MEASUREMENT OF INTERFACIAL TENSIONIN FLUID-FLUID SYSTEMS
J. DrelichCh. FangC.L. WhiteMichigan Technological University, Houghton, Michigan
INTRODUCTION
For more than a century, a variety of techniques have been
used to measure interfacial tensions between immisci-
ble fluid phases. A recent monograph by Rusanov and
Prokhorov (1) provides a broad review of the technical
literature on the interfacial tension techniques with de-
tailed discussion of the theoretical bases and instrumenta-
tion. Additional valuable sources of information on the in-
terfacial tension measurement methods include selected
chapters in Refs. 2–5. In this article, we present a very
brief overview of the most common techniques used in
interfacial tension measurements. The reader is encou-
raged to explore Refs. 1–5 and references therein for fur-
ther details.
This article is organized as follows. ‘‘Classical Inter-
facial Tension Measurement Methods’’ reviews the me-
thods that are used in surface chemistry laboratories. A
short comparison of these techniques is presented at the
end of the section. This comparison has been prepared to
guide a selection of the experimental method for mea-
surements of interfacial tension in liquid-fluid systems,
including systems with surfactants, viscous liquids, or mol-
ten metals. Many of the industrial operations involve the
liquid-fluid interfaces, for which the composition is cons-
tantly refreshed and does not reach equilibrium. The im-
portance of such dynamic interfacial tensions is increa-
singly recognized to be essential to the understanding and
control of interfacial processes in multiphase, multicom-
ponent systems. ‘‘Dynamic Interfacial Tension Measure-
ments’’ discusses a freshly created interface. In ‘‘Measure-
ment of Ultralow Interfacial Tension’’ an example of:
when the value of interfacial tension is significantly less
than 1 mN/m is discussed. Ultralow interfacial tensions
are common in the fluid systems of advanced tech-
nologies of liquid-liquid emulsification processes when
effective surfactant solutions are used. Finally, in ‘‘Mic-
rotensiomery,’’ we discuss the methods of interfacial
tension measurements that have been applied (or have
potential to be applied) to microinterfaces of microdrop-
lets. Fundamental research on the interfacial properties of
nanomaterials (materials and particles with microstructur-
al features on the micrometer or nanometer scale) and
droplets of micrometer-sized or nanometer-sized dimen-
sion will be an important challenge in the rapidly deve-
loping field of nanotechnology.
CLASSICAL INTERFACIAL TENSIONMEASUREMENT METHODS
Fig. 1 shows a classification of common interfacial ten-
sion measurement methods, both classical and modern.
Group I represents examples of techniques commonly
used for direct measure of the interfacial tension with a
microbalance. The techniques in group II are those in
which interfacial tension can be determined from direct
measurement of capillary pressure. Analysis of equilib-
rium between capillary and gravity forces is employed in
the techniques of groups III and IV. Group III techniques
rely on the balance between surface tension forces and a
variable volume of liquid, whereas Group IV techniques
fix the volume of a liquid drop and measure the distortion
of that drop under the influence of gravity. Group V in-
cludes techniques where the shapes of fluid drops are dis-
torted by centrifugal forces and are used to measure ultra-
low interfacial tensions.
Group I: Direct MeasurementUsing a Microbalance
Interfacial tension at fluid-fluid interfaces is a reflection
of the excess energy associated with unsaturated inter-
molecular interactions at the interface. This excess energy
tends to drive interfaces to adopt geometries that mini-
mize the interfacial area, and this tendency can be inter-
preted as a physical force per unit length (i.e., a tension)
3152 Encyclopedia of Surface and Colloid Science
Copyright D 2002 by Marcel Dekker, Inc. All rights reserved.
applied in the plane of the interface. The excess energy
per unit area (E/A) is numerically equal to this force per
unit length (F/L), which is numerically equal to the in-
terfacial tension (g).
To directly measure interfacial tensions using a mic-
robalance, a plate, ring, rod, or other probe of simple shape
is brought into contact with the interface. If the probe is
completely wetted by one of the liquids, this liquid will
adhere to the probe and climb as the result of capillary
force, increasing the interfacial area and leading to a force
tending to pull the probe toward the plane of the interface
(Figs. 2 and 3). This restoring force is directly related to
the interfacial tension and can be measured by a micro-
balance. The force (F) acting along the three-phase contact
Fig. 1 Classification of techniques for interfacial tension measurements that are discussed in this article.
Fig. 2 A schematic of the Wilhelmy plate method. Fig. 3 Illustration of the ring method.
M
Measurement of Interfacial Tension in Fluid-Fluid System 3153
line is exactly equal to the weight of the liquid meniscus
standing above the plane of the fluid-fluid interface. This
force, measured by the microbalance, is used to calculate
the interfacial tension:
g ¼ F
p cos yð1Þ
where p is the perimeter of the three-phase contact line and
y is the contact angle measured for the liquid meniscus in
contact with the object surface.
The two principal techniques used for direct measure-
ment of interfacial tension using the microbalance are
Wilhelmy plate and du Nouy ring methods. The Wilhelmy
plate technique is used in both static and detachment
modes, whereas du Nouy ring technique is strictly a de-
tachment technique. In the static measurement, the plate
remains in contact with liquid during the entire cycle of
interfacial tension measurement. If the instrument ope-
rates in the detachment mode, the interfacial tension is
measured by measuring the force required to separate the
ring or plate from contact with the interface.
Wilhelmy plate technique
A vertical thin plate is used in this technique (Fig. 2) (6).
The commercial plates are made of roughened platinum-
iridium alloy or platinum. The metal plate must be cleaned
from organic contaminants by an organic solvent and then
flamed before the experiment. Both roughening and clean-
ing of the plate surface are used to maintain good wetting
of the plate by the test liquid. It should be noted that
materials other than platinum or platinum-iridium alloy,
such as glass, mica, and steel (1, 5) have also been used.
Nevertheless, good wetting of the test liquid to the plate is
always necessary. The use of plates made of material other
than metal is a ‘‘must’’ requirement in the case of certain
liquids such as during the measurements of the interfacial
tension between a heavy nonpolar liquid (i.e., carbon tet-
rachloride) and immisible, but lighter, polar liquid (i.e.,
water). For such systems, the plate should be hydrophobic.
Several polymers, especially fluorinated polymers, can be
used for this purpose. Adsorption and self-assembling of
organic amines on the surface of the platinum plate could
also be a solution to this problem.
