New fundamental concepts in emulsion rheology

ELSEVIER
Current Opinion in Colloid & Interface Science 4 (1999) 231-238
www.elsevier.nl/locate/cocis
New fundamental concepts in emulsion rheology
T.G. Mason
Corporate Research Science Laboratory, Exxon Research and Engineering Co., Route 22 East, Annandale, NJ 08801, USA
Abstract
The field of emulsion rheology is developing rapidly due to investigations involving monodisperse emulsions having narrow
droplet size distributions. The droplet uniformity facilitates meaningful comparisons between experiments, theories, and
simulations. 0 1999 Elsevier Science Ltd. All rights reserved.
Keywords: Monodisperse emulsions; Droplet size distribution; Coalescence
1. Introduction
Emulsions consist of droplets of one liquid dispersed in another immiscible liquid. By contrast to
microemulsion phases, emulsions are not thermodynamic states. Instead, emulsions are metastable dispersions; external shear energy is used to rupture
large droplets into smaller ones during emulsification.
Surfactants that provide a stabilizing interfacial repulsion are typically introduced to inhibit droplet coalescence [l]. If the liquids are highly immiscible,
molecules of the dispersed phase cannot be exchanged between droplets, so coarsening of the
droplet size distribution due to Ostwald ripening is
negligible. When coalescence and ripening are suppressed, the emulsion can remain stable for years
even when osmotically compressed to form a biliquid
foam.
Emulsions exhibit highly varied rheological behavior that is useful and fascinating [2', 3-51. An emul-
sion's macroscopic constitutive relationships between
the stress and strain depend strongly on its composition, microscopic droplet structure, and interfacial
interactions. By controlling the droplet volume fracan emulsion can be changed from a simple
tion,
to an elastic solid having a
viscous liquid at low
substantial shear modulus at high
as shown
schematically in Fig. 1. This elasticity results from the
work done against interfacial tension, (T, to create
additional droplet surface area when the shear further deforms the already compressed droplets. The
elasticity of foams [6'], the gas-in-liquid counterpart
to concentrated emulsions, results from the same
mechanism, although Ostwald ripening of gas bubbles
usually causes the foam to age and its elasticity to
become weaker over time. The rheological properties
of such products as lotions, sauces, and creams are
typically adjusted by varying the composition or the
emulsification process to alter the droplet size distribution and hence packing. Additives such as polymers can also modify emulsion rheology by raising
+,
1359-0294/99/$ - see front matter 0 1999 Elsevier Science Ltd. All rights reserved.
PII: S 1 3 5 9 - 0 2 9 4 ( 9 9 ) 0 0 0 3 5 - 7
+
+,
T.G. Mason / Current Opinion in Colloid & Interface Science 4 (I 999) 231 -238
232
Figure 1
I
Dilute
Concentrated
Caged Packed Compressed
Uncaged
I
0
00
Viscous
I
I
I
& = 0.58
0
&CP
Elastic
0.64
' @
+
1
Current Opinion in Colloid & Interface Science
Schematic diagram of droplet positional structure and interfacial
morphology for disordered monodisperse emulsions of repulsive
droplets as a function of the volume fraction, 4,of the dispersed
phase. In the dilute regime at low q5, the droplets are spherical in
the absence of shear. As 4 is raised near the hard sphere glass
transition volume fraction, q5g = 0.58, the droplets become transiently caged by their neighbors. As q5 is further increased into the
concentrated regime, the droplets randomly close pack at q5RCP =
0.64, and become compressed with deformed interfaces for larger
4. As 4 + 1, the droplets become nearly polyhedral in shape and
form a biliquid foam. Dilute emulsions behave as viscous liquids,
whereas concentrated emulsions exhibit solid-like elasticity.
the viscosity of the continuous phase or by causing
adhesion between droplets without coalescence [71.
Emulsions comprised of viscoelastic polymeric liquids,
or blends, exhibit a rich rheological complexity arising
from the interplay of bulk and interfacial elastic contributions [ P I .
For years, measurements of emulsion rheology
[9-131 were not quantitatively understood because the
droplet size distributions had not been controlled and
no two emulsions had either the same distribution of
Laplace pressures, IIL = 2u/a, where a is the droplet
at
radius, or the same critical volume fractions,
which droplet packing would occur. Recently, measurements using monodisperse emulsions have established a conceptual foundation for quantitatively
understanding emulsion rheology, especially at high
[2', 14", 15", 161. In contrast to a recent opinion
[17], these studies show that polydispersity is important in emulsion rheology. The monodispersity has
facilitated comparisons between rheological experiments, theories, and simulations, and sparked a comparison with uniform hard sphere (HS) suspensions
and foams as + 1.
