7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


Surfactant spreading along thin liquid films on chemically patterned surfaces


Myroslava Hanyak, David Sinz, Jos Zeegers and Anton A. Darhuber

Mesoscopic Transport Phenomena Group, Department of Applied Physics
Eindhoven University of Technology, Den Dolech 2, 5612AZ Eindhoven, The Netherlands
E-mail: a.a.darhuber@tue.nl
Keywords: Surfactant spreading, Marangoni driven flow, chemically patterned surfaces

March 24, 2010



Abstract

The injection of surfactant solutions is a promising technique for enhanced oil recovery from sub-surface reservoirs.
Towards a quantitative understanding of the fluid-mechanical aspects of the process, we conducted a combined
experimental and numerical study of the spreading dynamics of soluble and insoluble surfactants on confined thin
liquid films. To good approximation the surfactant front propagates according to a power-law relation x ~ t". We
determined the spreading exponents a for different film thicknesses and initial conditions and found a favorable
agreement between experiments and simulations.


Introduction

The spreading of liquids has been the focus of numer-
ous scientific studies for many years. The technological
applications motivating this research range from coat-
ing processes, medical applications to the petrochemi-
cal industry. An application where confinement effects
play a major role in the spreading dynamics is oil re-
covery. After primary and secondary recovery, up to
about 60% of the originally present crude oil remains
in a reservoir (Shan & Schechter (1977); Lake (1989)).
Injection of surfactant solutions is considered a potential
means for extracting more oil from sub-surface reser-
voirs. Surfactants reduce interfacial tension, thereby fa-
cilitating deformations of oil-brine interfaces and oil ex-
traction. Initially, the injected surfactant solutions pene-
trate a reservoir along the path of least hydrodynamic re-
sistance, e.g. along large rock fractures, and potentially
do not directly reach the entire rock pore volume occu-
pied by crude oil. A driving force that transports surfac-
tants further into the pore structure is interfacial tension
gradients generated as a result of non-uniform surfactant
distributions. The resulting Marangoni stresses at fluid-
fluid interfaces locally induce flow from regions of lower
to regions of higher interfacial tension.
Surfactant spreading on thin liquid films has been
studied extensively in the past (Borgas & Grotberg
(1988); Troian et al. (1989, 1990); Gaver & Grot-
berg (1990, 1992); Jensen & Grotberg (1993); Grotberg


(1994); Jensen (1994, 1995); Grotberg & Gaver (1996);
Bull et al. (1999); Matar & Troian (1998, 1999); Fis-
cher & Troian (2003a,b); Warner et al. (2004); Jensen &
Naire (2006)). Using experiments and theoretical mod-
els based on the lubrication approximation, Troian et al.
as well as Grotberg and co-workers investigated axisym-
metric unsteady spreading of surfactant monolayers on
thin liquid films (Borgas & Grotberg (1988); Troian et
al. (1989); Gaver & Grotberg (1990)). Film thinning
was observed in the vicinity of the deposited surfactant
as well as film thickening and the formation of a rim near
the surfactant leading edge.
Jensen and Grotberg presented a model for the spread-
ing of soluble surfactants (Jensen & Grotberg (1993))
considering linearized sorption kinetics and fast vertical
diffusion across the film thickness, which allowed cross-
sectional averaging of the bulk concentration. It was
shown that different solubilities of the surfactant induced
qualitative differences in the flow patterns. Dussaud et
al. (2005) studied the dynamics of insoluble surfactant
monolayers spreading on glycerol films. Experimental
film thickness profiles were obtained by means of Moire
topography. To good approximation the surfactant front
expands according to a power law relation r ~ t" for
which a spreading exponent of a = 0.23 was found,
which is close to the analytically predicted value for a
finite quantity of deposited surfactant.
The mechanism of interfacial tension reduction by
surfactants appears highly beneficial for enhanced







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


Figure 1: Interference microscope image of a 1.5 mm
wide glycerol rivulet prior to surfactant deposition.