In the Wilhelmy plate method, the plate is put in a fixed
position relative to the horizontal surface of the liquid
(Fig. 2). Then, the force (F) vertically acting on the plate
by the liquid meniscus is measured by using a microba-
lance. The force applied to the plate is equal to the weight
of the liquid meniscus uplifted over the horizontal surface.
By measuring this force, the interfacial tension can be
calculated by using Eq. 1 where p = 2(L + t). Modern
instruments use plates of standard dimensions so that
measurements of the plate size and its weight are not re-
quired. Adsorption of organic compounds from the labo-
ratory environment or test solutions can be a major source
of experimental error when measuring surface tensions
using the Wilhelmy plate method.
Du Nouy ring method
In this method, the interfacial tension relates to the force
required to pull a wire ring off the interface (Fig. 3) (7, 8).
As in the case of Wilhelmy plate, the ring is usually made
up of platinum or platinum-iridium alloy of a radius (R)
of 2–3 cm. The radius (r) of the wire ranges from 1/30 to
1/60 of that of the ring (9).
Again, Eq. 1 describes in general the calculation pro-
cedure of the technique. Here, the perimeter ( p) of the
three-phase contact line is equal to twice the circumfe-
rence of the ring: p = 4pR. Because additional volume of
liquid is lifted during the detachment of the ring from the
interface, a correction factor ( f ) is required in Eq. 1 (8):
g ¼ F
p cos yf ð2Þ
The correction factor varies from about 0.75 to 1.05 and
depends on the dimensions of the ring (R, r), its surface
wettability (y), and difference in fluid density (Dr). The
tabulated f values in relation to R/r (for y = 0) can be
found in Ref. 8, and also calculated from the following
approximate equation (10):
f ¼ 0:725þ 9:075 � 10�4F
p3DrgR3� 1:679r
Rþ 0:04534
� �1=2
ð3Þ
The application range of Eq. 3 is: 0.045 � DrgR3/F �7.5. The maximum force is measured by the microbalance
(F ) and corresponds to detachment of the ring from the
interface. The F value is measured experimentally and
then Eq. 3 is used to calculate the correction factor f. The
interfacial tension is then calculated from Eq. 2. The in-
terfacial tension reading made by modern computerized
instrumentation does not require separate calculation of f,
since its calculation is incorporated in the software.
The high-accuracy measurements with the ring method
require that the plane of the ring remain parallel to the
interface. The major error in this technique is caused by
deformation of the ring, which is a very delicate probe and
subject to inadvertent deformation during handling and
cleaning. It is also important that perfect wettability of the
ring surface by the denser fluid be maintained (y = 0). If
perfect wetting is not achieved, additional correction of the
instrument reading is needed. Poor wetting of ring by the
3154 Measurement of Interfacial Tension in Fluid-Fluid System
denser fluid makes the measurement of interfacial tension
impossible to carry out. In the case of special measure-
ments requiring homemade rings, very large rings should
be avoided to avoid the small value of the correction factor
(see Eq. 3). If all of the necessary experimental precau-
tions are observed, this method can guarantee higher ac-
curacy than any other detachment method.
Group II: Measurement of Capillary Pressure
Interfacial tension is defined as the work required to create
a unit area of interface at a constant temperature, pressure,
and chemical potential. Because it is always positive for
interfaces between immiscible phases, interfacial tension
always tends to decrease the area of interface. This ten-
dency gives rise to a pressure difference between fluids on
either side of a curved interface, with the higher pressure
on the concave side of the interface. This pressure dif-
ference results in phenomena such as a capillary rise,
bubble and drop formation, etc. A formula describing the
pressure difference (DP) across the curved interface is
known as the Young-Laplace equation (11, 12):
DP ¼ g1
R1
þ 1
R2
� �ð4Þ
where R1 and R2 are the radii of curvature.
The pressure difference across a curved interface (DP)
can be measured in a number of ways (e.g., using a pres-
sure sensor or observing a capillary rise) and then be used
to calculate g if the radii of curvature are known. The most
common and probably one of the oldest methods in this
group of interfacial tension measurement techniques is a
maximum bubble pressure method that is briefly described
in the next paragraph. Modification of the maximum bub-
ble pressure method based on a continuous measurement
of varying pressure during growing bubble or drop is now
a basic technique in examination of dynamic (not equi-
librated) interfacial tension and is further discussed in
‘‘Dynamic Interfacial Tension Measurements.’’
Maximum bubble pressure
This method is based on measuring the maximum pressure
( p� ) to force a gas bubble out of a capillary into a liquid
(Fig. 4) (13, 14). The measured pressure is the sum of
capillary pressure (DP) caused by the interfacial tension
and the hydrostatic pressure (rAghA) caused by the liquid
column above the orifice of the capillary:
DP ¼ p� � rAghA ð5Þ
This pressure can be expressed as the height (h) of the
column of an imaginary liquid of density (Dr = rA�rB):
h ¼ DP
Drgð6Þ
Sugden (13) derived an expression to relate h with the
Laplace capillary constant a = 2g/(Drg) and the bubble
meniscus:
r
X¼ r
bþ r
a
� � zc
b
� � b2
� �1=2
ð7Þ
where X = a2/h, b = 2b2/a2, zc is the height of the bub-
ble, and b is the curvature radius at the apex (lowest point
of the bubble). Then he tabulated the minimum values of
Fig. 4 Maximum bubble pressure method. (A) A sequence illustrating the shape of bubble at three different stages of bubble growth.
(B) Relationship between pressure inside the bubble and radius of the bubble.
M
Measurement of Interfacial Tension in Fluid-Fluid System 3155
X/r as dependent of a given value of r/a within the range
0 < r/a � 1.5. Using this table, the surface tension can be
calculated by following an iteration procedure.
Direct and easier, but a little less accurate, calculation
of the interfacial tension can be done by using the fol-
lowing equation (5):
g ¼ DPr
21 � 2rDrg
3DP� ðrDrgÞ2
6DP2
!ð8Þ
As further discussed in the next section; the maximum
bubble and drop pressure technique or its modifications
have been very useful in studying the dynamic interfacial
tensions. This technique has also been attractive to exa-
mination of surface tension for molten metals (2).
Group III: Analysis of the Balance BetweenCapillary and Gravity Forces
Methods based on analysis of capillary effects, other than
the shape of a drop or meniscus, such as capillary rise and
drop volume or weight, are among the oldest surface ten-
sion measurement methods in use. A variety of modern
instruments, usually fully automated and computerized
(groups I, II, and IV), have replaced these methods in most
laboratories. We provide a short review of two techniques
that still might be attractive to researchers who have limi-
ted access to modern instrumentation.
