This document describes a microfluidic method for measuring interfacial tension between immiscible fluids using a microfluidic device. The device contains two tapered microchannels connected by a pair of modified Laplace sensors. Interfacial tension is determined by monitoring the pressure drop across the microchannels where the interfaces are formed and measuring the curvatures of the interfaces. The method was tested using oil/water systems and results agreed well with a commercial tensiometry. This provides a low-cost and fast way to measure interfacial tension in microfluidics.

1. A facile microfluidic strategy for measuring interfacial tension
Hongbo Zhou, Yuan Yao, Qiang Chen, Gang Li, and Shuhuai Yao
Citation: Applied Physics Letters 103, 234102 (2013); doi: 10.1063/1.4838616
View online: http://dx.doi.org/10.1063/1.4838616
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2. A facile microfluidic strategy for measuring interfacial tension
Hongbo Zhou,1,2
Yuan Yao,1
Qiang Chen,2
Gang Li,2
and Shuhuai Yao1,a)
1
Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science
and Technology, Hong Kong, China
2
State Key Laboratory of Transducer Technology, Shanghai Institute of Microsystem
and Information Technology, Chinese Academy of Science, Shanghai, China
(Received 7 October 2013; accepted 14 November 2013; published online 2 December 2013)
We report a facile method for measuring interfacial tension (IFT, c) of immiscible fluids using a
microfluidic device. The IFT is determined by monitoring the pressure drop across a
microchannel, where a pair of modified Laplace sensors (formed by tapered channels) are
connected, and the curvatures of the interfaces in the tapered channels. The method was tested
with the model oil/water systems, and the results agreed well with a commercial tensiometry. We
expect this method to be easily implemented in common microfluidic laboratories and supply a
low-cost and fast way for interfacial tension measurement. VC 2013 AIP Publishing LLC.
[http://dx.doi.org/10.1063/1.4838616]
Interfacial tension (IFT) is an important physical prop-
erty of immiscible fluids, for it governs the structure, dynam-
ics, and stability of multiphase systems,1,2
e.g., emulsion,
detergent, pharmaceuticals, cosmetics, petroleum, etc. Due
to the large surface-to-volume ratio, IFT becomes the pre-
dominant force in microfluidics,3
compared to the volumetric
forces, such as gravity, inertial force, and so on. In microflui-
dics, the surface tension can exert significant stress that
results in free surface deformation or bulk liquid motion.4
Therefore, an accurate IFT measurement is critical in both
scientific research and practical applications.
Since the pioneer work of Young, Laplace, and Gauss in
the early 19th century, many classical methods have been
developed for IFT measurement.5
These methods are based
on force measurement (such as Wilhelmy plate and Du No€uy
ring), pressure adjustment (using a maximum bubble or
growing drop), or shape analysis (using a sessile drop or
pendant drop). Although these classical methods offer reli-
able and accurate results, the corresponding commercial
instruments are usually bulky and costly.
Growing effort has emerged to develop a convenient
method for measuring IFT in microfluidics. It is well known
that the competition between flow stress and interfacial ten-
sion deforms a droplet. Based on this foundation, Hudson
et al.6,7
reported a microfluidic approach for IFT measure-
ment. Droplets and flow gradients were generated in a micro-
fluidic device, and the interfacial tension was calculated by
analyzing the rate of droplet deformation. Xu et al.8
used a
simple coaxial microfluidic device for the measurement of
IFT based on the coflowing rupturing method. The interfacial
tension force was balanced with and calculated from viscous
force. In the above approaches, an accurate description of
the flow field is essential to establish the force balance equa-
tion. Another way for measuring IFT is based on the Young-
Laplace equation. Lee et al.9
reported measuring IFT in a
tapered micropipette. A given pressure was applied across
the interface, and the radius of curvature of the interface was
captured. Then, the IFT value was calculated based on the
Young-Laplace equation. Gu et al.10
used a tapered micro-
channel to form the interface of the two immiscible fluids. In
order to account for the interface asymmetry in both horizon-
tal and vertical directions, the contact angle was measured
firstly and then used to evaluate the radius of curvature in
both directions. In this method, a highly precise pressure
source or a transducer is required to ensure an accurate
result. Based on the competition between the flow resistance
and the capillary pressure, Li et al.11
demonstrated another
method to measure IFT between immiscible fluids flowing
through a pore array micro-structured device.
