Langmuir 2005, 21, 11651-11658 11651

Rheology of Asphaltene-Toluene/Water Interfaces

Danuta M. Sztukowski‡ and Harvey W. Yarranton*,†
Department of Chemical and Petroleum Engineering, University of Calgary,
Calgary, Alberta, Canada T2N 1N4

Received July 15, 2005. In Final Form: September 26, 2005

The stability of water-in-crude oil emulsions is frequently attributed to a rigid asphaltene film at the
water/oil interface. The rheological properties of these films and their relationship to emulsion stability
are ill defined. In this study, the interfacial tension, elastic modulus, and viscous modulus were measured
using a drop shape analyzer for model oils consisting of asphaltenes dissolved in toluene for concentrations
varying from 0.002 to 20 kg/m3. The effects of oscillation frequency, asphaltene concentration, and interface
aging time were examined. The films exhibited viscoelastic behavior. The total modulus increased as the
interface aged at all asphaltene concentrations. An attempt was made to model the rheology for the full
range of asphaltene concentration. The instantaneous elasticity was modeled with a surface equation of
state (SEOS), and the elastic and viscous moduli, with the Lucassen-van den Tempel (LVDT) model. It
was found that only the early-time data could be modeled using the SEOS-LVDT approach; that is, the
instantaneous, elastic, and viscous moduli of interfaces aged for at most 10 minutes. At longer interface
aging times, the SEOS-LVDT approach was invalid, likely because of irreversible adsorption of asphaltenes
on the interface and the formation of a network structure.

Introduction films are largely responsible for long-term emulsion

stability.1,17,21,23-25
Water-in-crude oil emulsions can be stabilized by several
Interfaces with a large elastic modulus experience a
components including asphaltenes,1-3 solids such as clays relatively large increase in energy when the interfacial
or corrosion products,4-9 and organic acids.10 The density area increases or surfactants such as asphaltenes are
and viscosity of the oil are also factors. Heating and the spread more thinly on the interface. Therefore, a droplet
addition of flocculants can overcome unfavorable density with an elastic film is less likely to deform during a collision
and viscosity conditions but cannot always promote with another droplet. Also, the Gibbs-Marangoni effect
satisfactory coalescence. In many cases, coalescence likely is likely to be stronger so that asphaltenes will migrate
depends on the rheological properties of the interface as to depleted areas more rapidly. Both factors will reduce
well as the size and concentration of solids on or near the the coalescence rate and enhance emulsion stability.
interface. Recent research has focused on the rheology of Attempts to quantify interfacial film compressibility
asphaltene interfacial films. and elasticity have been made via Langmuir film balance
Asphaltenes appear to adsorb at the interface (at least techniques,26-30 shear viscometric measurements,14,31-34
initially) as a monolayer varying between 2 and 9 nm.11
Over time, the asphaltenes appear to rearrange into a (12) Freer, E. M.; Radke, C. J. J. Adhes. 2004, 80, 481.
rigid mechanical film. These films have a large elastic (13) Freer, E. M.; Svitova, T.; Radke, C. J. J. Pet. Sci. Eng. 2003, 39,
modulus12-16 and visibly crumple when the interface is 137.
contracted.17-22 It has been widely hypothesized that these (14) Spiecker, P. M.; Kilpatrick, P. K. Langmuir 2004, 20, 4022.
(15) Bouriat, P.; El Kerri, N.; Graciaa, A.; Lachaise, A. Langmuir
2004, 20, 7459.
* To whom correspondence should be addressed. E-mail: (16) Bauget, F.; Langevin, D.; Lenormand, R. J. Colloid Interface
Sci. 2001, 239, 501.
hyarrant@ucalgary.ca. Tel: (403) 220 6529. Fax: (403) 282 3945. (17) Taylor, S. E. Chem. Ind. London 1992, October 19, 770.
† University of Calgary.
(18) Reisberg, J.; Doscher, T. M. Prod. Mon. 1956, November, 43.
‡ Now with Shell Canada Research, 3655 36 Street NW, Calgary,
(19) Strassner, J. E. J. Pet. Technol. 1968, 20, 303.
Alberta, Canada T2L 1Y8. (20) Jeribi, M.; Almir-Assad, B.; Langevin, D.; Henaut, I.; Argillier,
(1) Yarranton, H. W.; Hussein, H.; Masliyah, J. H. J. Colloid Interface J. F. J. Colloid Interface Sci. 2002, 256, 268.
Sci. 2000, 228, 52. (21) Yeung, A.; Dabros, T.; Czarnecki, J.; Masliyah, J. Proc. R. Soc.
(2) McLean, J. D.; Kilpatrick, P. K. J. Colloid Interface Sci. 1997, London, Ser. A 1999, 455, 3709.
196, 23. (22) Khristov, Khr.; Taylor, S. D.; Masliyah, J. Colloids Surf., A:
(3) Taylor, S. D.; Czarnecki, J.; Masliyah, J. J. Colloid Interface Sci. 2000, 174, 183.
2002, 252, 149. (23) Siffert, B.; Bourgeois, C.; Papirer, E. Fuel 1984, 63, 834.
(4) Kotlyar, L. S.; Sparks, B. D.; Woods, J. R.; Raymond, S.; LePage (24) Nordli, K. G.; Sjöblom, J.; Kizling, J.; Stenius, P. Colloids Surf.
Y.; Shelfantook, W. Pet. Sci. Technol. 1998, 16, 1. 1991, 57, 83.
(5) Kotlyar, L. S.; Sparks, B. D.; Woods, J. R.; Chung, K. H. Energy (25) Sheu, E. Y.; De Tar, M. M.; Storm, D. A.; DeCanio, S. J. Fuel
Fuels 1999, 13, 346. 1992, 71, 299.
(6) Yan, Z.; Elliot, J. A. W.; Masliyah, J. H. J. Colloid Interface Sci. (26) Jones, T. J.; Neustadter, E. L.; Whittingham, K. P. JCPT 1978,
1999, 220, 329. April-June, 100.
(7) Yan, N.; Gray, M. R.; Masliyah, J. H. Colloids Surf., A 2001, 193, (27) Ese, M.-H.; Galet, L.; Clausse, D.; Sjoblom, J. J. Colloid Interface
97. Sci. 1999, 220, 293.
(8) Gu, G.; Zhiang, Z.; Xu, Z.; Masliyah, J. H. Colloids Surf., A 2003, (28) Ese, M.-H.; Yang, X.; Sjoblom, J. Colloid Polym. Sci. 1998, 276,
215, 141. 800.
(9) Bensebaa, F.; Kotlyar, L.; Pleizier, G.; Sparks, B.; Deslandes, Y.; (29) Zhang, L. Y.; Lawrence, S.; Xu, Z.; Masliyah, J. H. J. Colloid
Chung, K. Surf. Interface Anal. 2000, 30, 207. Interface Sci. 2003, 264, 128.
(10) Horváth-Szabó, G.; Masliyah, J. H.; Czarnecki, J. J. Colloid (30) Zhang, L. Y.; Xu, Z.; Masliyah, J. H. Langmuir 2003, 19, 9730.
Interface Sci. 2001, 242, 247. (31) Eley, D. D.; Hey, M. J.; Lee, M. A. Colloids Surf. 1987, 24, 173.
(11) Sztukowski, D. M.; Jafari, M.; Alboudwarej, H.; Yarranton, H. (32) Mohammed, R. A.; Bailey, A. I.; Luckham, P. F.; Spencer, S. E.
W. J. Colloid Interface Sci. 2003, 265, 179. Colloids Surf., A 1993, 80, 237.