Capillary rise method
The basis for the capillary rise method is to measure the
height h of the meniscus in a round glass tube having the
known inner radius r, as shown in Fig. 5 (2, 15). For
small-diameter tubes (i.e., r < < h) the shape of the me-
niscus is spherical, and the surface tension can be calcu-
lated by using the following equation:
g ¼ Drghr
2 cos yð9Þ
Since the glass tubes are easy to clean with acids, bases,
and organic solvents, and because many of the liquids
perfectly wet the glass surface, the cosy term in the above
equation will often equal unity.
If the shape of the meniscus is not spherical, Eq. 9
should be replaced with (15):
g ¼ 1
2Drgrh 1 þ r
3h� 0:1288
r2
h2þ 0:1312
r3
h3
� �ð10Þ
The capillary rise method can be one of the most ac-
curate techniques used to make surface tension measure-
ments. Technical problems with the technique are related
to fabrication of a uniform bare capillary tube and precise
determination of its inside diameter. In addition, the ca-
pillary rise method is not very convenient for measuring
the interfacial tension between two liquids.
Drop volume or weight
In this method, the weight or volume of a drop falling from
a capillary with a radius r is measured (Fig. 6) (16, 17).
The weight (W) of the drop falling off the capillary cor-
relates with the interfacial tension through the following
equation (5):
W ¼ VDrg ¼ 2prgfrffiffiffiffiV3
p� �
ð11ÞFig. 5 Illustration of the capillary rise method.
Fig. 6 Schematic illustration of drop volume or weight method.
3156 Measurement of Interfacial Tension in Fluid-Fluid System
where V is the drop volume, r is the radius of the capillary,
and f is the correction factor required because only a
portion of the drop volume is released from the capillary
during detachment (2). The correction factor is a function
of r/V1/3, and this correlation was empirically determined
and tabulated by Harkins and Brown (17). It can also be
calculated from the empirical function (5):
frffiffiffiffiV3
p� �
¼ 0:167 þ 0:193rffiffiffiffiV3
p� �
� :0489rffiffiffiffiV3
p� �2
� 0:0496rffiffiffiffiV3
p� �3
ð12Þ
Because of small volume of each drop, many drops need
to be collected for the accurate measurement of drop
weight or volume. In modern instrumentation, the volume
of liquid and the number of droplets released from the
capillary can be determined very precisely and thus the
weight or volume of the individual drop is not difficult to
calculate (18).
Capillaries used in the drop weight or volume tech-
niques are usually made of glass; however, metal capil-
laries are also used on occasion (1). Glass is wetted by
many liquids, is transparent, and is relatively easy to clean.
Capillary tubes specifically fabricated for routine inter-
facial tension measurements are now difficult to purchase
in the U.S. market; however, glass capillaries can be pro-
duced relatively easily in glass workshops.
The measurements of interfacial tension with the drop
weight or volume technique are very simple but, unfortu-
nately, sensitive to vibrations on the other side. Vibrations
of the apparatus can cause premature separation of the drop
from the end of the capillary before the drop reaches the
critical size. In addition, the measurements in multicom-
ponent solutions when adsorption occurs might not reflect
equilibrium saturation of the solutes at the interface.
Group IV: Analysis ofGravity-Distorted Drops
Interfacial tension causes interfaces to behave as elastic
membranes that always tend to compress the liquid. In the
absence of other forces (e.g., in zero gravity), the liquid
surface has a natural tendency to form spherical shapes to
minimize the interfacial area per unit volume of liquid and
thus, to minimize the excess energy of the interface. The
shape of an interface in a gravitational field (Fig. 7) de-
pends on the competition between the capillary and gra-
vitational forces and can be described by the Bashforth-
Adams equation (19):
gsinf
xþ 1
R1
� �¼ 2g
bþ Drgz ð13Þ
Eq. 13 is often expressed in a dimensionless form as:
sinfx=b
þ 1
R1=b¼ 2 þ Drgb2
gz
bð14Þ
where g is the interfacial tension; Dr = �A��B equals
the difference in density of fluids; R1 is the radius of cur-
vature; x is the radius of rotation of point S around the z
axis; f is the angle of R2 vector with the axis of symmetry;
b is the radius of curvature at the apex of the curvature; and
g is the acceleration due to gravity. Fig. 7 shows the de-
tails of drop geometry.
The techniques of curved interface shape analysis are
particularly attractive to researchers because they do not
require advanced instrumentation. The experimental setup
requires a camera with a low-magnification lens to record
the shape of the drop. The interfacial tension can be easily
calculated from the dimensions of the pendant drop, ses-
sile drop, or liquid meniscus taken from the photographic
picture and by using numerical solutions to the above
equations. Modern instruments, however, use image anal-
ysis software whose role is to match the entire drop profile
to the best fit of the theoretical curve (e.g., the Bashforth-
Adams equation) describing the shape of the drop (14).
These advances significantly improved the precision of
the techniques and reduced the time of the measurement,
providing an opportunity for examination of the interface
aging process. Probably the most advanced software, axi-
symmetric drop shape analysis, was introduced by Neu-
mann and co-workers (20). Since advanced instrumen-
tation is not always available to researcher, a brief reviewFig. 7 Definition of dimensions and coordinates describing the
sessile drop.
M
Measurement of Interfacial Tension in Fluid-Fluid System 3157
of classical approaches of interfacial tension determination
from the shape of the interface seems to be appropriate.
Pendant drop method
In a simple method, two parameters of the pendant drop
that should be experimentally determined are the equa-
torial diameter D and the diameter d at the distance D
from the top of the drop (Fig. 8) (21, 22). The interfacial
tension is then calculated from the following equation (2,
21, 22):
g ¼ DrgD2
Hð15Þ
The shape dependent parameter (H ) depends on a value of
the ‘‘shape factor’’ S = d/D. Tables including the set of
1/H vs. S values are available in several references (1, 22).
The values of 1/H can also be calculated from the fol-
lowing empirical formula (23):
1
H¼ B4
Saþ B3S3 � B2S2 þ B1S � B0 ð16Þ
where Bi (i = 0, 1, 2, 3, 4) and a are empirical constants
for a certain range of S, which are shown in Table 1.