for <
+,,
flocculation fractionation [MI, controlled shear rupturing [19', 201, controlled coalescence [21"], membrane emulsification [22'], phase-separating binary
mixtures under shear [23], and classic Bragg extrusion
of the dispersed phase through a pipette into a flowing
continuous phase [24]. An example of a monodisperse
silicone oil-in-water emulsion stabilized by sodium
dodecylsulfate (SDS) with ii = 0.5, Pa = 0.1, and =
0.6 is shown in Fig. 2. The emulsion can be diluted to
or an osmotic pressure, II, can be applied
lower
If II is
through centrifugation or dialysis to raise
applied rapidly, the disordered positional structure of
can be quenched in. Light
the droplets at low
scattering experiments on index-matched bulk emulhave demonstrated this disordered
sions at high
glassy structure [2'1.
1
+,
+.
+
+
3. Droplet interactions
Interactions between the deformable interfaces of
droplets play an important role in emulsion rheology.
For incompressible dispersed phases, the most basic
interaction is that of excluded volume. The second
basic repulsive interaction results from work done
against u to create additional droplet surface area
when two droplets deform as they are forced together.
Finally, the surfactant typically provides a short-range
repulsion (disjoining pressure) that prevents droplet
coalescence. The net consequence of these repulsions
is depicted in Fig. 3 by the rise in both lines for the
droplet pair interaction potential, U, near and below
Figure 2
+
+ +,
+
2. Monodisperse emulsions
Traditional methods of emulsification, such as
stirring and shaking typically lead to droplet size distributions that are uncontrolled and have a large
polydispersity, defined as Pa = Sa/ii, where is the
average droplet radius and Sa is the S.D. However,
many methods for making monodisperse emulsions
with Pa = 0. 1 now exist. These include depletion
Current Opinion in Colloid & Interface Scienci
Optical micrograph of a concentrated monodisperse emulsion of
uniformly sized droplets having an average radius Z = 0.5 wm,
polydispersity Pa = 0.1, and volume fraction q5 = 0.6. Some droplet
ordering has been induced by the shear when the microscope slide
is prepared.
T.G. Mason / Current Opinion in Colloid & Interface Science 4 (I 999) 231 -238
the separation r = 2a. Describing how the droplets’
interfaces deform as they are forced together is complicated, so the surfactant’s repulsive contribution is
usually crudely represented by a thickness, h, of the
film between the droplets [25]. Since h must be considered when droplets pack, the effective volume fraction, +eff, is slightly larger than +:+e,, = +[1+ 3h/
(2a)], valid for h << a and weakly deformed droplets.
Repulsive emulsions do not have potentials which
exhibit a deep potential well relative to k,T (dashed
line - Fig. 31, where k , is Boltzmann’s constant and
T is the temperature, but attractive emulsions do
(solid line - Fig. 3). Droplets in attractive emulsions
flocculate or gel. Depletion attractions can arise from
surfactant micelles [181, polymers [71, or even smaller
droplets [26]. Other attractions can be induced by
adding excess salt to emulsions stabilized by ionic
surfactants [27] or changing the solvent quality [28].
However, even a small density difference between the
continuous and dispersed phases can lead to rapid
gravity-driven creaming of flocs or aggregates, so
measuring the rheology of attractive emulsions can be
problematic. We focus on the rheology of repulsive
emulsions and comment about attractive emulsions
when appropriate.
233
Figure 3
I
L
$4
\,
Repulsive
00
00
Schematic diagram of the pair potential, U, as a function of
separation, r, between the centers of two identical interacting
droplets. The dashed line depicts a repulsive positive potential, and
the solid line depicts an attractive potential with a well that is
significantly deeper than the thermal energy, k,T, so that droplets
can flocculate or aggregate. Both potentials rise toward low r
because of the short-range stabilizing repulsion of the surfactant
and the resistance of the droplets to deformation due to surface
tension.
or aggregates as i, is increased. For strong attractions,
tenuous gels of droplets [27] even exhibit weak elastic
shear moduli.