10.1021/la051921w CCC: $30.25 © 2005 American Chemical Society

Published on Web 11/04/2005
11652 Langmuir, Vol. 21, No. 25, 2005 Sztukowski and Yarranton

and oscillatory drop measurements,12,13,15,16,35 Generally, natant was decanted and the solvent evaporated until only dry
these studies indicate that the elastic and viscous moduli asphaltenes remained. Asphaltenes and fine solids made up 97
increase when the continuous phase becomes more and 3 wt %, respectively, of the asphaltene-solids mixture.37
paraffinic and when the interface is aged. The measured Only solids-free asphaltenes were used in this work.
Interfacial Tension. Interfacial tension (IFT) was measured
elastic and viscous moduli also depend on the crude oil (or using an IT Concept Tracker drop shape analyzer (DSA). The
asphaltene) concentration in the continuous phase. Some hydrocarbon phase was loaded into a syringe and injected through
authors have observed an increase in the elastic modulus a U-shaped needle into an optical glass cuvette containing reverse
with an increase in asphaltene or crude oil concentra- osmosis water provided by the University of Calgary water plant.
tion,13,14 whereas others have noted variable behavior.35 A droplet was formed at the tip of the needle and illuminated.
Although the effects of solvent quality, time, and The profile of the droplet was captured using a CCD camera and
continuous-phase composition on interfacial elasticity analyzed using a video image profile digitizer board connected
have been examined, few attempts have been made to to a personal computer. The bench was placed on a wooden
model the rheology. Most notably, Freer and Radke12 platform and a foam mat in order to remove potential vibrations.
The shape of the drop results from the balance between the
examined asphaltene adsorption and the rheology of model
forces of interfacial tension and gravity. The interfacial tension
toluene-water interfaces in terms of a combination of force acts to minimize the surface area and tends to pull the
purely diffusional relaxation and viscoelastic behaviors. droplet into a spherical shape. The gravity force acts upward on
Their study of an aged, 0.005 wt % asphaltene-toluene- the droplet and therefore tends to elongate the droplet because
water interface showed that the total, elastic, and viscous the droplet phase is less dense than the phase in the cuvette. The
moduli at different frequencies could be modeled suc- equations determining the drop profile can be solved from the
cessfully with the Lucassen-van den Tempel (LVDT) and Laplace equation and hydrostatic calculations.40 As long as the
Maxwell viscoelastic models. The need for a mechanical density of the two phases and the shape of the droplet are known,
component in their model showed clearly the importance the equations can be fitted to the measured drop profile, and the
interfacial tension can be obtained from the best-fit parameters.
of irreversible adsorption effects and was consistent with
A Laplacian shape was observed for drops varying from 8 to 30
previous visual observations of interfacial “rigid” skins.17-22 µL. In the current work, 22 µL droplets were employed for all
The purpose of this work is to (1) examine the effect of measurements.
asphaltene concentration and aging time on the rheology IFT values of several organic solvents over distilled water
of the water/hydrocarbon interface and (2) extend the were measured with the DSA and found to be within 1% of
LVDT approach to these systems. The hydrocarbon phases published values. In the current work, the DSA was used to
consisted of 0.002 to 20 kg/m3 (approximately 0.0002 to gather the interfacial tension of asphaltene-toluene solutions
2 wt %) asphaltenes in toluene. The interfaces were aged over water for times up to 16 h. Measurements were made every
up to 16 h. second during the first 2 to 3 min after drop formation and then
every 10 s.
Elasticity. Interfacial elasticity, , is defined as follows
Experimental Methods
Materials. Asphaltenes were precipitated from Athabasca dγ dγ