The pendant drop technique, as other interfacial tension
measurement techniques, requires extreme cleanliness to
obtain good quality and reproducible results. Here, the
needle used for hanging the drop should be well cleaned
and the climbing of the interface over the outer surface of
the needle should be avoided. Needles made of stainless
steel or glass that are relatively easy to clean with acids,
bases, and organic solvents are most often used in surface
chemistry laboratories. It is recommended that needles
with a diameter that is less than 0.5 D be used (21). The
diameter of the needle should not be too small, however,
because this reduces the value of d and, consequently, the
precision of interfacial tension determination.
Sessile drop method
This method is based on the analysis of the profile of the
drop sitting on a solid substrate, as shown in Fig. 7 (24,
25). It is recommended that substrates used in sessile drop
measurements be poorly wetted by the drop, i.e., they
should have a contact angle larger than 90 degrees. In a
simple experimental approach, one first needs to locate
the equator of the drop, and then measure the height from
the top of the drop to its equator (ze). For a very large
sessile drop, an analytical expression for the interfacial
tension is as follows (5):
g ¼ Drgz 2e
2ð17Þ
From a practical point of view, it is often difficult to pre-
cisely locate the equator of the drop and measure ze for
many drops. Although the large drop is almost flat, loc-
ating the top of the drop is sometimes experimentally
difficult. It should be recognized, however, that large
drops are not required if tabulated dependencies of drop
shape parameters, based on the Bashford-Adams analysis
(Eq. 14) are used (19, 25).
Practical Comments
Most of the techniques reviewed in this section have been
commercialized. Table 2 summarizes the accuracy, com-
Fig. 8 Pendant drop.
Table 1 Empirical constants for Eq. 16
Range of S A B4 B3 B2 B1 B0
0.401–0.46 2.56651 0.32720 0 0.97553 0.84059 0.18069
0.46–0.59 2.59725 0.31968 0 0.46898 0.50059 0.13261
0.59–0.68 2.62435 0.31522 0 0.11714 0.15756 0.05285
0.68–0.90 2.64267 0.31345 0 0.09155 0.14701 0.05877
0.90–1.00 2.84636 0.30715 � 0.69116 � 1.08315 � 0.18341 0.20970
3158 Measurement of Interfacial Tension in Fluid-Fluid System
mercial availability, and suitability of these techniques for
various types of fluid-fluid systems. The accuracy of most
of these techniques for pure liquid-gas systems is about
0.1 mN/m. The capillary rise technique is capable of
significantly better accuracy than the others in Table 2.
Most of the interfacial tension measurement techniques
listed in Table 2, including the capillary rise method, have
been successfully applied to liquid-liquid systems. Re-
duced accuracy of the detachment du Nouy ring method
is associated with difficulties in calibrating the weight of
the ring immersed in the less dense liquid. The same
problem can be expected in the interfacial tension mea-
surements using the Wilhelmy plate instrument. All tech-
niques in Table 2 yield reduced accuracy when applied to
liquid-liquid interfaces or when one or both of the liquids
is viscous.
The measurements with viscous liquids are always dif-
ficult to carry out due to problems with handling the
liquid, injection of a liquid sample of the required volume
into the instrument, low–velocity liquid flow, and long–
time viscous effects during deformation of the interface.
Two techniques are particularly recommended to examine
the surface tension of viscous liquids: the Wilhelmy plate
(not a detachment option!) and the sessile drop methods.
In both techniques, samples can be equilibrated for se-
veral hours before the measurements are taken.
It is important to recognize that any interfacial ten-
sion measurement can be strongly influenced by inter-
facially active solutes or impurities that are accidentally
introduced into the fluid-fluid system or present on solid
surfaces that act as part of the measurement system (1,
2). Any solid surfaces that make contact with liquids
(e.g., plates, rings, and capillary tubes) must be careful-
ly cleaned prior to making measurements. Furthermore,
some interfacially active contaminants can be introduced
from the skin or breath of laboratory workers. Finally, it is
important to note that interfacial tensions are influenced
by temperature, which should be controlled and reported
for all measurements.
When using techniques that depend on a known wet-
tability of a solid probe by one of the liquids, surface active
solutes (whether present intentionally or as impurities) can
seriously influence the interfacial tension measurements.
Interfacially active solutes in a liquid phase can adsorb not
only on the fluid-fluid interfaces but on the liquid-solid
interfaces as well. This adsorption will affect wettability
of the solid surface (the cosy term in Eqs. 1 and 2) and,
therefore, influence the measured result. In principle, such
effects can be eliminated by employing solid probes of
alternate materials to which the solute does not adsorb, but
plates and rings are not usually available in a wide range
of alternative materials.
Even when adsorption to solid-liquid interfaces is not a
problem, it is important to allow fluid-fluid interfaces to
achieve equilibrium before making a measurement. When
equilibrium is achieved rapidly (within a few seconds),
the drop volume technique may be suitable. If equilibra-
tion requires longer times, sessile drop, Wilhelmy plate,
or other quasi-static techniques may be more appropriate.
This consideration applies to any fluid-fluid system in
which kinetically limited processes (adsorption, viscous
flow, etc.) take place.
Because of the relatively high temperatures involved
and their reactivity with many gases and solids, surface
tension measurements on liquid metals pose special chal-
lenges. The four principal techniques that have been em-
ployed are the maximum bubble pressure method, the
sessile drop method, the drop volume or weight method,
and the pendant drop method (26, 27). It is important that
measurements on liquid metals be carried out in inert
Table 2 Accuracy and suitability of classic techniques used in interfacial tension measurements
Method
Accuracy
½mN=m�
Suitability
for surfactant
solutions
Suitability
for two-liquid
systems
Suitability for
viscous liquids
Suitability for
melted metals
Commercial
availability
Wilhelmy plate �0.1 Limited Good Very good Not recommended Yes
Du Nouy ring �0.1 Limited Reduced accuracy Not recommended Not recommended Yes
Maximum bubble 0.1–0.3 Very good Very good Not recommended Yes Yes
pressure
Capillary rise <<0.1 Very good Very good, Not recommended Not recommended Not
experimentally
difficult
Drop volume 0.1–0.2 Limited Good Not recommended Yes Yes
Pendant drop �0.1 Very good Very good Not recommended Yes Yes
Sessile drop �0.1 Good Very good Very good Yes Not
M
Measurement of Interfacial Tension in Fluid-Fluid System 3159
gas environment to avoid reactions with gases and other
phases. Oxygen and other reactive gases are known to exert
strong effects on the surface tension of selected metals,
even when present in parts per million concentration (27).