oil recovery (EOR). Natural oil reservoirs, however,
are highly complex systems, which contain multi-
component mixtures at high temperatures and pressures,
with lengthscales varying from nanometers to kilome-
ters. Moreover, each reservoir has unique features in
terms of rock- and oil composition, pore structures and
fractures. Since phenomena associated with surfactant-
enhanced EOR are not entirely understood, we focus
our attention on single-pore-level investigations at the
micron-scale and above.
In order to facilitate a quantitative comparison be-
tween experiments and numerical simulations, we study
the spreading of soluble and insoluble surfactants along
thin liquid films deposited on chemically patterned sur-
faces. The hydrophilic/hydrophobic patterns confine liq-
uid to predefined regions on the substrate surface in the
shape of long and narrow stripes. This allows us to study
the effect of geometrical confinement and a non-zero
curvature of the interface on the surfactant spreading dy-
namics.


Experimental setup and procedures

Chemically patterned surfaces were fabricated using
vapor deposition of self-assembled monolayers of
1H,1H,2H,2H-perfluorooctyl-trichlorosilane (PFOTS,
purity > 97%, Sigma Aldrich product number 448931)
on single-side polished Si substrates of dimensions
50mm x 50mm x 0.5mm. For this purpose, patterns
were created by masking the hydrophilic regions
with photo-resist and leaving the hydrophobic ones
unmasked. Prior to the patterning process the substrates
were cleaned using an oxygen plasma cleaner. Before
deposition of the base liquid the hydrophilic regions
were cleaned using a mixture of hydrogen peroxide and
sulfuric acid. Liquid films of anhydrous glycerol (purity


Figure 2: Interference microscope image of the surfac-
tant deposition using a Hamilton micro-syringe.


99%, Sigma Aldrich product number 49767) with a
thickness ho in the range of ho 1 10 pm were
deposited on the hydrophilic regions of the substrates
using spin-coating. As an insoluble surfactant we
used cis-9-octadecenoic acid oleicc acid, purity 99%,
Sigma Aldrich product number 01008). As a soluble
surfactant we used sodium dodecyl sulfate (SDS, purity
99%, Sigma Aldrich product number 71727).
In the case of oleic acid, small amounts of pure undi-
luted surfactant (0.1 to 0.2pl) were deposited on the
rivulets using a Hamilton micro-syringe as a dip-pen.
In the case of SDS, droplets of a glycerol-SDS solu-
tion of varying concentration were deposited. The dy-
namics following the deposition of the surfactant were
monitored by means of interference microscopy using
an Olympus BX51 upright microscope and an LED
light source that provided bandpass-limited illumination
in the spectral range between approximately 440 and
470 nm.



Experimental results

Figure 1 shows an interference microscope image of a
liquid rivulet of width w 1.5mm prior to deposi-
tion of surfactant. Using a micro-syringe as a dip-pen
a small amount of surfactant is deposited on the rivulets,
as shown in Fig. 2. Subsequently, film thinning occurs
in the vicinity of the deposited droplet and a local max-
imum or rim develops in the rivulet height profile and
moves along the rivulet away from the deposited surfac-
tant droplet as shown in Fig. 3. From numerical simu-
lations described below we know that the rim is located
just behind the leading edge of the spreading surfactant
front. Therefore, we monitor its propagation to evaluate
and optimize the surfactant spreading dynamics. Fig-
ure 4 shows a typical measurement of the rim position







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


that accounts for the influence of Marangoni stresses,
hydrostatic and capillary pressure gradients. For an in-
soluble surfactant the bulk concentration is zero. An
equation for surfactant surface transport can be derived
(Borgas & Grotberg (1988); Troian et al. (1990)) in-
cluding the effects of surfactant convection due to the
motion of the bulk liquid as well as surface diffusion.