4. Dilute emulsion rheology
5. Glass transition in colloidal emulsions
Predictions of the viscosity, q, of dilute monodisperse emulsions have been tested empirically at low
enough shear rates that the shear stress, T, is less
than IIL and there is little droplet deformation and
no rupturing. Steady shear viscosity measurements for
+e,, < 0.4 [15] agree with simulations of monodisperse
HS suspensions [29] at large Peclet numbers, Pe =
q ? / ( k B T / U 3 )>> 1, where convection dominates diffusion, yet at small Capillary numbers, Ca =
q i , / ( a / a ) a 1, where the droplets are not greatly
deformed. By contrast to Taylor’s theory for emulsion
viscosity [30], q(+) is well described by HS predictions
[29,31] even when the external viscosity, qe, is larger
than the internal droplet viscosity, qi.From this, one
can infer that the Gibbs elasticity opposing gradients
in the surfactant concentration on the droplet interfaces through the Marangoni effect, is typically large
enough to decouple external flow from that within the
droplets. However, polydisperse emulsion viscosities
can depart from the monodisperse HS prediction,
especially at higher because hydrodynamic interactions between droplets depend upon the distribution
and especially +c. As Ca + 1, a recent simulation [32]
predicts that emulsions with = 0.3 may exhibit a
pronounced shear thinning behavior (q decreasing as
i, increases). Finally, attractive emulsions can be shear
thinning even at dilute due to the breakup of flocs
+,
+
+
The identification of features of the colloidal glass
transition [33,34] in emulsion rheology is one of the
most important recent conceptual advances [14”1.
For hard spheres, the colloidal glass transition occurs
when the spheres become sufficiently concentrated
that a given droplet becomes caged by its neighbors
indefinitely. Thermal excitations are insufficient to
destroy these cages when exceeds the glass transition volume fraction, +g. Light scattering and rheology measurements for HS are consistent with the
mode coupling theory prediction of +g = 0.58 [35”1,
[36’] (see Fig. 1). For
< +g, the cages are transient and break up over time scales that diverge as
+e,, + +g. By analogy to HS, an emulsion’s lowfrequency linear shear response for +e,, near +g
should be dominated by a plateau elastic modulus,
GIP, that is entropic in origin and scales with the
thermal energy density: GIth k B T / V f ,where V, is
the translational free volume per droplet. Since V,
[a(+, - +)eff]3G1thwould diverge at +c for hard
spheres (or for emulsions if (T + a). For deformable
droplets, G’, does not diverge but instead approaches
IIL.Because Gth a - 3 , the entropic elasticity and the
glass transition dynamics are most noticeable for
emulsions with sub-micron radii. For < +g and IIL
zz=- k , T / l / f , the emulsion’s frequency-dependent
+
-
-
-
+
T.G. Mason / Current Opinion in Colloid & Interface Science 4 (I 999) 231 -238
234
storage modulus, G’(o) and loss modulus, G”(o),
resemble those of a glassy HS suspension [37’] and
can be described using mode coupling theory. By
contrast, compressed emulsions with +eff significantly
larger than +c still exhibit slow relaxation resulting in
G”(o)> G’(o) as o + 0 due to droplet deformability
and finite h. The relationship between the emulsion’s
macroscopic rheology and the these slow glassy microscopic relaxations in the droplets’ positional and
interfacial structures is a subject of current interest. A
modified mode coupling theory has been proposed to
describe the glassy dynamics of disordered soft materials [38]. However, the connection between this theory’s parameters and the microscopic droplet structure and dynamics remains to be elucidated.
6. Linear viscoelastic shear moduli of compressed
emulsions
New developments in optical microrheology have
enhanced our understanding of the frequency-dependent linear viscoelastic moduli of compressed emulsions. Diffusing wave spectroscopy (DWS) [39] has
been used to measure the time-dependent mean
square displacement, < A r 2 ( t )> , of droplets in concentrated turbid monodisperse emulsions, and G ’(0)
and G”(w) are obtained using a generalized
Stokes-Einstein relation [40”,41]. This method is
approximate because it treats the emulsion as an
isotropic viscoelastic continuum. By using DWS to
probe high w and mechanical rheometry to probe low
o,the storage and loss moduli of a silicone oil-in-water
= 0.8 and a = 0.5 km have been
emulsion with
measured over nine decades in o,as is shown by the
solid (G’) and dashed (G”) lines in Fig. 4. At low w,
G’(o) dominates G”(w),exhibits a plateau, and rises
at high frequencies as G’(o) o1I2.This scaling and
a corresponding ‘anomalous viscous loss’ in G”(0)
implied by the Kramers-Kronig relations has been
predicted based on a theory of the collective slipping
motion of clusters of droplets in random directions
due to the disorder [42’]. The persistence of G’(o)
o1I2in measurements for
<+c
may be due to a
crossover between this collective slipping motion and
the simple diffusive entropic relaxation of the unpacked droplet structures, as in HS predictions [43,44].
By contrast, G”(o) exhibits a minimum at intermediate frequencies and rises rapidly at high frequencies
as G”(o) o where it dominates G’(o). The rise in
G”(o) toward low o reflects droplet rearrangements
that slowly relax the emulsion’s quenched-in glassy
structure. Although HS mode coupling theory cannot
predict an emulsion’s viscoelastic spectra, it provides
a conceptual basis for explaining the development of
the plateau in G’(o) and minimum in G”(o) through
I+
-
+
-
-
Figure 4
I
lo6 -
/-
lo5 -
Gh\e
G’
/
/
lo4 -
/
/
/
/
G”
---
lo3- ,
/
/
/
I
I-
--_*.