DYNAMIC INTERFACIALTENSION MEASUREMENTS
In fluid-fluid systems containing interfacially active so-
lutes, a freshly created interface will not generally be in
compositional equilibrium with the two immiscible fluids
it separates. It is only after solute redistribution from one
or both phases (i.e., adsorption) has occurred that this
interface will achieve its equilibrium state. It is sometimes
important to measure the interfacial tension of freshly
created interfaces, and such measurements yield what is
known as ‘‘dynamic surface tension.’’ A detailed review
of experimental techniques, theoretical background, and
literature on the measurements of dynamic interfacial ten-
sions was recently published by Dukhin et al. (3). Another
valuable source of analysis of adsorption at the interface
and dynamic interfacial tension is the book published by
Joos (28).
Table 3 provides a characteristic time range for the
selected interfacial tension measurement techniques. Of
different techniques already discussed in this article, the
capillary rise method is not recommended for dynamic
interfacial tension measurements. The techniques dis-
cussed in the next sections are not very suitable for exa-
mination of dynamic effects at interfaces either.
Interfacial tension changes that occur over time in-
tervals of at least several seconds (and continue over se-
veral minutes, hours, or days) can be studied by using
most of the classical techniques discussed in the previous
section. For example, Fig. 9 shows the results of inter-
facial tension relaxation between bitumen and water of
varying pH value recorded with the Wilhelmy plate ins-
trument (30). In this bitumen-water system, the dynamic
character of the interfacial tension is caused by diffusion
of natural surfactants from the bitumen to interface and
aqueous phase, and surfactant reaction with ions dissolved
in water (31).
As emphasized in the previous section, examination of
the interfacial tension for surfactant solutions using clas-
sical techniques should be carried out with caution. Sur-
factants often adsorb on the solid surfaces of equipment
used in measurements and change the wetting character-
Table 3 Characteristic time range for common interfacial tension measurement techniques
Method Time rangea Comments
Wilhelmy plate >10 s Some of the surfactants might alter the wetting properties
of the plate, causing the change of measurement
conditions (possible source of error)
Du Nouy ring >30 s Same as above
Pendant drop >10 s Strongly surface active chemicals might cause the release
of pending drop before completion of the measurement
Sessile drop >10 s Some of the surfactants might alter the wetting properties
of a solid support substantially changing the shape of
the sessile drop
Drop volume/weight 1 s–20 min Hydrodynamic effects associated with releasing liquid
volume and circulation of liquid inside the drop
sometimes significantly reduce the accuracy of the
interfacial tension measurements
Maximum bubble pressure 1 ms–100 s Difficulties with determination of the real surface age and
problems with hydrodynamic effects in the vicinity
of interface
Growing drop/bubble >10 msb Not available commercially
Oscillating jetc 1–10 ms Not available commercially
Pulsating bubblec 5 ms–0.2 s Not available commercially
aBased on Dukhin et al. (3).bIt is claimed by MacLeod and Radke (29) that the dynamics interfacial tension can be measured for several hours, although Ref. 3 specifies the upper
limit as 600 s.cMethods not discussed in this article.
3160 Measurement of Interfacial Tension in Fluid-Fluid System
istics of a solid surface. This effect usually causes expe-
rimental problems in the Wilhelmy plate, du Nouy ring,
and sessile drop techniques (see comments in Table 3).
Short-time interfacial tension and wetting effects play
important roles in high–volume industrial processes such
as froth flotation of particles and droplets, detergency,
foam or froth generation, and stability (3). In these pro-
cesses, dynamic interfacial tensions become more crucial
to the success of the technology than the equilibrium (or
near-equilibrium) interfacial tension. This issue has been
emphasized in the literature (3, 32, 33), but straightforward
links between dynamic interfacial tensions and (e.g., pro-
cess efficiencies) have not yet been well established. This
research area is just evolving, and the continued funda-
mental research will probably establish a better connection
of dynamic interfacial phenomena with practical needs.
Four basic techniques for measurements of the dynamic
interfacial tension at short intervals include the maximum
bubble pressure, growing drop (bubble), oscillating jet,
and pulsating bubble methods (Table 3). Neither the os-
cillating jet technique nor the pulsating bubble technique
is discussed in this article. Bases of these techniques are
provided in Refs. 1–3 and references therein.
The maximum bubble (drop) pressure method and its
modifications have been the most popular techniques used
in research conducted in recent years. Apparatus for ma-
king these measurements are also available commercially.
The maximum bubble pressure technique was briefly des-
cribed in ‘‘Classical Interfacial Tension Measurement Me-
thods.’’ Following is a short description of a modification
of the maximum bubble pressure technique that is suitable
for dynamic surface tension measurements.
Growing Drop (Bubble) Method
Modern instrumentation permits the pressure inside a bub-
ble or drop to be precisely and continuously measured as it
forms and detaches from the end of a capillary (3, 29, 34,
35). The geometry of a drop or bubble can also be mo-
nitored during growth and detachment by using advanced
videographic equipment. This ability to simultaneously
monitor both pressure and geometry (size and shape) of
bubbles or drops as they form allows dynamic interfacial
tensions to be evaluated over a range of growth rates.
Furthermore, the same experimental approach allows mea-
surement of surface tensions using approaches normally
applied to systems in (or near) equilibrium, such as the
drop volume and maximum pressure drop techniques.
Fig. 10 describes an experimental approach used by
MacLeod and Radke (29) for measurement of dynamic
interfacial tension using the growing drop technique. In
Fig. 9 Dynamic interfacial tension measured between bitumen
and water at 60�C using the Wilhelmy plate technique. The pH
values for water at the beginning (t = 0) and at the end of the
measurements (t = 90 min) are listed in the figure legend. (The
results are from Ref. 30.)
Fig. 10 Schematic of the growing drop apparatus used by MacLeod and Radke. (From Ref. 29.)
M
Measurement of Interfacial Tension in Fluid-Fluid System 3161
this apparatus, a liquid drop or gas bubble is formed and
released from a capillary by using a precise micropump to
carefully control the growth rate of the drop or bubble. A
pressure transducer is used to simultaneously monitor and
record the internal pressure in the drop or bubble, while
its size and shape are recorded by using a video camera.
These experiments can be carried out for a range of flow
rates ranging from near equilibrium growth (very low
flow rates) to highly nonequilibrium growth conditions
(very rapid bubble or drop growth).