bitumen, a coker-feed bitumen that has been treated to remove ) )A (1)
d ln A dA
most of the large solids and all of the water. As discussed in
previous studies,36-39 native solids are usually associated with where γ is the interfacial tension and A is the interfacial area.
the asphaltene fraction and coprecipitate with asphaltenes. Elasticity is a measure of the change in interfacial energy with
Hence, because the material precipitated from bitumen is actually a change in interfacial area. In an oscillating system, elasticity
a mixture of asphaltenes and solids, it is referred to as is a complex quantity and has both a real and an imaginary
asphaltene-solids. component defined as follows
To precipitate asphaltene-solids, reagent-grade n-heptane
purchased from Van Waters & Rogers Ltd. (VWR) was added to  ) ′ + i′′ (2)
Athabasca bitumen in a 40:1 (cm3/g) ratio. The mixture was
sonicated for 45 min at room temperature and then left to where ′ is the real component, or elastic modulus, and ′′ is the
equilibrate for 24 h. After settling, the supernatant was filtered imaginary part, or viscous modulus. The total modulus represents
through a Whatman no. 2 filter paper without disturbing the a change in the energy of the system with a corresponding change
whole solution. At this point, approximately 10% of the original in area. The elastic modulus can be thought of as the energy
mixture remained unfiltered. Additional n-heptane was added stored in the system, and the viscous modulus, as the loss energy.
to this solution in a 4:1 (cm3/g) ratio of n-heptane to the original The elastic and viscous moduli can also be expressed in terms
bitumen mass. The mixture was sonicated for 45 min, left of the total modulus, ||, and phase angle, φ, as follows:
overnight, and finally filtered using the same filter paper. The
yield of asphaltene-solids from bitumen was 15.1% as reported ′ ) d ) || cos φ (3)
previously.37
To separate asphaltenes from fine solids, asphaltene-solids
were dissolved in reagent-grade toluene purchased from VWR and
in a ratio of 100 cm3 of toluene per gram of asphaltene-solids.
The mixture was sonicated for 20 to 40 min to ensure complete ′′ ) ωηd ) || sin φ (4)
asphaltene dissolution and solids dispersion. The mixture was
allowed to stand for 1 h, after which it was centrifuged at 4000 The viscous modulus is the product of the frequency of oscillation,
rpm (1640 RCF) for 6 min. To recover asphaltenes, the super- ω, and the interfacial viscosity, ηd. In this work, sinusoidal
oscillations were employed.
(33) Acevedo, S.; Escobar, G.; Gutierrez, L. B.; Rivas, H.; Gutierrez, The measured total modulus depends on a number of
X. Colloids Surf., A 1993, 71, 65. experimental parameters including the size of the drop, the
(34) Li, M.; Xu, M.; Ma, Y.; Wu, Z.; Christy, A. Fuel 2002, 81, 1847. amplitude of oscillations, the frequency of oscillations, and the
(35) Aske, N.; Orr, R.; Sjoblom, J. J. Dispersion Sci. Technol. 2002, interface aging time. As mentioned earlier, the initial size of the
23, 809. drop was 22 µL. This corresponds to an interfacial area of
(36) Sztukowski, D. M.; Yarranton, H. W. J. Dispersion Sci. Technol.
2004, 25, 299. approximately 38 mm2. Jafari41 examined the effect of the
(37) Sztukowski, D. M.; Yarranton, H. W. J. Colloid Interface Sci.
2005, 285, 821. (40) Bashforth, F.; Adams, J. C. An Attempt to Test the Theories of
(38) Gafonova, O. V.; Yarranton, H. W. J. Colloid Interface Sci. 2001, Capillary Action; Cambridge University Press: Cambridge, England,
241, 469. 1883.
(39) Yarranton, H. W.; Masliyah, J. H. AICHE J. 1996, 42, 3533. (41) Jafari, M. MSc. Thesis. University of Calgary, Calgary, 2005.
Rheology of Asphaltene-Toluene/Water Interfaces Langmuir, Vol. 21, No. 25, 2005 11653

tension to the bulk concentration of asphaltenes, (2)

calculation of the instantaneous elasticity, and (3) cal-
culation of the elastic and viscous moduli.
Relation of Interfacial Tension to Bulk Asphaltene
Concentration. First, the interfacial tension is modeled
using the binary form of the Butler surface equation of
state (SEOS)42,44