I,
,
, ‘,
,
,
,
,
-
Frequency-dependent linear storage modulus, G’( w ) (solid line)
and loss modulus, G ” ( w ) (dashed line) of a concentrated monodisperse emulsion with ii = 0.5 y m and 4 = 0.8 based on mechanical
oscillatory measurements at low w < lo2 rad/s and optical measurements using Diffusing wave spectroscopy (DWS) at high w .
The low frequency plateau modulus, GI,, given by the inflection
point in G ’ ( w ) of the DWS measurements has been rescaled to
G’, of the mechanical measurements in order to correct for order
unity errors introduced by the non-spherical shape of the droplets
and the continuum approximation in the generalized Stokes-Einstein equation. At high w , G ’ ( w ) scales as wl/*. The minimum in
G “ ( w ) is indicative of slow glassy relaxations in the droplet structure.
droplet caging. In other noteworthy experiments, DWS
has been used to probe thermally-induced droplet
shape fluctuations [45’1 and foam film dynamics [461
and coarsening [471.
7. Elasticity of concentrated emulsions
The universal +dependence of the linear plateau
elasticity of disordered concentrated monodisperse
emulsions has been established. Measurements on
four emulsions having different a are described by:
Grp(+eff)
= 1.5(o/a)(~+,~
- + c ) [14”1 where 4, has
been identified as random close packing of monodisperse spheres, +c = +RCP = 0.64 [48]. Although a
quasi-linear rise in Grp(+eff had been previously
measured [lo], little insight into the reported +c =
0.715 could be offered due to polydispersity. The
quasi-linear rise contrasts with a two-dimensional theory of ordered droplets in which Grp(+eff)jumps
discontinuously from zero to the Laplace pressure
scale at +eff = + c [49]. Recent simulations of the
shape of three-dimensional droplets deformed by
plates [50”] using surface evolver software [511 have
demonstrated an anharmonic repulsion between
droplets that depend on the coordination number, 2 ,
of neighboring droplets; this anharmonicity is in ac-
T.G. Mason / Current Opinion in Colloid & Interface Science 4 (I 999) 231 -238
cord with an earlier theory [52] and leads to a more
gradual increase in G'p(+eff)above + c . By combining
the average z-dependent anharmonic potentials with
a disordered three-dimensional droplet positional
structure and applying a small shear strain, Grp(+eff)
has been calculated [53"] and agrees well with the
measurements. These simulations also show the nonaffine motion of the disordered droplets. Measurements and simulations of the osmotic equation of
state, II(+eff)[14"] exhibit a remarkable similarity to
Grp(+eff)
for +eff immediately above + c . However, as
+eff + 1, II diverges and the measured G',
approaches a constant that lies within 10% of a prediction of GrP(l)= 0.5a/u [541 and simulations that consider different droplet structures [55]. Attractions do
not usually affect compressed emulsion elasticity
strongly because droplet deformation dominates the
rheology, but attractions can significantly increase G',
for +eff near and below + c by comparison to repulsive
emulsions [2,561.
235
Figure 5
A
rupturing
oooo.,
.coalescence
0)
0
-
zY
log
y Current Opinion in Colloid & lntelface Science
Schematic log-log diagram of the steady shear stress, T, as a
function of the shear rate, j~ (solid line) for a concentrated emulsion. As y increases, T rises above the elastic yield stress, T,,, as
viscous contributions become important. As T approaches the
Laplace pressure scale, u / a (dashed line) the droplets can deform,
stretch, and rupture, as shown at right. Depending upon the interfacial properties, the droplets may also recombine through coalescence.
measure the steady-shear viscous stress: T~ = T - 7,.
For (beff < 0.7, the flow is uniform, and T~ +", where
x = 1/2 at (Peff = 0.63 to x = 2/3 at +eff = 0.58. A
theory [60] and a simulation for incompressible foams
, no general prediction exists
[611 predict T~ j 2 I 3but
for x(+eff). For +eE > 0.7, the emulsion can fracture
[15,62] and is not uniform throughout the rheometer's gap. However, fracturing can be suppressed if
the gap is very small. Shear rupturing viscoelastic
polydisperse emulsion in a thin gap can lead to a
monodisperse emulsion of smaller droplets [19'1, [631.
Extensions of theories on the capillary instability
modified by membrane curvature elasticity [64] and
on the stability of cylindrical domains in phaseseparating binary fluids in a shear flow [65] may provide
future insight into emulsification. Another interesting
instability occurs when draining foams are driven by
viscous flows of the continuous phase [66'].