Fig. 11 shows selected results of MacLeod and Radke
(29) for growth of 0.25 mM aqueous decanol droplets for
a range of droplet growth rates between 5 and 100 mm3/
min. The plots of interfacial tension vs. time show ini-
tially increasing, reaching a maximum, and then decrea-
sing as a function of time. The positive slope of the g vs. t
curves for t < 1 results from the depletion of decanol
adsorption due to rapid expansion (stretching) of the
interface when the bubble is small (see Fig. 4A). As the
drop geometry proceeds beyond hemispherical shape
(Fig. 4C), the relative rate of surface area growth decrea-
ses, allowing decanol from the bulk liquid to replenish the
surface adsorption. The decrease in interfacial tension as-
sociated with this increase in adsorption yields the negative
slope observed in the g vs. t curves for t > 1. As expected,
the largest dynamic interfacial tensions, approaching those
for pure water, are observed for droplets formed at the
highest capillary flow rates. Conversely, the lowest values
(approaching the equilibrium interfacial tension for this
solution) were observed for droplets growing at very slow
rates. At drop formation times approaching 100 s, inter-
facial tensions for drops formed at all flow rates approach
the equilibrium value for the 0.25 mM aqueous 1-decanol
solution.
The zero time for each measurement in Fig. 11 cor-
responds to the moment of detachment for the previous
drop. Data points for a given capillary flow rate in Fig. 11
start at the time where the drop reaches a hemispherical
shape (Fig. 4B), which also corresponds to the point at
which the interfacial tension can be evaluated by using the
maximum pressure method. Interfacial tension measure-
ments using the drop-volume method are, of course, de-
termined at the point where the drop detaches from the
capillary and correspond to the last data point in the
corresponding curve for the growing drop method. These
two techniques, therefore, provide ‘‘snapshots’’ of the in-
terfacial tension values in dynamic systems, and they
bracket the family of curves determined by the growing
drop method. The growing drop method provides the very
important advantage of continuously recording the inter-
facial tension throughout the drop formation and allows
the competing kinetic effects of interfacial stretching and
solute transport for adsorption to be explored.
MEASUREMENT OF ULTRALOWINTERFACIAL TENSION
Recovery of petroleum using tertiary oil recovery tech-
nology; cleaning of solid surfaces from dirt, grease, and
oil; formulation of stable emulsions; in situ remediation
of oil-contaminated soil with surfactant solutions; and
other applications often rely on lowering the interfacial
tension between immiscible liquids to ultralow values
(much less than 1 mN/m) using surfactants. The measure-
ments of such low interfacial tensions are extremely dif-
ficult to perform with classical interfacial tension mea-
surement methods reviewed in ‘‘Classical Interfacial
Tension Measurement Methods’’ or the dynamic tech-
niques discussed in the previous section (e.g., see the ac-
curacy values for methods shown in Table 2). For the
measurements of ultralow interfacial tensions, the spin-
ning drop technique has been developed at both laboratory
and commercial scales (36–39). The basis of this tech-
nique is discussed in the following paragraph. An ad-
ditional method designed for measurements of ultralow
interfacial tensions was proposed by Lucassen (40) and
is based on the analysis of the shape of the drop suspended
Fig. 11 Dynamic surface tension of 0.25 mM aqueous decanol
solution droplets growing in air at 23�C. Based on the experi-
mental data presented by MacLeod and Radke. (From Ref. 29.)
3162 Measurement of Interfacial Tension in Fluid-Fluid System
in liquid with a density gradient. The need for a strict
control of liquid density limits this latter technique to rela-
tively few applications.
Spinning Drop Technique
This technique relies on the fact that gravitational ac-
celeration has little effect on the shape of a fluid drop
suspended in a liquid, when drop and the liquid are con-
tained in a horizontal tube spun about its longitudinal axis
(Fig. 12) (36, 37). At low rotational velocities (o), the
fluid drop will take on an ellipsoidal shape, but when o is
sufficiently large, it will become cylindrical. Under this
latter condition, the radius (r) of the cylindrical drop is
determined by the interfacial tension, the density diffe-
rence (Dr) between the drop and the surrounding fluid,
and the rotational velocity of the drop. As the result, the
interfacial tension is calculated from the following equa-
tion (38):
g ¼ 1
4r3Dro2 ð18Þ
The spinning drop method has been very successful in
examination of ultralow interfacial tensions down to 10�6
mN/m (39). For example, Fig. 13 shows the interfacial
tension values for octane drops suspended in an aqueous
phase saturated with ethoxylated alcohols (41). As shown
in Fig. 13, the interfacial tension for the octane-water-
CnE4 system varied from about 1 to 10�4 mN/m and de-
pended on both temperature in the system and length of
the hydrocarbon chain in the chemical structure of etho-
xylated alcohol (Ref. 41 provides additional examples).
The minimum in the interfacial tension vs. the temperature
curve coincides with the phase inversion temperature, at
which both hydrophilic and oleophilic natures of surfac-
tant are in balance.
MICROTENSIOMETRY
Criminology, biology, and pharmaceutical processing are
among a number of fields in which material quantities of
interest may be too small to apply conventional tensio-
metric techniques. Furthermore, the developing field of
nanotechnology promises to yield novel structures on a
nanometer scale, the interfaces of which are sure to be the
subject of considerable study. The study of interfaces on
the nanometer scale can be very important because they
may exhibit properties that are very different from their
macroscopic counterparts. For example, knowledge of
partition and adsorption of surfactants and other interfa-
cially active components of two-liquid systems is often
crucial for the control of emulsion formulation and sta-
bility. It has recently been demonstrated that interfacial
tension of microscopic droplets may differ significantly
from the interfacial tension of macroscopic drops for the
same surfactant solutions (42). This difference arises from
dissimilar partitioning of surfactants into two immiscible
liquids and is due to the effect of an enlarged interfacial
area. In this regard, it becomes critical to conduct the study
of interfacial phenomena, including the measurements of
interfacial tension, on a length scale that is characteristic
of the individual elements of the emulsion.
Microtensiometry is the study of interfaces on very
small particles and in finely dispersed systems. The micro-
pipette technique, discussed first, is closely related to tech-
niques depending on pressure differentials across curved
interfaces that have already been presented. Techniques
based on atomic force microscopy (AFM) offer the pos-
sibility of imaging nanometer-sized particles and directly
measuring their interactions. AFM-based techniques are
relatively new and still very much under development.
Fig. 12 Schematic of the rotating drop method.
Fig. 13 The effect of temperature on interfacial tension mea-
sured between octane and aqueous phase saturated with CnE4.
Graph based on the experimental data presented in Ref. 41.
