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Pendant Drop Measurements
Application note: TN316d
Industry section: all
Author: Dr. Tobias Winkler
Date: December 2010
Method: Drop Shape Analysis Drop Shape Analysis
System DSA100 System DSA30
Determining the surface tension of liquids by measurements on
pendant drops
Keywords: Methods, surface tension, interfacial tension, pendant drop
Introduction
Among the numerous measuring methods for surface and interfacial tension between fluids, the optical
pendant drop method is particularly elegant: It requires only a very small sample volume, not much
apparatus, has few limiting conditions and is, when used correctly, a very accurate method. This article
is intended to place current and future users of this method in the position of being able to achieve
reliable results rapidly. KRÜSS customers with DSA100, DSA30 instruments and most of the EasyDrop
versions already have access to this method with the help of a software module and minimal additional
equipment.
The main purpose of this article is to indicate the
parameters that influence the accuracy of a PD
Background measurement in order to place the user in a
position of being able to avoid errors and obtain
The pendant drop (PD) method is an optical a reliable result.
method for determining the surface or interfacial
tension of a drop of liquid by using the curvature
of the drop profile. Measuring principle
An advantage when compared with the
frequently used methods based on force At the tip of a needle a suspended drop of a
measurement, such as the Du Noüy ring specifically heavier liquid generated within a
measurement or the Wilhelmy plate specifically lighter phase (Fig. 1A). The lighter
measurement, is the very small sample volume phase is either air (surface tension
required (approx. 20-60 µL). In addition, measurements) or another liquid (interfacial
measurements are possible throughout a wide tension measurements).
pressure and temperature range (up to 690 bars
and up to 400°C with KRÜSS equipment). Users
of KRÜSS laboratory contact angle measuring
instruments can utilize the method to evaluate
the quality of the test liquids with very little effort
by checking their surface tension values.
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vertical direction. This results in the characteristic
A B
“pear shape” of a pendant drop.
Heavy
phase The degree of variation from a spherical shape
gives the relationship between the weight of the
P drop and its surface tension. If the difference in
densities between the phases is known then the
surface tension can be calculated from the drop
shape [1]. The shape is not freely scaleable; the
actual dimensions of the drop are used in the
Light phase calculation.
During a measurement the magnification of the
Fig. 1: Pendant drop (A); curved surface segment (B), video image is first determined in order to be
the radii of the horizontal (green) and vertical (blue) able to access the actual drop dimensions. The
circles of curvature define the surface curvature at drop shape is then determined from the video
point P.
image of the generated drop by gray level
Alternatively, the interfacial tension can be analysis. A numerical method is then used to
measured on an ascending drop, if the lighter vary a shape parameter known as B until the
phase is generated within a heavier one. calculated drop shape coincides with the actual
drop shape. The interfacial tension σ is then
The interfacial tension between the inner and calculated from the difference in density Δρ and
outer phases results in an increased pressure the adapted B parameter.
inside the drop. The relationship between the
difference in pressure Δp and the interfacial
tension is described by the Laplace equation Making a measurement
(Eq. 1):
A pendant drop measurement is carried out
⎛ 1 1 ⎞ simply and quickly. The following section
Δp = σ ⋅ ⎜⎜ + ⎟⎟ Eq. 1 describes the procedure and mentions some
⎝ R1 R 2 ⎠ easy to avoid obstructions on the way to a
Δp = pinner – pouter = Laplace pressure; σ = Interfacial reliable result.
tension; R1, R2 = Radii of horizontal and vertical circles
of curvature. 1. Preparing for the measurement
Surface tension results in the drops assuming 1.1 Instrument location
the smallest possible surface area; this means
that without other forces acting upon them drops Bright radiant light and vibrations that could
will be spherical. The effect of gravity deforms cause the pendant drop to oscillate make drop
the drops, because their weight generates a shape analysis difficult or could lead to unwanted
hydrostatic pressure within the drop (Eq. 2) which drop break-off from the needle. This means that
makes a contribution to the inner pressure and the location should be as vibration-free as
therefore, in accordance with Eq. 1, influences possible and that sunlight or bright room
the primary radii of curvature R1 and R2. illumination should be screened off.
