented by the upward action of the capillary
pressure. In the latter case the droplet sits on the surface of the
packed bed, which behaves like a superhydrophobic surface and,
over time, the liquid evaporates. A small depression is left on the
bed surface where the droplet was initially deposited. At inter-
mediate wettability (82� < q < 100�, which corresponds to 27 mN
m�1 < gl < 45 mN m�1) the rather large particles (�100 mm)
attach strongly to the liquid surface and climb up the droplet
forming a closely packed coating.
In order to model the relation between surface tension and
wettability we use here the surface of a glass slide silanised in the
same fashion as the particles as a model surface. The slide is very
hydrophobic (advancing and receding water contact angles of
120� and 110�, respectively) and contact angle obtained with
various liquids are shown in Fig. S2 in ESI.† For a circular
capillary vertically immersed in a liquid, the transition between
wetting (i.e. capillary rise) and dewetting (i.e. capillary depres-
sion) occurs exactly at a contact angle of 90�. On a packed bed,
however, the geometry of the surface plays a substantial role. In
tightly packed beds the contact angle characteristic of neutral
wettability is around 60�.19 Here the bed packing is looser, to
enable marble formation. The transition from penetration to
non-penetration occurs at about 80� for the 90–106 mm particles.
At lower surface tensions the droplets penetrate the porous
bed. The kinetics of penetration at constant drop diameter is
given by eqn (1). The droplet diameter stays nearly constant for a
period of time – see Fig. 2b, 3a and b. The surface of the packed
bed is essentially a rough hydrophobic surface and it is not
surprising that the contact line stays pinned until evaporation
destroys the droplet (Fig. 3a and b). The penetration time can be
used to estimate correctly the advancing contact angle (Fig. S1 in
ESI†). This is because the model captures the physics of the
process, i.e. the capillary suction is well described by the Wash-
burn equation, the contact area between the liquid and the solid
is approximately constant (the contact line is pinned), and
evaporation is negligible at such short times. The penetration
time for a droplet of a given surface tension is characteristic of
the wettability of the porous material and is commonly used for
wettability determination, e.g. in soil science.32–34 However, in
our case the times are very short (�1 s, Fig. 2b) and therefore
practically inconvenient.
Particle coating dominates drop wetting behaviour when q $
qc � 90�. Hydrophilic and hydrophobic particles will partition
between a polar aqueous phase and air which is effectively
hydrophobic. Particles of intermediate hydrophobicity will
attach very strongly to the interface between the two phases.35–37
Thus the particles coating the liquid drop (Fig. 1e) are in a more
favourable energetic situation than those in the powder bed, i.e.
dry. The interfacial free energy gained for single a spherical
particle transferred from the air to the liquid surface is given
by38,39
DF ¼ glprp2(1 + cos q)2 (7)
Soft Matter
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We use contact angles measured on planar silanised surfaces to
estimate DF. The adsorption free energy for a hemispherical
droplet (rd ¼ 1 mm) fully covered with particles (rp ¼ 50 mm and
724 particles) is shown in Fig. 5. It is clear that the driving force
for coating the droplet with particles decreases sharply as the
surface tension increases.
Our results show a direct correlation between the area of the
droplet surface coated by particles and the liquid surface tension
(cf. Fig. 4 and 5). Crucially, maximum particle coating of
droplets occurs at conditions just above those where penetration
into the bed becomes significant (q$ qc). For drops of liquid with
much higher surface tension (gl > 45 mN m�1) the bed surface is
effectively superhydrophobic. Particle coating does not occur
unless the drop is rolled over the bed surface.
There is also a decrease when the surface tension drops below
20.0 mNm�1, but this region is masked in our experiments by the
very rapid liquid penetration (Fig. 2b). While particles should be
partially wetted, penetration needs to be sufficiently slow for
particle coating to occur. Particle coating may slow liquid
imbibition into the bed. In this case, typically the particles tend to
sink back into the bed with the liquid, which accounts for the
ring-shaped depressions left in the bed. This behaviour is more
apparent for small particles where liquid takes several seconds to
drain into the smaller channels in the porous bed.
We also see a partial coating, i.e. hp < hd, on droplets of 30 mN
m�1 < gl < 40 mN m�1 (Fig. 5). The most intuitive explanation
seems to be that the potential energy of the climbing particles
increases. However, the estimate of the work done against
gravity (mghp, where m is the mass of a single particle) is about
10 pJ, i.e. at least one order of magnitude lower than the esti-
mated free energy of adsorption (Fig. 5). As the packing of the
adsorbed particles is dense – patches of hexagonally arranged
spheres are clearly seen – we speculate that friction between the
coating particles is the limiting factor.