M
Measurement of Interfacial Tension in Fluid-Fluid System 3163
Micropipette Technique (43–45)
The micropipette technique was recently developed to
directly measure interfacial tensions of micrometer-sized
droplets. The technique was first used in examination of
vesicles (43, 44) and next liquid droplets (42, 45). In this
technique, the droplet is first captured at the tip of the glass
micropipette and then sucked into the pipette (Fig. 14A).
The interfacial tension is calculated from the minimum
pressure, at which the droplet extends a hemispherical pro-
trusion into the pipette, and by using the Laplace Eq. 4
in the following form (42):
Dp ¼ 2g1
Rp
� 1
Ro
� �ð19Þ
where Rp is the inner radius of the pipette and Ro is the
radius of the exterior segment of the droplet; the dimen-
sions of the pipette’s internal diameter must be smaller
than the diameter of the droplet.
In the conventional technique shown in Fig. 14A, the
large pressure difference required to draw the droplet into
the pipette when the droplet does wet or adhere to the pi-
pette surfaces, is a limitation. To avoid this limitation, a
two-pipette technique, with a separation force applied bet-
ween the pipettes to deform the droplet, has been used as
shown in Fig. 14B (45). In the two-pipette technique, the
separation force between the pipettes must also be mea-
sured, and the interfacial tension is calculated from the
force–drop deformation relation. Table 4 presents the re-
sults of interfacial tension measurements for water–orga-
nic liquid systems determined with this technique.
Atomic Force Microscopy
The application of AFM permits roughness, heterogeneity,
and interaction forces to be studied at submicroscopic
scales that may extend down to molecular sizes. Among
the most popular applications of the AFM are studies of
interactions between substrates and colloidal particles. The
AFM has not been established as a technique to measure
interfacial tensions directly: however, it appears to have
great potential for such measurements at the microscopic
and submicroscopic levels. The technique is currently be-
ing evaluated as a tool for measuring the wetting properties
of colloidal particles (48).
Fig. 14 Illustration of micropipette techniques. (A) Based on analysis of pressure differences required to suck a microdroplet into the
pipette. (B) Based on the examination of the force–drop deformation relation.
Fig. 15 Schematic of atomic force microscopy and its ap-
plication to measurements of surface tension for microdroplets.
Table 4 Results of interfacial tension measurements for the
organic solvent microdroplets in water obtained with the mic-
ropipette technique and their comparison to the similar results
measured for bulk two-liquid systems
System
Interfacial tension
measured for
microdroplets
[mN/m)
Interfacial tension
measured for
macrosystem
[mN/m)
Water-ethyl acetate 6.8 ± 0.6 6.8
Water-chloroform 30.9 ± 1.6 31.6
Water-benzene 33.7 ± 0.7 34.1
Water-toluene 36.4 ± 0.8 36.1
Water-hepto 40.3 ± 1.1 39.6
(From Ref. 45.)
3164 Measurement of Interfacial Tension in Fluid-Fluid System
AFM is a scanning probe technique based on measuring
interaction forces between a cantilever tip and a specimen
(Fig. 15). The force measurement is based on measuring
the deflection of the cantilever, which has a known spring
constant. The cantilever deflection is detected by the ref-
lection of a laser beam as shown in the figure. Movement
of the specimen under the cantilever tip (both in the ho-
rizontal plane for scanning, and vertically for force mea-
surements) is controlled very precisely by a piezoelectric
specimen stage (reverse systems with the piezoelectric
stage attached to the cantilever holder are also in use).
Interaction forces as small as 1pN (10�12 N) can be mea-
sured between the probe tip and the specimen.
Fig. 15 shows an approach for measuring the in-
terfacial tension between a probe tip and a microscopic
drop of liquid. The capillarity forces exerted on the tip by
the liquid can be measured as it is inserted into the drop
and as it is withdrawn and detaches from the drop. Cal-
culation of surface tensions from these force-distance
curves will depend on the shape of the probe tip, but the
equations should be similar to those for classical macro-
detachment techniques.
A major challenge in using the AFM technique to mea-
sure interfacial tensions is fabrication of appropriate probe
tips. Cylindrical tubes and spheres offer simple geometries
and may present the best near-term options. Carbon nano-
tubes have recently been used as AFM tips, and may offer
another promising approach (49).
REFERENCES
1. Rusanov, A.I.; Prokhorov, V.A. Interfacial Tensiometry;
Elsevier: Amsterdam, 1996.
2. Adamson, A.W.; Gast, A.P. Physical Chemistry of Surfa-
ces, 6th Ed.; John Wiley & Sons, Inc.: New York, 1997.3. Dukhin, S.S.; Kretzschmar, G.; Miller, R. Dynamics of
Adorption at Liquid Interfaces: Theory, Experiment, Appli-
cation; Elsevier: Amsterdam, 1995.
4. Hiemenz, P.C.; Rajagopalan, R. Principles of Colloid and
Surface Chemistry, 3rd Ed.; Marcel Dekker, Inc.: New
York, 1997.5. Sonntag, H. Koloidy; PWN: Warszawa, 1982.
6. Wilhelmy, L. Ueber die abhangigkeit der capillaritats-
constanten des alkohols von substanz und gestalt des
benetzten fasten korpers. Ann. Phys. Chem. 1863, 4 (29),177–217.
7. Lecomte du Nouy, P. A new apparatus for measuring sur-
face tension. J. Gen. Physiol. 1919, 1, 521–524.8. Harkins, W.D.; Jordan, H.F. A method for determination of
surface and interfacial tension from the maximum pull on a
ring. J. Am. Chem. Soc. 1930, 52, 1751–1772.9. Vold, R.D.; Vold, M.J. Colloid and Interface Chemistry;
Addison-Wesley Publishing Co.: London, 1983.
10. Zuidema, H.H.; Waters, G.W. Ring method for the de-
termination of interfacial tension. Ind. Eng. Chem. Anal.
Ed. 1941, 13, 312–313.11. Young, T. Miscellaneous Works; Peacock, G., Ed.; J. Mur-
ray: London, 1855; Vol. I, 418.
12. de Laplace, P.S. Mechanique Celeste. Supplement to Book
10; 1806.
13. Sugden, S. The determination of surface tension from the
maximum pressure in bubbles. J. Chem. Soc. 1922, 121,
858–866.14. Rehbinder, P.A. Dependence of surface activity and sur-
face tension of solutions upon temperature and concentra-
tion. Z. Phys. Chem. 1924, 111, 447–464.15. Lord Rayleigh, OM.; F.R.S. On the theory of the capil-
lary tube. Proc. R. Soc. London, Ser. A 1916, 92, 184–195.