Π ) γo - γ ) -
RT
a1[ln(1 - θ2) + 1 -
1
(
θ +
H 2
θ
S2 2 RT 2 ) ]
(5)

where subscripts 1 and 2 refer to the solvent and

surfactant, respectively, and Π is the surface pressure,
that is, the difference between the interfacial tension
Figure 1. Sinusoidal oscillation of drop area and IFT response between the pure solvent (toluene) and water, γo, and the
for 1 kg/m3 Athabasca asphaltenes at a toluene/water interface. interfacial tension of the solvent and surfactant versus
Interface aging time ) 1 h, ω ) 0.1 Hz. water, γ. R is the universal gas constant, T is temperature,
a1 is the interfacial area of a solvent molecule, S2 is the
amplitude of the oscillation on the measured elastic and viscous ratio of the interfacial area of the surfactant molecule to
moduli. For amplitudes up to 45% of the initial area, a Laplacian the area of the solvent molecule, θ2 is the fractional area
drop was maintained, and the total modulus did not vary surface coverage by the surfactant, and H is the enthalpy
significantly from that measured when the amplitude was as of mixing at infinite dilution. The first, second, and third
low as 2%. However, most experimenters have used amplitudes
that do not exceed 10% of the initial area.13,35,42 In the current
terms in eq 5 represent the ideal entropy of mixing, the
work, the amplitude of oscillations was 4 mm2, or 11% of the nonideal entropy of mixing caused by the difference in
initial area. size between solvent and surfactant molecules, and the
The elastic and viscous moduli can be measured as long as the enthalpy of mixing, respectively.42
interfacial tension does not change significantly during the The fractional surface coverage of the solute, θ2, is
interval in which the drop is oscillated. In the current study of related to the surfactant concentration in solution, c2,
asphaltene-toluene/water systems, the minimum time after through the following equation
which measurements were made was 10 min; that is, a droplet

[ ]
was formed at the tip of the capillary, and the IFT was recorded
c2 2θ2 S2H
for 10 min. No oscillations were applied during the aging time c′2 ) ) exp (1 - 2θ2) (6)
because it has been shown that for systems containing asphal- c2,θ)0.5 [2(1 - θ2)] S2 RT
tenes at concentrations exceeding 0.1 kg/m3, continuous oscil-
lation results in erroneous measurements that are excessively
affected by diffusion.35,41 In the current study, the interface aging where c′2 is the reduced concentration and c2,θ)0.5 is the
time was varied from 10 min to 16 h. Note that a fresh drop was half-saturation concentration. Note that the concentration
created for each aging time. After the desired aging time had given in eq 6 is the molar concentration. Also note that,
elapsed, the droplet was oscillated at a chosen frequency for a for ternary or higher-order systems, equations similar to
total of 10 complete cycles. The frequencies employed in the eq 6 apply for the reduced concentration of the surfactant
current study were 0.02, 0.033, 0.1, 0.2, and 0.5 Hz (periods of molecules in question.45 Equation 6 reduces to the Frumkin
50, 30, 10, 5, and 2 s, respectively). Note that 50 s oscillation
equation when the solvent and surfactant molecules are
periods were applied only to drops aged for 4 or more hours. Also
note that elasticity at a frequency higher than 0.5 Hz could not of equal size (i.e., S2 ) 1) and further to the Langmuir
be measured because there was too much scatter in the IFT equation when the enthalpy of mixing is ignored
response. (H/RT ) 0).
Figure 1 presents a typical example of the data collected with Calculation of Instantaneous Elasticity. The SEOS
the DSA. The example system is a droplet of a solution of is used to establish the relationship between the surfactant
Athabasca asphaltenes and toluene in a water medium. The concentration (or fractional surface coverage) and the
droplet was aged for 1 h and then oscillated at a frequency of 0.1 reduction in interfacial tension (or increase in surface
Hz (10 s period) with an amplitude of 4.1 mm2. The initial drop pressure). The second step is to find the instantaneous
area was 37.8 mm2. The measured phase angle was 16.6°, and elasticity, which is given by
the measured total modulus was 10.2 mN/m. Figure 1 shows
that the DSA data has some scatter, a byproduct of minor inertial
effects and the finite speed of the motor. However, the data can dγ
o ) (7)
be smoothed using the Tracker’s internal algorithms, as shown d ln Γ
by the ideal sinusoids imposed on both the area and IFT curves.
It was found that data smoothing was important for frequencies or the derivative of interfacial tension (eq 5) with respect
exceeding 0.2 Hz and at asphaltene concentrations lower than to the natural logarithm of the molar area of the interface,
approximately 0.01 kg/m3; under all other conditions unsmoothed
data and smoothed data resulted in the same phase angle and
Γ. Note that eq 7 is independent of the SEOS used. For
elasticity. the binary form of the Butler SEOS, the resultant
instantaneous elasticity is given by