In the simplified consideration above, we neglected the capil-
lary forces. Attached particles floating on droplet surfaces attract
each other to form a layer of close packed particle clusters.
Lateral capillary forces40,41 caused by deformation of the liquid
meniscus can be very strong. Paunov et al.42 showed that capil-
lary attraction between two particles of the same contact angle
Fig. 5 Theoretically predicted variation in the adsorption free energy for
a hemispherical droplet (rd ¼ 1 mm) fully covered with particles (rp ¼ 50
mm) with the liquid surface tension (gl) calculated using eqn (7).
Soft Matter
increases as the surface tension decreases. This will further
accentuate the experimental correlation shown in Fig. 4.
At very high gl, the droplets are not spontaneously coated by
particles. The gain in interfacial free energy due to particle
attachment is relatively low (Fig. 5). Evaporation dominates
droplet behaviour instead.Droplets of pure water (V¼ 10 mL, q¼108�) deposited on a particle bed evaporate in about the same time
as drops placed on a hydrophobic glass surface (�6000 s).
Consistent with the bed behaving like a superhydrophobic
surface, comparable evaporation times have been measured for
water droplets on polymeric substrates.20,21 For example, Sefiane
et al.21 found that 5 mLwater droplets deposited on PDMS-coated
silicon wafers evaporated within about 3000 seconds.
Evaporation of drops trapped on top of beds (q [ qc) can
cause particle coating due to the reduction in the droplet surface
area. Although the attached particles partly obscure the shape of
the drop, the time dependent variation in the shape of water–
ethanol binary drops shows several stages, corresponding to the
sequential evaporation of the different components.21,43 Ethanol
molecules diffuse to the droplet surface and evaporate first. The
drop radius then decreases as the contact line de-pins and the
contact angle increases to a value consistent with the water-rich
composition of the droplet surface. Coating occurs during this
period, perhaps driven by the stick–slip motion of observed for
drops at the late stages of drop evaporation.21,43 McHale et al.13
also observed drops on particle beds being coated by particles as
the droplet volume was reduced by evaporation.
The relative height of the particle coating that assembles
within minutes of contact for water–ethanol drops at q $ qc, is
however, significant (Fig. 4b). Under these conditions the rate of
particle coating is significantly larger than the rate of evapora-
tion. Typically, the coating is incomplete with the top portion of
the drop surface remaining exposed. The smaller area of the
droplet exposed to the atmosphere evaporates quickly. Reduc-
tion in the contact angle causes more coating and the drop radius
de-pins until the drop is fully coated by particles. Importantly,
the surface area of the hydrophobic particle coating does not
change over time. Instead the surface area of the drop decreases
until it is fully coated by particles. The presence of the complete
particle coating then causes significant retardation of droplet
evaporation.
We described here the spontaneous coating of liquid drops by
rather large solid particles. Similar to the contact angle depen-
dence of the colloidal structures formed by nanoparticle disper-
sions (foams, climbing films and marbles44), the height of the
particle coating depends on the particle contact angle and the
surface tension of the liquid. This selective process has potential
applications where mixed colloids are assembled into granular
structures. Foods such as milk that are spray dried into powders,
for example, are mixtures of fat droplets, proteins and sugars.
Using spontaneous particle coating as a precursor to drying
could control the spatial distribution of particles of different
wettability in the agglomerates and hence influence powder
rehydration processes (sinking, re-dispersion, dissolution).
Conclusions
We have described the behaviour of drops deposited on powder
beds as the wettability of the particles was varied systematically
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by increasing the liquid surface tension, while keeping the
contribution of the droplet kinetic energy at a minimum. Liquid
drains into the pores of beds of wettable particles due to capillary
suction. The time taken for all the liquid to penetrate into the bed
increases with the surface tension until, just above the critical
wetting tension, it becomes very long. Particles attach to the
liquid surface as the drop spreads over the bed. The attached
particles form a hexagonally close-packed layer that encapsulates
the drop surface. The height of the particle coating decreases as
the liquid surface tension is increased. Thus drops with high
surface tension must be rolled forcefully on beds of low surface
energy particles for encapsulation to occur. Rolling causes liquid
circulation within the drops that carries attached particles away
from the bed so that the drops become fully coated with particles,
irrespective of the liquid surface tension (providing it is greater
that the critical wetting tension).
Acknowledgements
CPW acknowledges receipt of an Australian Research Council
Future Fellowship. This research was supported under the
Australia Research Council Linkage Project funding scheme
(project LP0667608). It was also supported by the Department of
Innovation, Industry, Science and Research (Australian
Government) through the Australia-India Strategic Research
Fund.
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