-
8. Non-linear rheology of concentrated emulsions
Basic concepts for understanding yielding, fracture
flow, and emulsification are beginning to appear. A
schematic illustration of these phenomena for a concentrated emulsion is shown in Fig. 5, along with a
. low +, the stress apcorresponding plot of ~ ( 9 ) At
proaches a constant defined to be the yield stress, T ~
For higher y, the interplay of the fluid viscosities with
the interfacial structures within the emulsion cause
the shear stress to increase. For 7 < I I L , droplet
rearrangements occur, but for T = IIL the droplets
can stretch, rupture, and, possibly even coalesce.
Given these complex phenomena at large 9 yielding
just beyond the linear regime has mostly been studied. Mechanical oscillatory measurements of the yield
strain, y, = TJG',, show that yy is much less than
unity and rises linearly: yy(+eff = 0.3 (+eff - + c ) for
+eff > +c = +RCP [15"]. Combined with G'p(+eff),this
implies that T , varies nearly quadratically above + c :
T , = 0.5 (u/u)+eff(+eff - &I2. A new optical technique has provided microscopic insight into yielding.
DWS has been applied to concentrated emulsions
[57"1, hard sphere suspensions [%I, and foams [591
that are sheared between two transparent plates at a
controlled strain amplitude and frequency. The strain
induces periodic echoes in the intensity autocorrelation function that are used to deduce the proportion
of droplets that rearrange irreversibly. A comparison
of DWS echo to mechanical measurements implies
that yielding occurs when only approximately 5% of
the droplets rearrange irreversibly [57"]. Beyond the
yield regime, mechanical rheometry has been used to
-
+
.
9. Emulsions of viscoelastic materials
Emulsions need not be comprised solely of isotropic
viscous liquids, but may include viscoelastic or
anisotropic liquids such as polymers [ P I or liquid
crystals [67]. Bulk and interfacial energy storage combine to provide a wide range of rheological behavior
[68',69-71'1.
The measured G'(o) and G"(o)of
copolymer blends [71'] have been successfully compared to a theory of spherical inclusions of an isotropic
viscoelastic material in an isotropic viscoelastic matrix
[72"]. In the non-linear regime, droplets in blends
have been stretched by an elongational shear and can
form ellipsoids or long needles [691; such shears can
lead to cusped ends and tip streaming modes of
T.G. Mason / Current Opinion in Colloid & Interface Science 4 (I 999) 231 -238
236
droplet breakup [73]. Finally, a theoretical picture of
how compatibilizers inhibit droplet collisions during
copolymer emulsification has been developed [741.
10. Conclusions
Monodisperse emulsions have provided much new
insight into emulsion rheology, including the notion
of colloidal glasses of deformable droplets, yet many
challenges remain. Perhaps the most important is to
understand how polydispersity affects emulsion rheology. This could be studied by combining different
monodisperse emulsions to control the polydispersity.
Other rheological frontiers lie in crystalline emulsions
with ordered droplet structures, binary emulsions,
emulsions of liquid crystals, multiple emulsions,
inverse emulsions, attractive emulsions, and in shearinduced droplet rearrangements, deformation, rupturing, and coalescence.
References and recommended reading
w
of special interest
of outstanding interest
[l] Bibette J, Leal-Calderon F. Surfactant-stabilized emulsions.
Curr Opin Colloid Interface Sci 1996;1:746-751.
[2] Mason TG, Krall AH, Gang H, Bibette J, Weitz DA.
Monodisperse emulsions: properties and uses. In: P. Becher,
editor. Encyclopedia of emulsion technology, New York
Marcel Dekker, Inc., 1996:299-336.
A general introduction to monodisperse emulsions, including details on depletion fractionation angle-dependent light scattering,
linear and non-linear rheology, and the rheology and structure of
attractive monodisperse emulsions.
[3] Lequeux F. Emulsion rheology. Curr Opin Colloid Interface
Sci 1998;3:408-411.
[4] Tadros TF. Fundamental principles of emulsion rheology and
their applications. Colloid Surfaces A 1994;91:39-55.
[5] Barnes HA. Rheology of emulsions - a review. Colloids
Surfaces A 1994;91:89-95.
[6] Durian DJ. Fast, non-evolutionary dynamics in foams. Curr
Opin Colloid Interface Sci 1997;2:615-621.
This paper concisely describes recent advances in the related subject of foams.
[7] Meller A, Stavans J. Stability of emulsions with non-adsorbing polymers. Langmuir 1996;12301-304.
[8] Pal R. Rheology of emulsions containing polymeric liquids.
In: P Becher, editor. Encyclopedia of emulsion technology.
New York Marcel Dekker, 1996:93-263.