16. Tate, T. On the magnitude of a drop of liquid formed un-
der different circumstance. Phil. Mag. 1864, 27, 176–180.
17. Harkins, W.D.; Brown, F.E. The determination of surface
tension (free surface energy), and the weight of falling
drops: the surface tension of water and benzene by the
capillary height method. J. Am. Chem. Soc. 1919, 41,499–525.
18. Miller, R.; Hofmann, A.; Schano, K.H.; Halbig, A.; Hart-
mann, R. Measurement of surface and interfacial tensions
with an automatic drop-volume tensiometer. Parfuem. Kos-
met. 1992, 73, 390–397.19. Bashforth, F.; Adams, J.C. An Attempt to test the Theory of
Capillary Action; Cambridge University Press: London,
1883.
20. Lahooti, S.; del Rio, O.I.; Neumann, A.W.; Cheng, P.
Axisymetric Drop Shape Analysis (ADSA). Applied Sur-
face Thermodynamics; Neumann, A.W., Spelt, J.K., Eds.;
Marcel Dekker, Inc.: New York, 1996; 441–507.
21. Andreas, J.M.; Hauser, E.A.; Tucker, W.B. Boundary ten-
sion by pendent drops. J. Phys. Chem. 1938, 42, 1001–1019.
22. Stauffer, C.E. The measurement of surface tension by the
pendent drop technique. J. Phys. Chem. 1965, 69, 1933–1938.
23. Misak, M.D. Equations for determining 1/H versus S
values in computer calculations of interfacial tension by
pendent drop method. J. Colloid Interface Sci. 1968, 27,141–142.
24. Quincke, G. Ueber die capillaritats-constanten des queck-
silbers. Ann. Phys. Chem. 1858, 4 (15), 1–48.25. Padday, J.F. The profiles of axially symmetric menisci.
Trans. R. Soc. London 1971, A269, 265–293.26. Lang, G. Surface Tension of Liquid Elements. Handbook of
Chemistry and Physics, 72nd Ed.; Lide, D.R., Ed.; CRCPress: Boca Raton, 1992; 133–145, Chapter 4.
27. Eustathopoulos, N.; Nicholas, M.G.; Drevet, B. Wettabi-
lity at High Temperatures; Pergamon: Amsterdam, 1999;
Chapter 4.
28. Joos, P. Dynamic Surface Phenomena; VSP: Zeist, The
Netherlands, 1999.
M
Measurement of Interfacial Tension in Fluid-Fluid System 3165
29. MacLeod, C.A.; Radke, C.J. A growing drop technique for
measuring dynamic interfacial tension. J. Colloid Interface
Sci. 1993, 160, 435–448.30. Drelich, J. The Role of Wetting Phenomena in the Hot
Water Process for Bitumen Recovery from Tar Sand.
Ph.D. Dissertation, The University of Utah: Salt Lake
City, Utah, USA, 1993.
31. Rudin, J.; Wasan, D.T. Mechanisms for lowering of in-
terfacial tension in alkali/acidic oil systems. Colloids Surf.
1992, 68, 81–94.32. Rosen, M.J. Surfactants and Interfacial Phenomena;
Wiley-Interscience: New York, 1976.
33. Dynamic Properties of Interfaces and Association Struc-
tures; Pollai, V., Shah, D.O., Eds.; ACS Press: Champaign,
Illinois, 1996.
34. Passerone, A.; Liggieri, L.; Rando, N.; Ravera, F.; Ricci,
E. A new experimental method for the measurement of the
interfacial tension between immiscible fluids at zero bond
number. J. Colloid Interface Sci. 1991, 146, 152–162.
35. Horozov, T.; Arnaudov, L. A novel fast technique for mea-
suring dynamic surface and interfacial tension of surfactant
solutions at constant interfacial area. J. Colloid Interface
Sci. 1999, 219, 99–109.36. Vonnegut, B. Rotating bubble method for the determina-
tion of surface and interfacial tensions. Rev. Sci. Instr.
1942, 13, 6–16.37. Princen, H.M.; Zia, I.Y.Z.; Mason, S.G. Measurement of
interfacial tension from the shape of a rotating drop. J.
Colloid Interface Sci. 1967, 23, 99–107.
38. Couper, A.; Newton, R.; Nunn, C. A simple derivation of
Vonnegut’s equation for the determination of interfacial
tension by the spinning drop technique. Colloid Polym.
Sci. 1983, 261, 371–372.
39. Manual of the Spinning Drop Tensiometer Site 04; Kruss
GmbH: Hamburg, Germany, 1995.
40. Lucassen, J. The shape of an oil droplet suspended in an
aqueous solution with density gradient. J. Colloid Interface
Sci. 1979, 70, 355–365.41. Sottmann, T.; Strey, R. Ultralow interfacial tensions in
water-n-alkane-surfactant systems. J. Chem. Phys. 1997,106, 8606–8615.
42. Yeung, A.; Dabros, T.; Masliyah, J. Does equilibrium
interfacial tension depend on method of measurement? J.
Colloid Interface Sci. 1998, 208, 241–247.43. Evans, E.; Skalak, R. Mechanics and Thermodynamics of
Biomembranes; CRC Press, Inc.: Boca Raton, Florida,
1980.
44. Evans, E.; Needham, D. Physical properties of surfactant
bilayer membranes: thermal transitions, elasticity, rigidity,
cohesion, and colloidal interactions. J. Phys. Chem. 1987,91, 4219–4228.
45. Moran, K.; Yeung, A.; Masliyah, J. Measuring interfacial
tensions of micrometer-sized droplets: a novel microme-
chanical technique. Langmuir 1999, 15, 8497–8504.46. Sarid, D. Scanning Force Microscopy; Oxford University
Press: New York, 1991.
47. Wiesendanger, R. Scanning Probe Microscopy and Spec-
troscopy: Methods and Applications; Cambridge Univer-
sity Press: Cambridge, Massachusettes, 1994.
48. Ecke, S.; Preuss, M.; Butt, H.-J. Microsphere tensiometry to
measure advancing and receding contact angles on indi-
vidual particles. J. Adhesion Sci. Technol. 1999, 13, 1181–
1191.49. Dai, H.; Hafner, J.H.; Rinzler, A.G.; Colbert, D.T.; Sma-
ley, R.E. Nanotubes as nanoprobes in scanning probe mic-
roscopy. Nature 1996, 384, 147–151.
3166 Measurement of Interfacial Tension in Fluid-Fluid System
Top Related