[ ]
Theory

( )
RT θ2 1 H
The interfacial tension and elasticity data of the o ) - + 1- θ + 2 θ22 (8)
asphaltene/toluene system was modeled using the a1 (θ2 - 1) S2 2 RT
Lucassen-van den Tempel (LVDT) approach.43 Three
major steps were applied: (1) relation of the interfacial (43) Lucassen, J.; Van Den Tempel, M. Chem. Eng. Sci. 1972, 27,
1283.
(42) Lucassen-Reynders, E. H.; Cagna, A.; Lucassen, J. Colloids Surf. (44) Butler, J. A. V. Proc. R. Soc. London, Ser. A 1932, 135, 348.
2001, 186, 63. (45) Lucassen-Reynders, E. H. Colloids Surf., A 1994, 91, 79.
11654 Langmuir, Vol. 21, No. 25, 2005 Sztukowski and Yarranton

Figure 2. Asphaltene apparent (self-associated) molar mass Figure 3. Effect of frequency on the total modulus of Athabasca
as a function of asphaltene concentration. asphaltenes dissolved in toluene at concentrations from 0.005
to 20 kg/m3. The interface was aged for 10 min. The lines are
Calculation of Elastic and Viscous Moduli. The visual aides.
final step is to calculate the total, elastic, and viscous
moduli. A key assumption is that relaxation is purely suggesting that asphaltene monomers self-associate into
diffusional. The effect of diffusion is accounted for as larger aggregates as their concentration in the bulk
follows43 solution increases. Because there is some controversy over
asphaltene molar mass, the data are presented in terms
o of molar concentration (mol/m3) when compared with
|| ) (9) modeling results but in mass concentration (kg/m3)
[1 + 2ζ + 2ζ2]1/2 otherwise.
where ζ is a diffusion parameter given by Interfacial Rheology at 10 Minute Aging Time.
Figure 3 shows the effect of frequency on the measured
D dc 2 total modulus of asphaltenes in toluene after 10 min of
ζ2 ) ( )
2ω dΓ
(10) interface aging. At low frequencies, the interfacial area
changes relatively slowly, and there is sufficient time for
and D is the diffusivity of the surfactant. Also, the diffusion from the bulk phase or within the interface to
characteristic time of diffusion, τD, is related to the affect the measurement. Diffusion acts to reduce the
diffusional parameter and the frequency, ω, through the change in interfacial tension and therefore reduces the
following: measured elasticity. As the frequency increases, the total
elasticity eventually reaches a plateau where diffusion
1 no longer affects the measurement. The plateau can be
τD ) (11)
ζ2ω considered to be the instantaneous elasticity, o. The
instantaneous elasticity is an intrinsic property of the
The elastic and viscous moduli can be found individually interfacial film.
from Figure 3 shows that diffusion effects are apparent in all
of the measurements except at asphaltene concentrations
1+ζ below 0.01 mol/m3 (0.02 kg/m3) and then only at frequencies
′ ) d ) o (12)
1 + 2ζ + 2ζ2 above 0.1 to 0.2 Hz. These results are consistent with
those of Freer and Radke.12 Figure 3 also shows that the
and trends with concentration are approximately the same at
any given frequency. Nonetheless, the effect of concentra-
ζ tion was examined in detail at four different frequencies:
′′ ) ωηd ) o (13)
1 + 2ζ + 2ζ2 0.033, 0.1, 0.2, and 0.5 Hz.
The total, elastic, and viscous moduli versus asphaltene
Note that for an SEOS and the above elasticity expressions concentration after 10 min of interface aging are shown
to be valid the adsorption of the surfactant on the interface in Figure 4. At low concentrations, the measured total
must be reversible, equilibrium must be attained, and modulus corresponds to the instantaneous elasticity
there can be no mechanical film present. because the effects of diffusion are negligible. However,
as the concentration (or correspondingly the surface
Results and Discussion pressure) increases, the effects of diffusion increase.
All asphaltene concentrations were measured on a mass During drop expansion, the interface is stretched, and
basis; however, the surface equation of state is based on asphaltene-free pockets develop on the interface. At high
molar concentrations. The relationship between asphal- concentrations, there is a large supply of asphaltenes in
tene molar mass and asphaltene concentration was the bulk; therefore, a large concentration gradient exists
determined with vapor pressure osmometry (VPO) and is between the stretched areas of the interface and the bulk
presented in Figure 2.46 Consistent with previous work,11 solution. Hence, molecules migrate to the interface quickly
the molar mass increases with increasing concentration, (i.e., diffusion is very fast), and interfacial tension increases
less than it would if no diffusion occurred. During
(46) Sztukowski, D. Ph.D. Thesis. University of Calgary, Calgary, expansion and contraction, the effect is to reduce the total
2005. modulus.
Rheology of Asphaltene-Toluene/Water Interfaces Langmuir, Vol. 21, No. 25, 2005 11655

Figure 4. Measured and modeled elasticity of solutions of Athabasca asphaltenes in toluene over water for oscillation frequencies
f of (a) 0.033, (b) 0.1, (c) 0.2, and (d) 0.5 Hz. The interface was aged for 10 min.