A good yet lengthy introduction to the highly varied rheological
properties of polymer containing emulsions. Extensive references
are given.
[9] Princen HM. Rheology of foams and highly concentrated
emulsions: experimental study of the yield stress and wall
effects for concentrated oil in water emulsions. J Colloid
Interface Sci 1985;105:150-171.
[lo] Princen HM. Rheology of foams and highly concentrated
emulsions: static shear modulus. J Colloid Interface Sci
1986;112427-437.
[ l l ] Princen HM. Osmotic pressure of foams and highly concen-
trated emulsions theoretical considerations. Langmuir 1986;
2519-524.
[12] Princen HM, Kiss AD. Osmotic pressure of foams and highly
concentrated emulsions determination from the variation in
volume fraction with height in an equilibrated column
1987;3:36-41.
[13] Princen HM. Rheology of foams and concentrated emulsions
an experimental study of the shear viscosity and yield stress
of concentrated emulsions. J Colloid Interface Sci 1989;128:
176-187.
[14] Mason TG, Lacasse M-D, Grest GS, Levine D, Bibette
J, Weitz DA. Osmotic pressure viscoelastic shear moduli of
concentrated emulsions. Phys Rev E 1997;56:3150-3166.
Measurements of the volume fraction dependence of the osmotic
pressure and plateau shear modulus of disordered monodisperse
emulsions are compared to three dimensional simulations that
incorporate anharmonic droplet repulsions. Excellent agreement is
found without any adjustable parameters. The concept of the glass
transition in concentrated emulsions is introduced.
[15] Mason TG Bibette J. Weitz DA. Yielding and flow of
smonodisperse emulsions. J Colloid Interface Sci 1996;179:
439-448.
Mechanical measurements of the steady-shear and non-linear rheology of monodisperse emulsions from the dilute to the concentrated regimes.
[16] Mason TG, Bibette J, Weitz DA. Elasticity of compressed
emulsions. Phys Rev Lett 1995;75:2051-2054.
[17] Bonvankar RP, Case SE. Rheology of emulsions, foams, and
gels. Curr Opin Colloid Interface Sci 1997;2:584-589.
[18] Bibette J, R o n D, Nallet F. Depletion interactions and
fluid-solid equilibrium emulsions. Phys Rev Lett 1990;65:
2470-2473.
[19] Mason TG, Bibette J. Shear rupturing of droplets in complex fluids. Langmuir 1997;13:4600-4613.
An experimental method for producing concentrated monodisperse
emulsions through shear-induced droplet rupturing in a thin gap is
presented.
[20] Mason TG, Bibette J. Emulsification in viscoelastic media.
Phys Rev Lett 1996;77:3481-3484.
[21] Deminiere B, Colin A, Leal-Calderon F, Muzy JF, Bibette J.
Cell growth in a three dimensional cellular system undergoing coalescence. Phys Rev Lett 1999;82:229-232.
The authors present striking microscopic and light scattering observations of ordered droplet structures arising from controlled coalescence.
[22] Omi S . Preparation of monodisperse microspheres using the
Shirasu porous glass emulsification technique. Colloids Surfaces A 1996;109:97-107.
An experimental method for making monodisperse emulsions using
membrane or porous glass emulsification is described.
Min KYI Goldberg WI. Nucleation of a binary liquid mixture
under steady-state shear. Phys Rev Lett 1993;70:469-472.
Bragg SL, Nye JF. A dynamical model of crystal structure.
Proc R Soc A 1947;190:474-481.
Princen HM, Aronson MP, Moser JC. Highly concentrated
emulsions: the effect of film thickness and contact angle on
the volume fraction in creamed emulsions. J Colloid Interface Sci 1980;75:246-270.
Steiner U, Meller A, Stavans J. Entropy driven phase separation in binary emulsions. Phys Rev Lett 1995;74:4750-4753.
Bibette J, Mason TG, Gang H, Weitz DA, Poulin P. Structure
of adhesive emulsions. Langmuir 1993;9:3352-3356.
Poulin P, Bibette J. Adhesion of water droplets in organic
solvent. Langmuir 1998;14:6341-6343.
Ladd AJC. Hydrodynamic transport coefficients of random
dispersions of hard spheres. J Chem Phys 1990;93:3484-3494.
T.G. Mason / Current Opinion in Colloid & Interface Science 4 (I 999) 231 -238
[30] Taylor GI. The viscosity of a fluid containing small drops of
another fluid. Proc R SOCA 1932;138:41-48.
[31] Beenakker CWJ. The effective viscosity of a concentrated
suspension of spheres. Physica A 1984;128:48-81.
[32] Lowenberg M, Hinch EJ. Numerical simulation of a concentrated emulsion in shear flow. J Fluid Mech 1996;321:395-419.