Here, we report a facile microfluidic method for IFT
measurement. We first introduce the working principle and
measurement procedures. We measured the IFT of the com-
monly used oil/water system and compared them with the
results from a commercial tensiometry. Furthermore, we dis-
cussed the error sources of our method.
As illustrated in Fig. 1, the IFT microfluidic device con-
tains a pair of tapered microchannels (represented as a and b
tapered channel), to which two water columns are connected.
H represents the level height of water column with respect to
the tapered channel (as illustrated in Fig. 1(b)). The pressures
in the oil and water phase are Po and Pw, respectively. Pa
represents the atmospheric pressure. Then
Pw ¼ Pa þ qgH; (1)
where q is the density of water and g is gravity acceleration.
When an oil/water interface exists, a pressure different
across the interface is generated according to the Young-
Laplace equation10,12
Pw À Po ¼ c
1
Rh
þ
1
Rv
; (2)
where Rh and Rv represents the radius of curvature in the hor-
izontal and vertical direction. Equations (1) and (2) apply for
both the two tapered channels in the device. Then, the differ-
ence of a and b channel yieldsa)
meshyao@ust.hk
0003-6951/2013/103(23)/234102/4/$30.00 VC 2013 AIP Publishing LLC103, 234102-1
APPLIED PHYSICS LETTERS 103, 234102 (2013)
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3. ðPwa À PoaÞ À ðPwb À PobÞ ¼ c
1
Rha
þ
1
Rva
À
1
Rhb
þ
1
Rvb
: (3)
As the height of the tapered microchannel (h) is uniform
(as shown in Fig. 1(c)), contact angle h on the inner surface
of the microchannel (with the same material) is constant.
According to the relationship 2Rv*cosh ¼ h, we can assume
that in the tapered channels, the radii of curvature in the ver-
tical direction are the same, Rva ¼ Rvb. Then, Eq. (3) is sim-
plified as
ðPwa À PwbÞ À ðPoa À PobÞ ¼ c
1
Rha
À
1
Rhb
: (4)
To simplify this equation further, the two water column lev-
els are adjusted to kept a same height, that is, P0
wa ¼ P0
wb and
DH0
¼ 0. Equation (4) is simplified as
DP0
ab ¼ P0
oa À P0
ob ¼ c
1
R0
hb
À
1
R0
ha
: (5)
To measure the pressure drop DPab across point a and b (as
shown in Fig. 1(a)), the water column levels are tuned as
DH
00
to make the oil/water interface in the two tapered chan-
nel be the same, R
00
ha ¼ R
00
hb. Thus, from Eq. (4), we can
obtain
P
00
wa À P
00
wb ¼ P
00
oa À P
00
ob ¼ DP
00
ab: (6)
We maintain stable flow rate during the measurement, that
is, DP0
ab ¼ DP
00
ab ¼ DPab. Combining Eqs. (1), (5), and (6),
the relationship between the water column level height dif-
ference DH
00
and interfacial tension is expressed as
qgDH
00
¼ DPab ¼ c
1
R0
hb
À
1
R0
ha
: (7)
The microfluidic device was fabricated in poly(dime-
thylsiloxane) (PDMS) using standard soft lithography techni-
ques. The PDMS replica casted from the SU-8 mold has a
tapered channel with varying width from 20 lm to 100 lm
and a uniform depth of 60 lm. A glass slide was spin-coated
with another PDMS mixture (prepolymer and curing agent
ratio of 20:1) to form a thin PDMS layer. After being baked
at 60
C for 45 min, the glass slide and the PDMS replica
were stacked and bonded together by diffusion bonding
method,13
which ensure all the microchannel surfaces are
made of PDMS.
We measured the oil-water IFT in the fabricated device.