- + V. V

or+ V. V7
8t I /t


Figure 3: Interference microscope image of the region
around the rim after it propagated 7 mm from the edge
of the deposited surfactant droplet.


xrim(t). To good approximation it follows a power law
behavior xrim(t) ~ t", where the spreading exponent a
quantifies the displacement efficiency of a given surfac-
tant.
Experimental results for the insoluble surfactant oleic
acid spreading on straight glycerol rivulets of uniform
width show spreading exponents in the range a 0.28-
0.41. For comparison the soluble surfactant SDS yields
higher values of the spreading exponent a 0.45 -
0.55, apparently independent of initial film height and
surfactant concentration in the range studied.



Numerical simulations

For the thin liquid films considered, the small-slope ap-
proximation can be applied to derive an evolution equa-
tion for the subphase height profile (Oron et al. (1997))


in


10 100
time [s]


1000


Figure 4: Rim position as a function of time. The
straight line corresponds to a power law relation Xrim
t' with the spreading exponent a = 0.32.


-Vh -
3/ V

2Vh


h3 (1)
Vp =0 (1)

h2F
- -Vp
] 0 (2)
-DsVr] 0 (2)


p = -V2h


where h, F and p are rivulet height, surfactant surface
concentration and capillary pressure, p and p are the
fluid viscosity and density, respectively, and D, repre-
sents the surfactant surface diffusivity.
The dependence of surface tension 7 on surfactant
concentration F for the case of oleic acid on glycerol has
been measured by Gaver & Grotberg (1992). We fitted
their experimental data with the following expression

7 7m + II exp(-AF2) (4)

where Im = 24 mN/m is the maximum spreading pres-
sure, 7m 39 mN/m is the asymptotic value of the
surface tension and A 0.5m4//12 is a fit parame-
ter. Thus, we consider a realistic, non-linear equation of
state 7(F) connecting surface tension and surface con-
centration for this insoluble surfactant.
In the case of soluble surfactants, we add a flux term
J to the convection-diffusion equation (2) that accounts
for surfactant adsorption and desorption. Moreover, we
include a convection-diffusion equation for the height-
averaged bulk concentration Co (Jensen & Grotberg
(1993)).


C00 h
+ V7 -VC0
DL 2t


2/Vh


Db
b V [hVCo]
h

L k


h2F
DV (5)
DSvF] J (5)


ki Co) (6)


where Db is the surfactant bulk diffusivity, ki and k2
are the rate constants of adsorption and desorption, re-
spectively. We assume that the flux of surfactant corre-
sponding to bulk-surface exchange is given by (Jensen
& Grotberg (1993))


J(F, Co) = kiCo k










7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


We measured the dependence of surface tension on bulk
concentration for SDS in glycerol and represent the data
with the following fit function


7 = 7m + n, exp(-AlCo)


where I, = 24.5mN/m, 7, z 39 mN/m and A1
44 /mol.
These systems of equations for insoluble (1-4) or sol-
uble surfactants (5-8) are solved numerically with the
finite element software Comsol Multiphysics 3.5 using
the following boundary conditions


Oh







y 2
0(x, Y t)
h(O,y,t)


(oc, y,t)

O (O,y,t)
09


v--f v--


Oh
0= AX0, t)

o (X0t)
dy
OF

oy


0

0(y)
0

0


where f(y) ho(1 4y2/w2) is the boundary height
profile, which is parabolic if the influence of gravity
is neglected. The boundary conditions for the height-
averaged bulk surfactant concentration are equivalent to
those for the surface concentration.
We use the following initial conditions (ICs) for the
height profile and pressure


h(x,y,0) = f(y),


02 f
p(r, y, 0) Of (17)


Regarding the IC for the insoluble surfactant concentra-
tion we consider the following two cases. In the case of
finite surfactant supply, a limited initial quantity of sur-
factant is distributed in the region 0 < x < L (illustrated
by the shaded area in Fig. 5) according to


F(x, y, 0) 0.5F (1


[20 L )
tanh I-(x L)


which is subsequently depleted in the course of the
spreading process. Here, F = 3.5 pl/m2 is the concen-
tration where according to the equation of state (4) the
surface tension essentially reaches its asymptotic value
7m.
In our experiments, however, the deposited surfactant
quantity is large and consequently does not deplete as