[33] van Megen W, Underwood SM. Glass transition in colloidal
hard spheres: measurement and mode-coupling-theory analysis of the coherent measurement intermediate scattering
function. Phys Rev E 1994;49:4206-4220.
[34] van Megen W, Underwood SM. Glass transition in colloidal
hard spheres: mode-coupling theory analysis. Phys Rev Lett
1993;702766-2769.
[35] Cummins HZ, Li G, Du WM, Hernandez J. Relaxation
oo
dynamics in super cooled liquids: experimental tests of the
mode coupling theory. Physica A 1994;204:169-201.
This paper introduces the fundamental concepts behind mode
coupling theory and how it has been used to interpret experiments
on colloidal and molecular glasses.
[36] Gotze W, Sjogren L. Relaxation processes in super-cooled
liquids. Rep Prog Phys 1992;55:241-376.
Mode coupling theory for hard spheres in a vacuum is derived in
full detail.
[37] Mason TG, Weitz DA. Linear viscoelasticity of colloidal
hard sphere suspensions near the glass transition. Phys Rev
Lett 1995;75:2770-2773.
Mode coupling theory is used to explain the frequency dependence
of the linear viscoelastic moduli of concentrated hard sphere suspensions near the glass transition.
[38] Hdbraud P, Lequeux F. Mode-coupling theory for the pasty
rheology of soft glassy materials. Phys Rev Lett 1998;
81:2934-2937.
[39] Weitz DA, Pine DJ. Diffusing-wave spectroscopy.In: Brown
W, editor. Dynamic Light Scattering. Oxford: Oxford University Press, 1992652-720.
[40] Mason TG, Gang H, Weitz DA. Diffusing-wave-specoo
troscopy measurements of viscoelasticity of complex fluids. J
Opt SOCAm A 1997;14:139-149.
A method for obtaining the frequency-dependent linear viscoelastic
moduli from optical measurements of the time-dependent mean
square displacement using a generalized Stokes Einstein relation is
presented. Diffusing wave spectroscopy is used to probe the moduli
of concentrated hard sphere suspensions and emulsions.
[41] Mason TG, Weitz DA. Optical measurements of the linear
viscoelastic moduli of complex fluids. Phys Rev Lett
1995;74:1250-1253.
[42] Liu AJ, Ramaswamy S, Mason TG, Gang H, Weitz DA.
Anomalous viscous loss in emulsions. Phys Rev Lett
1996;76:3017-3020.
A model for the high-frequency linear viscoelasticity of concentrated emulsions is presented. The collective motion of groups of
droplets along randomly-oriented slip planes leads to contributions
to the storage and loss modulus which vary as the square root of
the frequency.
[43] Lionberger RA, Russel WB. High frequency modulus of hard
sphere colloids. J Rheol 1994;38:1885-1908.
[44] de Schepper IM, Smorenburg HE, Cohen EGD. Viscoelasticity in dense hard sphere colloids. Phys Rev Lett 1993;
70:2178-2181.
[45] Gang H, Krall AH, Weitz DA. Thermal fluctuations of the
shapes of droplets in dense and compressed emulsions. Phys
Rev E 1995;52:6289-6302.
Angstrom scale fluctuations on the surfaces of thermally-excited
colloidal droplets are measured using Diffusing wave spectroscopy.
[46] Gopal AD, Durian DJ. Fast thermal dynamics in aqueous
foams. J Opt SOCAm A 1997;14:150-155.
[47] Durian DJ, Weitz DA, Pine DJ. Multiple light scattering
237
probes of foam structure and dynamics. Science 1991;
252686-688.
[48] Berryman JG. Random close packing of hard spheres and
disks. Phys Rev A 1983;27:1053-1061.
[49] Princen HM. Rheology of foams and highly concentrated
emulsions: elastic properties and yield stress of a cylindrical
model system.. J Colloid Interface Sci 1983;91:160-175.
[50] Lacasse M-D, Grest GS, Levine D. Deformation of small
oo
compressed droplets. Phys Rev E 1996;54:5436-5446.
Surface evolver simulations of a single droplet deformed by varying
numbers of plates pressed against it reveal an anharmonic droplet
interaction potential that depends on the coordination number.
[51] Brakke KA. The surface evolver. Exp Math 1992;1:141-165.
[52] Morse DC, Witten TA. Droplet elasticity in weakly compressed emulsions. Europhys Lett 1993;22:549-555.
[53] Lacasse M-D, Grest GS, Levine D, Mason TG, Weitz DA.
oo
A model for the elasticity of compressed emulsions. Phys Rev
Lett 1996;76:3448-3451.