Figure 4 shows that the interface is mostly elastic (i.e.,

negligible viscous modulus) for asphaltene concentrations
less than 0.01 mol/m3 (0.02 kg/m3). Diffusion begins to
affect the measurements at approximately 0.01 mol/m3,
and a viscous modulus appears.
Modeling Interfacial Rheology. Interfacial Tension.
The SEOS is first fit to interfacial tension data. The fit
for interfacial tension measurements of asphaltenes in
toluene versus water after 60 s, 10 min, and 4 h of contact
is shown in Figure 5. The fit parameters are the enthalpy
of mixing, the area of an asphaltene molecule, the shape
factor, and the half-saturation concentration. For lack of
a better value and the sake of simplicity, the enthalpy of
mixing was assumed to be negligible. The average
interfacial area of an asphaltene that best fit the data
was 1.4 nm2. This value is within the range reported in
the literature27,47,48 and is within 7% of the area obtained Figure 5. Measured and modeled interfacial tension of
from a plot of interfacial tension versus the logarithm of Athabasca asphaltenes dissolved in toluene versus water at 23
asphaltene concentration for the same Athabasca as- °C and interface aging times of 60 s, 10 min, and 4 h.
phaltenes.11 Hence, it appears that the Gibbs isotherm is
a good approximation of the molecular area of an adsorbed The area of toluene is expected to be slightly larger than
asphaltene, even if the Gibbs isotherm assumes Langmuir- the area of benzene. On the basis of the lengths of the
type adsorption (because S2 ) 1). However, the Gibbs bonds between carbon atoms in the benzene molecule,
isotherm would not fit the IFT for concentrations less than the area is about 0.15 nm2. Also, the average area occupied
0.01 mol/m3. by a molecule on an interface will likely be larger than the
The ratio of the molecular areas, S2, was set to 5 so as size of the molecule itself.
to obtain a realistic interfacial area for toluene, 0.28 nm2. The half-saturation concentrations were then adjusted
to fit the low-concentration data. Concentrations of 0.07,
(47) Rogel, E.; León, O.; Torres, G.; Espidel, J. Fuel 2000, 79, 1389. 0.03, and 0.007 mol/m3 were found to fit the data at 60 s,
(48) Bhardwaj, A.; Hartland, S. Ind. Eng. Chem. Res. 1994, 33, 1271. 10 min, and 4 h, respectively. Note that theoretically the
11656 Langmuir, Vol. 21, No. 25, 2005 Sztukowski and Yarranton

Figure 6. Diffusion coefficient for Athabasca asphaltenes

dissolved in toluene as a function of asphaltene concentration,
determined from eq 14. Figure 7. Measured and modeled elasticity of solutions of
Athabasca asphaltenes in toluene over water. The oscillation
half-saturation concentration is applicable at equilibrium is frequency 0.033 Hz, the interface was aged for 10 min, and
and should therefore be constant. However, the equilib- D ) 3 × 10-11 m2/s.
rium value of the interfacial tension of asphaltene
solutions over water is difficult to assess because me- As a first pass, the diffusion coefficient was taken to be
chanical rigidity affects the measurements relatively 3 × 10-11 m2/s, which falls in the range shown in Figure
quickly. Hence, the half-saturation constant has been used 6. The instantaneous elasticity, the elastic modulus, and
as a fitting parameter. In fact, as discussed later, the LVDT the viscous modulus were then determined from eqs 8,
model assuming purely diffusional relaxation is valid only 12, and 13, respectively. The predictions are compared
at short interface aging times (i.e., before the formation with the experimental data for 10 min of aging and an
of mechanical films). Hence, the half-saturation constants oscillation frequency of 0.033 Hz in Figure 7. It is obvious
are only physically meaningful at very short aging times. from Figure 7 that the match was successful only for
Elastic and Viscous Moduli. To use the LVDT model, asphaltene concentrations less than 0.005 mol/m3. To
the diffusion coefficient must be known for asphaltene- determine if the whole range of asphaltene concentration
toluene solutions over water. The diffusion coefficient, D, could be matched, the diffusion coefficient was treated as
can be deduced from the interfacial tension at short times a fitting parameter. It was found that a concentration-
using the equation given by Campanelli and Wang49 dependent asphaltene diffusivity of the following power
law form