Figure 5: Numerical simulations of the spreading dy-
namics of the insoluble surfactant oleic acid on a glyc-
erol rivulet for ho 0 7.5 pm, w = 1.5 mm, L = w/4, and
gravity effects neglected. Panel (a) illustrates the initial
condition where the shaded area depicts the surfactant
deposition region. Panels (b) and (c) show the rivulet
height profile after the rim has propagated the distance
of (b) Ax w/2 and (c) Ax 5w/4.


fast as in the finite supply model. To mimic such a con-
tinuous surfactant supply, we impose a constant surface
concentration in the region of surfactant deposition, i.e.,
F(x, y, t) F= const in the interval 0 < x < L.
Figure 5 shows typical snapshots of the surfactant
spreading process of the insoluble surfactant oleic acid
on rivulets of glycerol, where the colors represent the
subphase height profile. The computed spreading ex-
ponent a for finite supply of an insoluble surfactant is
found to be in the range of 0.25 0.27, while the ex-
ponent for continuous supply ranges from 0.38 0.42,
depending on the value of the rivulet center height.
Equivalent simulations have been performed for solu-
ble surfactant spreading and typical examples for finite
surfactant supply are shown in Fig. 6. The black and
















E


.
IL r =1\ y

Sc,=o

0.1.
1 10 100 1000
Time [s]

Figure 6: Rim position Xrim(t) for a finite quantity of
insoluble and soluble surfactants spreading on a glyc-
erol rivulet for ho = 7.5 pm, w = 1.5 mm, L = w/4, and
gravity effects neglected. Curves (1) and (3) correspond
to oleic acid and SDS spreading on a rivulet with uni-
form initial height profile (depicted by the blue line in
the inset), respectively, whereas curve (2) corresponds
to SDS and a non-uniform initial rivulet center height as
sketched by the red line in the inset.


blue curves labeled (1) and (3) correspond to oleic acid
and SDS spreading along a glycerol rivulet with uniform
initial height profile h(x, y,t 0) f(y) as shown in
the inset of Fig. 6 (blue curve). Curve (2) was calculated
for a non-uniform IC for the height profile, as illustrated
by the red curve in the inset,

h(x
h(x > L,y,t 0)= f(y) (20)

which represents deposition of a large droplet of SDS-
glycerol solution. The spreading exponents for t >
500 s for oleic acid [curve(l)] and SDS with uniform IC
[curve (3)] are a 0.26, whereas for SDS and a non-
uniform IC a significantly higher value of a = 0.41 was
found.


Summary and conclusions

We conducted an experimental and numerical study
of surfactant spreading on straight glycerol rivulets on
chemically patterned surfaces. Using interference mi-
croscopy and a numerical model based on lubrication
theory, we monitored the development and propagation
of a rim in the liquid height profile after surfactant depo-
sition at the rivulet-air interface. The spreading surfac-
tant front followed to good approximation a power-law


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


behavior x ~ t", where the spreading exponents deter-
mined from experiments (a = 0.28 0.38) and simula-
tions (a = 0.25 0.42) compare favorably in the case
of insoluble surfactants.
We found that for insoluble surfactants and uniform
initial rivulet height profiles, the initial film thickness
has little effect on the spreading exponents. Continuous,
i.e. unlimited surfactant supply led to higher exponents
and increased the influence of the rivulet aspect ratio as
compared to the case of finite supply. Experiments for
soluble surfactants indicated that a is independent of the
surfactant concentration in the range investigated. Sim-
ulations revealed a considerable dependence of a on ini-
tial conditions in the case of non-uniform rivulet height
profiles.

Acknowledgments

The authors would like to thank Steffen Berg and Axel
Makurat from Shell International Exploration and Pro-
duction (Rijswijk, The Netherlands) for the inspiring
collaboration. The authors gratefully acknowledge that
this research is supported partially by the Dutch Tech-
nology Foundation STW, applied science division of
NWO and the Technology Program of the Ministry of
Economic Affairs.

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7th International Conference on Multiphase Flow,
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