Full three dimensional simulations of disordered monodisperse
emulsions subjected to osmotic compression and small shear strains
are used to calculate the volume fraction dependencies of the
osmotic pressure and linear shear modulus.
[54] Stamenovic D. A model of foam elasticity based upon the
laws of Plateau. J Colloid Interface Sci 1991;145:255-259.
[55] Kraynik AM, Reinelt DA. Linear elastic behavior of dry soap
foams. J Colloid interface Sci 1996;181:511-520.
[56] Manoj P, Watson AD, Hibberd DJ, Fillery-Travis AJ, Robins
MM. Characterization of a depletion-flocculated polydisperse
emulsion: steady state rheological investigations. J Colloid
Interface Sci 1998;207:294-302.
[57] HBbraud P, Lequeux F, Munch JP, Pine DJ. Yielding and
oo
rearrangements in disordered emulsions. Phys Rev Lett
1997;78:4657-4660.
The general optical technique of diffusing wave spectroscopy echo
experiments is presented. By applying an oscillatory sinusoidal
strain to a concentrated emulsion and examining echoes in the
DWS intensity correlation function, the proportion of droplets that
go through reversible and irreversible trajectories is deduced. The
volume fraction dependence of the yield strain is also determined
and agrees with mechanical rheometry.
[58] Haw MD, Poon WCK, Pusey PN, HBbraud P, Lequeux F.
Colloidal glasses under shear strain. Phys Rev E 1998;
58:4673-4682.
[59] Hohler R, Cohen-Addad S, Hoballah H. Periodic non-linear
bubble motion in aqueous foam under oscillating shear strain.
Phys Rev Lett 1997;79:1154.
[60] Schwartz LW, Princen HM. A theory of extensional viscosity
for flowing foams and concentrated emulsions. J Colloid
Interface Sci 1987;118:201-211.
[61] Reinelt DA, Kraynik AM. Simple shearing flow of a dry
Kelvin soap foam. J Fluid Mech 1996;311:327-342.
[62] Yoshimura AS, Prud'homme RK. Response of an elastic
Bingham fluid to oscillatory shear. Rheol Acta 1987;
26:428-436.
[63] Aronson MP. The role of free surfactant in destabilizing
oil-in-water emulsions. Langmuir 1989;5:494-501.
[64] Powers TR, Goldstein RE. Pearling and pinching: propagation of Rayleigh instabilities. Phys Rev Lett 1997;78:
2555-2558.
[65] Frischknecht A. Stability of cylindrical domains in phase-separating binary fluids under shear flow. Phys Rev E 1988;
58:3495-3514.
[66] Hutzler S, Weaire D, Crawford R. Convective instability in
foam drainage. Europhys Lett 1998;41:461-465.
The authors have discovered a new type of convective instability in
a draining foam driven by a flow of the continuous liquid phase that
opposes the buoyancy force on the bubbles.
238
T.G. Mason / Current Opinion in Colloid & Inteface Science 4 (I 999) 231 -238
[67] Poulin P, Weitz DA. Inverted and multiple nematic emulsions. Phys Rev E 1998;57:626-637.
[68] Huitric J, MCdCric P, Moan M, Jarrin J. Influence of composition and morphology on rheological properties of polyethylene/polyamide blends. Polymer 1998;39:4849-4856.
Measurements of the linear and steady shear rheology of a blend as
a function of volume fraction are presented. Cryofracture SEM
microscopy reveals the relationship between the rheological
properties and continuous-dispersed phase inversion.
[69] Gramespacher H, Meissner J. Melt elongation and recovery
of polymer blends morphology, and influence of interfacial
tension. J Rheol 1997;41:27-44.
[70] Vinckier I, Moldenaers P, Mewis J. Transient rheological
response and morphology evolution of immiscible polymer
blends. J Rheol 1997;41:705-718.
[71] Lacroix C Grmela M, Carreau PJ. Relationships between
rheology and morphology for immiscible molten blends of
polypropylene and ethylene copolymers under shear flow. J
Rheol 1998;42:41-62.
Measurements of the frequency-dependent storage and loss moduli
are compared to a theory by Palierne. Excellent agreement is
found.
[72] Palierne JF. Linear rheology of viscoelastic emulsions with
oo
interfacial tension. Rheol Acta 1990;29:204-214.
A theory for the frequency-dependent linear shear moduli of spherical inclusions of one viscoelastic phase in another is presented.
Interfacial and bulk elastic contributions to the viscoelastic moduli
are taken into account.
[73] Milliken WJ, Leal LG. Deformation and breakup of viscoelastic drops in planar extensional flows. J Non-Newtonian Fluid
Mech 1991;40:355-379.
[74] Milner ST. How do copolymer compatibilizers really work?
MRS Bulletin 1997;2238-42.