The commonly used oils in microfluidics, such as mineral oil
(M5904), silicone oil (DC200), and hexadecane (H6703),
purchased from Sigma-Aldrich, were used in the experi-
ments. The oil phase was pumped into the microchannel
using a syringe pump (210P, KD Scientific). Two 30 ml cyl-
inders were connected to the tapered microchannels using
Luer taper and silicone tubes (Inner diameter: 0.8 mm, Cole
Parmer). An oil/water interface was formed in each tapered
channel. A CCD camera (EXi Blue, Q-IMAGING) was
mounted on an inverted microscope (Eclipse Ti, Nikon) to
capture the oil/water interface. A home-made MATLAB code
was used to fit and measure the curvature of the oil/water
interface. The measured data were compared with the results
obtained from a commercial interfacial tensiometry
(Digidrop, GBX).
A typical measuring process can be divided into two
steps. First, the levels of the two water columns are kept the
same height, DH0
¼ 0, and R0
ha and R0
hb in the tapered chan-
nel are captured and measured (Fig. 2(a)). Second, the levels
of the water columns are changed until the oil/water interfa-
ces in the two channels arrive at the same location where the
curvatures of the interfaces are the same (Fig. 2(b)). The
height difference (DH00
) between the levels of two water col-
umn, or DPab, is measured. Finally, the interfacial tension c
is calculated according to Eq. (7).
People usually expect using flow resistance model12,14
(DPab ¼ Q*rsample, where Q represents the flow rate of the oil
phase in the microchannel and the flow resistance rsample is
calculated using the classic formula for fully developed duct
flow in a rectangular channel) to calculate DPab and further
simplify the two-step measuring procedure. However, taking
hexadecane, for example, we obtained a discrepancy as
much as 122% in DPab, as compared to the hydraulic pres-
sure measured in height difference (DH00
). This large discrep-
ancy may be due to the unexpected dimension change in the
microchannels as many organic oils swell PDMS15
and
severely change the scheming dimension of the PDMS-based
molded microchannels. Therefore, to ensure an accurate IFT
value, it is essential to evaluate the hydraulic pressure differ-
ence across microchannels using integrated pressure sensors.
In the experiments, we varied the flow rate (and thus
DPab) and measured the curvatures accordingly. The results
FIG. 1. (a) Schematic illustration of the microfluidic device for IFT mea-
surement. (b) Detailed illustration of the water/oil interface in the tapered
microchannel. (c) Cross sectional views of the oil/water interface in the hori-
zontal and vertical directions.
234102-2 Zhou et al. Appl. Phys. Lett. 103, 234102 (2013)
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4. of DPab versus 1/Rhb-1/Rha were plotted in Fig. 2(c). In the
figure, the solid lines were the fitted lines and their slopes
represent the values of IFT (48.3 mN/m and 25.2 mN/m for
mineral oil/water and silicone/water interface, respectively).
The two-step measuring procedure was also preformed for
other oil/water system, and the results were summarized and
listed in Table I. Our measured values agree well with the
results obtained from the commercial tensiometry.
Compared with the precedent IFT measurement techni-
ques using a tapered micropipette9
or a microchannel,10
our
method based on a pair of Laplace pressure sensors16,17
formed by two tapered channels and water columns has in-
herent advantages. First, in our method, instead of using a
single hydrostatic head to measure pressure difference across
oil/water interface, the pressure difference across two points
in a microchannel is measured by a pair of integrated
Laplace pressure sensors, which eliminate the use of a highly
precise pressure source or a transducer. Second, with the
help of a pair of Laplace pressure sensors, the interface cur-
vature in the vertical direction (Rva and Rvb) is eliminated;
the uncertainty in measuring the interface curvature in this
direction (as the actual contact angle is hard to be deter-
mined) can be avoided. Third, as the principle is independent
of the channel dimension (as shown in Eq. (7)), our method
eliminates any potential influence due to the flow and/or ge-
ometry change in the microchannel, which makes the
method more robust and easy to be implemented.