ΔpHyd = Δρ ⋅ g ⋅ l (Eq. 2) 1.2 Choice of needle diameter
ΔpHyd = Hydrostatic pressure; Δρ = Difference in density
A deformation of the drop that is adequate for the
between heavier and lighter phase; g = Gravitational measurement is only achieved when the drop is
acceleration; l = Vertical distance between measuring sufficiently large. This is why a large needle
point and needle opening. diameter should be selected in order to be able
to generate correspondingly large drops. The
As the hydrostatic pressure is height-dependent KRÜSS standard needles for pendant drops
– it is minimal directly below the needle opening have a diameter of about 1.8 mm and are
and increases in a vertical direction as the suitable for most measurements. Narrower
distance from the needle increases – the needles should only be used when, because of a
curvature of the drop surface also alters in a low surface tension and/or a large difference in
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density, drop break-off from the standard needle The maximum width of the needle image is
occurs quickly. limited by the fact that the whole of the generated
drop must also be visible on the screen.
1.3 Determining the image magnification The two measuring lines for determining the
magnification should be at a distance of at least
As the actual weight of the drop itself plays a 20 pixels from one another (Fig.3), and should
major role in the calculation, in addition to the also be at the height at which the diameter was
density and acceleration due to gravity (see determined.
below), the absolute size of the drop must also
be known. This is determined from the image,
and therefore the magnification of the image
must be determined using an object whose
dimensions are known before the measurement
itself can be made. The magnification is a
sensitive parameter whose determination should
be carried out with the greatest care.
Fig.3: Proper distance between the two measuring lines
The outer diameter of the needle seen on the for determining the magnification
screen is normally used as the reference size.
This diameter should be determined with an As the optimal needle width on the screen and
accuracy of at least 10 µm in the lower section of the suitable image settings are frequently only
the needle used for determining the known after drop generation, the determination of
magnification in order to eliminate any possible the magnification factor is often carried out after
height-dependent diameter variations. The tool drop generation and image adjustment, directly
used, for example an external micrometer, before the measurement itself. In any case, each
should be positioned so that the diameter is alteration to the image adjustment described
measured at right angles to the optical axis. In below means that a new determination of the
this way errors due to possible variation of the magnification factor is absolutely essential.
needle profile from a true circle can be
eliminated. 1.4 Generating the pendant drop and drop image
optimization
The capillary tip must be located vertically on the
screen and must not be tilted. Fig. 2 clearly For PD analysis the drop must be significantly
shows that a needle tilted on the screen results deformed by the force of gravity; the drop shape
in a considerable error in the magnification factor must differ considerably from that of a true
and therefore represents a significant source of sphere. Normally the most favorable deformation
error for the results. is obtained when the drop is just before the point
of break-off from the needle tip. In order to avoid
premature drop break-off, the drop should be
generated as slowly and vibration-free as
possible. Fig. 4 shows a drop with a suitable
deformation and one with an inadequate one.
A9 B8
Fig. 2: Influence of tilted needle on the magnification A9 B8
factor. In (A) the correct factor is measured; in (B) the
result varies by 0.5%.
The outline of the needle should be readily
visible and the image should be sharp. For
determining the magnification factor a rule of
thumb states that the width of the needle outline
should occupy at least 10% of the whole screen Fig. 4: Adequately (A) and inadequately (B) deformed
width. Otherwise the scale will be too small, and pendant drops.
the size resolution for the measurement will be
poorer. In a similar way to the needle width on the
screen, a sufficiently large drop image is required
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for accurate measurements, because as the
magnification of the drop shape increases, the
number of pixels available for the analysis also
increases. This is why the drop and needle max. 40
together should occupy as much of the screen in
a vertical direction as possible (Fig. 5).
A9 B8
170-200
Fig. 5: Drops with correct (A) and too low (B)
magnification. Fig. 8: Gray level values of the drop and surrounding
phase under optimal illumination.
After the magnification the sharpness of the
image should be optimized, as fuzziness results
in less accurate profile recognition by the 1.5 Excluding evaporation effects
software. Fig. 6 shows a correctly focused image
Preventative measures against evaporation
and a fuzzy one.
should be taken with volatile liquids or sample
components, as otherwise the drops will be
A9 B8 reduced in volume and may also lose their
optimally deformed shape. In addition, with
solutions of surface-active substances their
surface concentration and therefore their surface
tension can alter, so that a constant measured
value cannot be obtained.
Help is provided by carrying out the
Fig. 6: Correct (A) and incorrect (B) focus setting.
measurement in a covered glass cuvet, on
The brightness of the background illumination whose base several drops of the liquid to be
should also be optimized. If the light intensity is analyzed are placed. As the vapor pressure in
too dark then the contrast between the the filled cuvet corresponds approximately to that
background and the drop will also be too weak; of the drop surroundings, evaporation is reduced.
this means that profile recognition by the Measurement in a cuvet also protects the drop
software will be incorrect or even impossible. In against vibrations caused by air movements and
contrast, too bright background illumination can can therefore also be a good idea for non-volatile
lead to over-illumination of the drop, which then samples.
appears narrower than it actually is. Fig. 7 shows 1.6 Recording the stationary value
the influence of the illumination on the contrast
between the drop and background. The variation of surface tension with time
mentioned above can also occur without
A9 B8 C8 evaporation for surfactants which only migrate
slowly to the boundary. The slow flow rate of
high-viscosity liquids means that the formation of
the final drop shape can take some time. In such
cases we recommend that the interfacial or
Fig. 7: Drop image with suitable (A), too dark (B) and surface tension is measured as a function of time
too bright (C) background illumination. and that the stationary value is regarded as
being the result.