γ(t) ) γo - 2RTco
x3Dt
7π
(14) D ) ac2b (15)

where γ and γo are the interfacial tension of the surfac- was required to fit the elastic and viscous moduli in Figure
tant-solvent solution and pure solvent over water (or 7 where a and b are constants. The numerical values of
another immiscible liquid), respectively, R is the universal a and b that best fit the elasticity data are 3 × 10-14 m2/s
gas constant, T is the temperature, co is the bulk and -0.6, respectively.
concentration of surfactant, and t is the time. Equation Equation 15 indicates that the required diffusivity at
14 shows that for the short-time diffusion approximation the lowest asphaltene concentration considered here is
to apply, a plot of γ versus t1/2 should be linear. The approximately 10-12 m2/s and decreases to approximately
diffusion coefficient can then be deduced from the slope 10-14 m2/s at the highest concentrations. Hence, the
of the plot. Figure 6 shows the calculated diffusion diffusivity required to match the full range of asphaltene
coefficient as a function of bulk asphaltene concentration. concentration is anywhere from two to four orders of
Equation 14 was found to be useful only at low asphaltene magnitude lower than the values of Norinaga et al.50 or
concentrations. At asphaltene concentrations greater than the values obtained from the short-time diffusion ap-
0.2 kg/m3 (0.1 mol/m3), the interfacial tension decreased proximation shown in Figure 6.
during droplet formation, and the value of IFT at time Why is the diffusivity needed to match the full range
zero (i.e., when the droplet was fully formed) was less of asphaltene concentration so much smaller? One reason
than the pure-solvent IFT. is that the diffusion coefficient relevant to the relaxation
Norinaga et al.50 used pulsed field gradient spin-echo of asphaltenes at the interface is not the bulk diffusion
NMR to determine the diffusivity of Kafji vacuum residue coefficient as deduced from the short-time diffusion
asphaltenes in pyridine. They found that the diffusivity approximation. Although asphaltenes diffuse to the
decreased from about 1.4 × 10-10 to 0.9 × 10-10 m2/s when interface quite quickly, their movement at the interface
the bulk asphaltene concentration increased from roughly during droplet expansion/contraction may be retarded
1 to 20 kg/m3. The data in Figure 6 show a similar decrease because of the formation of skins at the interface. The
in diffusion coefficient with concentration but are ap- formation of viscous films may result in slower diffusion
proximately 1 order of magnitude smaller than the values along the interface during oscillation; therefore, the bulk
given in the work of Norinaga et al. diffusion may not be representative during interfacial
relaxation. Sheu et al.51 speculated that the rearrangement
(49) Campanelli, J. R.; Wang, X. H. J. Colloid Interface Sci. 1999,
213, 340.
of asphaltenes on the interface may be slower than the
(50) Norinaga, K.; Wargardalam, V. J.; Takasugi, S.; Iino, T.;
Matsukawa, S. Energy Fuels 2001, 15, 1317. (51) Sheu, E. Y.; Storm, D. A.; Shields, M. B. Fuel 1995, 74, 1475.
Rheology of Asphaltene-Toluene/Water Interfaces Langmuir, Vol. 21, No. 25, 2005 11657

Figure 8. Effect of interface aging time on the elastic and

viscous moduli of Athabasca asphaltenes dissolved in toluene.
The oscillation frequency is 0.033 Hz. Closed symbols - elastic
modulus, open symbols - viscous modulus. The lines are visual
aides.

diffusion process and can therefore become the “bottleneck”

of the equilibrium kinetics.
This argument is supported by the work of Freer and
Radke.12 As mentioned previously, they measured the
elastic and viscous moduli of an asphaltene-toluene-
water interface at an asphaltene concentration of 0.005
wt % (approximately 0.05 kg/m3) over six decades of
frequency. They used a combination of the LVDT model
and a Maxwell viscoelastic model to match their data.
Because their data was collected at a constant asphaltene
concentration, the instantaneous elasticity predicted from
a surface equation of state was not required. Rather, they
regressed o, the characteristic time of diffusion, τD, (eq Figure 9. Measured and modeled elasticity of solutions of
11), and two other parameters that were required for the Athabasca asphaltenes in toluene over water for oscillation
Maxwell viscoelastic part of the model until a satisfactory frequencies f of (a) 0.033 and (b) 0.1 Hz. The interface was aged
match was obtained over the entire frequency range. They for 4 h.
found a characteristic diffusion time of 25 s. In our work,
a similar characteristic time of diffusion of 88 s is obtained
at a concentration of 0.05 kg/m3 (0.03 mol/m3). Hence,
both applications of the LVDT model require similar
diffusivities.
Figure 4a-d compares the predicted instantaneous,
elastic, and viscous moduli with experimental data for
asphaltene-toluene over water interfaces aged for 10 min.
The same values of a and b in eq 15 are used for each
oscillation frequency. The model matches appear to be
satisfactory, although the viscous modulus is slightly
overpredicted at lower frequencies.
Effect of Interface Aging. The elastic and viscous
moduli of asphaltenes at a toluene/water interface are
given in Figure 8 for an oscillation frequency of 0.033 Hz.
The data are reported versus mass concentration because
Figure 10. Film ratio of the interface of droplets of Athabasca
the apparent asphaltene molar masses were not measured asphaltenes in toluene surrounded by water.41
over time. The elastic modulus increases significantly over
16 h, whereas the viscous modulus increases only mar- parisons. Nonetheless, the general trends regarding the
ginally. The largest increases in the moduli occur for effect of contact time are consistent.
“intermediate” asphaltene concentrations, that is, con- The increase in the moduli over time could not be
centrations varying between 0.01 and 1 kg/m3 (0.05 and predicted with the Lucassen-van den Tempel model, as
0.5 mol/m3). The rise in the moduli is consistent with other shown in Figure 9. A likely explanation for the model
work.12-15,35 Unfortunately, a quantitative comparison of failure is that irreversible adsorption occurs and a
the data shown in Figure 8 with the literature is difficult mechanical film forms. Figure 10 shows the film ratio of
because the asphaltene source, concentration, and solvent asphaltene-toluene/water interfaces as a function of time
vary significantly. Furthermore, some of the studies were and asphaltene concentration.41 The film ratio is the area
conducted on crude oil drops rather than asphaltene- of the interface at which the interfacial film crumples
heptol drops.13,35 The effect of resins and other surface- over the initial area of the interface. Such crumpling is
active constituents of the oil impedes meaningful com- evidence of rigid, irreversible film formation. Figure 10
11658 Langmuir, Vol. 21, No. 25, 2005 Sztukowski and Yarranton