We conducted the error analysis for our method. From
Eq. (7), the relative error can be expressed as18
dðcÞ
c
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
dðDH00
Þ
DH00
2
þ
R0
haR0
hb
ðR0
hb þ R0
haÞ
!2
dðR0
hbÞ
ðR0
hbÞ2
!2
þ
dðR0
haÞ
ðR0
haÞ2
!2
2
4
3
5
v
u
u
u
t : (8)
According to this equation, the relative errors in measuring
the height and curvatures are the two major error sources of
our method. In the experiments, the resolutions of the meas-
ured height and the curvatures are 0.5 mm and 0.2 lm,
respectively. For a situation of DH ¼ 50 mm, Rha ¼ 80 lm,
and Rhb ¼ 40 lm, the total relative error can be estimated as
much as 1.1%. Another error source might be associated
with the contact angle hysteresis of the triple line on the
microchannel surface. One way has been adopted to alleviate
this error: the heights of the two water columns are changed
in the same direction (up or down) to keep the contact angles
in the two channels in the same status (advancing or receding
contact angle).25
As the working principle does not depend on the proper-
ties of the test reagents, this method can be used to other
immiscible liquid/liquid, liquid/gas systems, or more complex
mixtures including surfactants. In microfluidics, surfactants
are usually used to adjust IFT of the oil/water system.20
Surfactants decrease the liquid surface tension. Above a cer-
tain point where the surface concentration is saturated, surfac-
tants begin forming self-assembled aggregates as micelles, and
the surface tension remains unchanged. The corresponding
concentration is surfactant critical micelle concentration
(CMC), a key parameter of surfactants. IFT measurement pro-
vides an effective way for CMC determination.21
To demon-
strate the performance of our method, we used our
microfluidic device to examine surfactant effect on IFT and
determine the CMC of surfactant (Span 80). We varied the
concentration of Span 80 in mineral oil/water system, and
the two-step measuring procedure was preformed to acquire
TABLE I. Comparison of IFT results between the microfluidic device and
tensiometry.
Interface
c (mN/m)
using microfluidics
c (mN/m) using
tensiometry
Mineral/water 48.3 6 1.1 51.0
Silicone oil/water 25.2 6 0.8 26.2
Hexadecane/water 43.5 6 1.0 44.8
Soybean oil/water 24.8 6 0.7 26.5
FIG. 2. On-chip IFT measurement results. The two measuring steps: (a) the
levels of the two water columns are kept the same height, DH0
¼ 0; (b) the
levels of the water columns are changed till the interfaces are the at same
location of the tapered channels so that R00
ha ¼ R00
hb. Inset shows the fitted cur-
vature R. The scale bar is 350 lm. (c) DPab versus (1/Rhb-1/Rha) for mineral
oil and silicone oil. Each data point was obtained from ten independent
measurements. All the measurements were performed at 22
C.
234102-3 Zhou et al. Appl. Phys. Lett. 103, 234102 (2013)
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5. the corresponding IFT value. As shown in Fig. 3, for a mixture
of Span 80 in mineral oil (concentration less than 0.1 mM), the
IFT value depends strongly on the concentration of the surfac-
tant. While the concentration is higher than 1 mM, the IFT
value remains relatively constant (3.1 mN/m). Two fitted lines
indicate these two trends, and the intersection point indicates
CMC (0.23 mM) for Span 80 in mineral oil/water system.
When adopting the same environment temperature, this value
agrees well with the reported data.22–24
Moreover, by combin-
ing the well-developed microfluidic techniques, we can extend
the method to studying dynamic IFT.9,19,25
To summarize, we demonstrate a facile approach in
which in situ IFT measurement is performed in a microflui-
dic device coupled with a syringe pump and a microscope
(the necessary instruments in any microfluidic laboratories).
We described the working principle, design, and operation of
the microfluidic device and discussed the error sources of the
measurement. We measured the IFT of different oil/water
systems and complex mixtures with surfactant. The results
are in good agreement with those from the commercial
tensiometry. Compared with other IFT methods, our micro-
fluidic strategy is low-cost, accurate, and easy in operation.
This work was supported by the Direct Allocation Grant
(No. DAG12EG07-13) from HKUST and the National
Science Foundation of China (No. 61006086).
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See supplementary material at http://dx.doi.org/10.1063/1.4838616 for
the effect of the proposed approach on the potential hysteresis of the
meniscuses, and a possible way for monitoring dynamic IFT.
FIG. 3. On-chip measured IFT of Span 80 in mineral oil/water vs. Span 80
concentration. The data are fitted by two dashed lines. All the measurements
were performed at 22
C.
234102-4 Zhou et al. Appl. Phys. Lett. 103, 234102 (2013)
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