As a suitable guideline for the illumination
intensity the gray level value of the dark part of
the drop should have a maximum of 40 and the
surrounding phase should have 170-200 (Fig. 8).
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2. Carrying out the drop shape analysis 2.3 Setting the baseline for the analysis
The baseline is used to define which part of the
Measurement irregularities can also result from
drop profile will be used for the drop shape
incorrect software settings or occur when
analysis. This means that a reliable result can
carrying out the drop shape analysis itself. The
only be obtained when this line is applied to the
following sections show where the sources of
drop profile at the correct height. In principle, the
error are to be found when making a
baseline should be placed as near as possible to
measurement.
the needle tip, but far enough away from it so
that it excludes that part of the drop profile whose
2.1 Required system parameters shape is influenced by contact with the needle.
In order to be able to make a PD measurement Whether the baseline has been applied correctly
the densities of the heavy and light phases as can be evaluated by seeing whether the fit line
well as the value of the acceleration due to generated by the software corresponds exactly to
gravity must be entered in the software. The the profile of the whole drop (Fig. 10A). If this is
values at the particular measuring temperature the case then it can be assumed that the profile
must be used for the densities of the participating analysis will be reliable.
phases. For surface tension measurements the
density of the surrounding air which despite of its
low value still has an influence on the result, A9 Base-
line
B8
should also be entered.
For the acceleration due to gravity the
international standard value of 9.80665 m/s² is
entered in the software as the default value. This
should be replaced by the local value at your
location; this can normally be obtained from your
national physical institute. Fit
Fig. 10: (A) Fit depicts drop profile correctly and
2.2 Sensibility of profile recognition in the provides an accurate result; (B) Fit clearly varies from
analysis software drop profile and provides an inaccurate result.
The sensitivity of the profile recognition is If there are significant variations between the fit
expressed by the determined difference in gray and drop profile (Fig. 10B) the position of the
levels that is considered as the transition baseline should be altered until the variations
between the drop and the surrounding phase. disappear.
For sharp drop images with a good contrast a
value of around 30 is recommended – this is the In order to assure reproducibility it is
default setting for “profile detection” in the recommended that all quantities influencing the
KRÜSS software. With poorly recognizable result are included in the measurement report:
phase transitions the value can be reduced. If the the gravitational acceleration, the density values
sensitivity is set incorrectly then the software of the two phases, the needle diameter and the
cannot determine the drop profile, or cannot magnification.
determine it correctly (Fig. 9). If this is the case
then the value in the software must be adapted
until the drop profile is recognized correctly. Summary
A9 B8 C8 As an optical method, the pendant drop
measurement is an accurate method which can
be carried out with little exertion. It is based on
the analysis of the profile of a pendant drop
deformed by the force of gravity. With the aid of a
numerical adaptation of the shape parameter B
Fig. 9: Influence of the “Profile Detection” value on the interfacial or surface tension can be
profile recognition: (A) Correct value, profile found calculated from the drop shape.
completely; (B) Value too low, no profile found; (C)
Value too high, profile only partly found.
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The dosing needle is used as the reference
object for determining the actual drop dimensions
from the drop image. The exact determination of
its diameter, image size and vertical position
influence the accuracy in the same way as the
size, sharpness and brightness of the drop
image.
The real size of the drop is also of crucial
importance. Only when it weighs enough the
deformation required for the measurement, the
variation from a true sphere will be sufficient.
Physical limiting conditions, such as the density
of the drop liquid and the surrounding phase and
the local value of the acceleration due to gravity
must be determined exactly. Influences that
falsify the measurement, such as vibrations,
interference from light or sample evaporation can
be avoided by suitable setup conditions and
working inside a cuvet.
For the profile analysis itself a suitable sensitivity
for determining the phase transition must first be
set. A good height must be found for the
baseline, which separates that part of the drop
deformed by contact with the needle from the
region to be analyzed. The most important
criterion for this is the degree of agreement
between the optical and calculated profile line.
Literature
[1] Song B, Springer J.: J Colloid Interface Sci.
1996 Dec 1;184 (1):77-91.
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