shows that film ratios appear even at very short aging water interfaces. Furthermore, aging effects cannot be
times (less than 10 min). accounted for with this type of model.
For the SEOS-LVDT approach to be valid, asphaltenes
must be adsorbed reversibly. Therefore, it is not surprising Acknowledgment. The financial support of NSERC,
that the modeling approach required modified diffusivities Alberta Ingenuity, and the Alberta Energy Research
at short aging times and failed at longer times. The small Institute is greatly appreciated. We also thank Syncrude
diffusion coefficients required to match the data suggest Canada Ltd. for bitumen samples.
that asphaltene diffusion along the interface, rather than
bulk diffusion to and from the interface, dominates the Nomenclature
rheology. Therefore, an SEOS-LVDT modeling approach a ) fitting parameter
does not strictly apply to asphaltene interfacial films. It a ) interfacial area of a molecule (nm2/molecule)
is possible to use a viscoelastic models such as the Maxwell A ) area of the drop at any given time (mm2)
model used by Freer and Radke;12 however, curve-fitted b ) fitting parameter
parameters are required. co ) bulk concentration of surfactant (mol/m3)
c′2 ) reduced concentration (-)
Conclusions c2,θ)0.5 ) half-saturation concentration (mol/m3)
D ) diffusion coefficient (m2/s)
The rheological properties of asphaltene-toluene/water
H ) enthalpy of mixing (J/mol)
interfaces are sensitive to asphaltene concentration and R ) universal gas constant (8.314 J/mol‚K)
aging time. The elastic modulus reached a maximum at S2 ) shape factor, ratio of the area of a surfactant molecule
asphaltene concentrations of approximately 0.1 to 0.2 kg/ to the area of a solvent molecule
m3 (0.05 to 0.1 mol/m3) and decreased over the range of t ) time (s)
concentrations typically encountered in oil field emulsions. T ) temperature (K)
Hence, oils with higher asphaltene concentrations can
potentially form less stable emulsions than oils with low Greek Symbols
asphaltene concentrations. γo ) interfacial tension of pure solvent over water
The elastic modulus increases with aging at all as- (mN/m)
phaltene concentrations. The increasing modulus is γ ) interfacial tension of surfactant-solvent solution over
consistent with the gradual formation of interfacial skins. water (mN/m)
The trend is also consistent with the observation that Γ ) moles adsorbed per area of interface (mol/m2)
 ) total modulus (mN/m)
aged emulsions are typically more stable than fresh
′ ) elastic modulus (mN/m)
emulsions. The viscous modulus did not increase with ′′ ) viscous modulus (mN/m)
aging time. d ) interfacial elasticity (mN/m)
The interfacial rheology of fresh asphaltene-toluene/ ζ ) diffusion parameter (-)
water interfaces can be modeled with the LVDT approach. ηd ) interfacial viscosity (mN/m‚s)
However, it is necessary to use a concentration-dependent θ ) fractional surface coverage (-)
asphaltene diffusivity that is orders of magnitude smaller τD ) characteristic time of diffusion (s)
than the expected bulk-phase diffusivity. The low diffu- φ ) phase angle (rad)
sivity suggests that diffusion at the interface rather than Π ) surface pressure (mN/m)
diffusion in the bulk phase controls the time-dependent ω ) frequency (rad/s)
interfacial behavior. There may be resistance to mass Subscripts
transfer at the interface because the asphaltenes have
formed a surface network. LVDT does not account for 1 ) solvent (toluene)
2 ) surfactant (asphaltenes)
molecular interactions at the interface; therefore, strictly
speaking, the model is invalid for the asphaltene-toluene/ LA051921W