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1 Introduction
The measurement of the contact angle formed by
a droplet of liquid placed on a horizontal surface
– the so-called sessile drop – has been of interest to
scientists and others for at least 200 years, since
Young first reported his observations [1]. From this
parameter, much valuable information can be calcu-
lated, notably surface energy values. These in turn
can provide information on surface contamination
or the wettability of a surface [2]. For this reason,
the measurement of contact angles is of importance
in a wide range of scientific and technological fields,
including medicine, surface science, surface engi-
neering, and industries producing inks and coatings
for plastics and textile goods as described by Adam-
son [3], Hansen [4], Zisman, and coworkers [5].
The earliest measurements, such as that of Young, used
a protractor or a similar graduated scale for measuring
the angle. Various other techniques were developed,
such as the so-called half-angle method, discussed
below. The assumption that the sessile drop was
spherical, or formed part of a sphere, underpinned
the basis of these methods wherein the contact angle
values were computed using the principles of Euclid-
ian geometry.
The two most widely-used such methods were:
– Constructing a tangent by drawing a line orthogo-
nal to the drop radius that intersects the point of
contact with the horizontal surface – the triphase
point;
– The so-called half-angle method uses a line drawn
from the triphase point to the apex of the circle
(Fig. 1). This is of course valid only for perfect
circles.
Over the years, there have been modest advances,
notably US Patent 5,268,733 where an image of the
drop is projected onto a protractor screen [6]. Rather
than being calibrated in degrees, the screen is cali-
brated at half-scale. The protractor can be moved to
the triphase point, and the trace that intersects the apex
will give the contact angle. This approach is inher-
ently imprecise since the apex is a flat region cover-
ing a range of angles. There have also been several
specialized advances customized for production-line
environments [7].
Computerised Measurement of Contact Angles
By Darren L. Williamsa, Anselm T. Kuhnb, Mark A. Amanna, Madison B. Hausingera, Megan M. Konarika and
Elizabeth I. Nesselrodea
a Chemistry Department, Sam Houston State University, Huntsville,
USA
b Publication service Ltd., Stevenage Herts, Great Britain
Fig. 1: Contact angle measurement using the half-angle
method of drawing a line from the triphase point to the apex
of the drop. A more precise method measures b and h by
drawing a rectangle that connects the triphase points and
the apex of the drop
2 Manual Methods Using Digital Images
Computer graphics software packages and USB
camera microscopes have simplified and improved the
accurate measurement of contact angles via image
analysis. There are a range of techniques available
in the common image manipulation programs like
CorelDraw [8] and Adobe Photoshop [9]. The authors
prefer the freely-available ImageJ software package
[10] for its ever-expanding flexibility.
The complexity of contact angle analysis ranges from
the simple visual estimation of the contact angle
using an angle measurement tool to the mathemati-
cally rigorous technique found in the Low-Bond Axi-
symmetric Drop Shape Analysis (LBADSA) Plugin
[11] for ImageJ.
The manual technique of drawing a circle or ellipse
onto a cross-sectional image of a sessile drop allows
an estimate of the true circularity (or otherwise) of
the droplet image. The software packages [8–10]
include an angle measurement tool wherein a line is
drawn across the baseline of the drop connecting the
left and right triphase points. The angle of the base-
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line and the drop-edge tangent at the triphase point
provides an estimate of the contact angle (Fig. 2).
This approach is potentially more precise than the
half-angle method, but manual angle measurement is
dependent upon analyst technique.
3 Digitization and Computation
In the decade beginning 1990, adoption of a more
sophisticated approach began. Rather than attempting
to measure the contact angle directly, the x, y coordi-
nates of a digital image of the drop edge are obtained.
This can be done either manually, with a point-and-
click routine, or automatically, using a contrast-
dependent edge detection algorithm. Freedom from
the limitations of spherical geometry allowed the
adoption of a much more general approach.
3.1 Computational Models
The inherent weaknesses of a spherical model had
long been recognized. Digitization highlighted the
fact that many sessile drops are not, in fact, spherical
nor even axisymmetric as many had assumed. Large
droplets are distorted by gravitational forces. Thus,
four models have become common in the computa-
tion of drop shape [12]. These are given in Table 1 with
the conditions under which they are or are not valid.
3.2 Computer Programs for
Contact Angle Measurement
All suppliers of commercially available goniometers
now provide associated computer software for inter-
pretation of results. In general, these programs are of
high quality and are very sophisticated. For under-
standable reasons, these suppliers are reluctant to
disclose the principles used, and in most cases, do
not make them available except to purchasers of their
instruments. However, at least three such programs
have been put into the public domain, and these form
the basis of the present paper.
Tab. 1: Four drop shape models and conditions for their validity [12] (reproduced by
kind permission of Dr. Frank Thomsen, Messrs Krüss GmbH)
Circle Conic section Polynomial Young-Laplace
Contact angle measuring range
0–20°
10–100°
100–180°
Drop weight (volume·density)
Low
High
Very high
Deposition
Static (contour without needle)
Dynamic (contour with needle)
Contour Shape
Symmetrical
Slightly asymmetrical
Very asymmetrical
Fig. 2: A computer-drawn ellipse and baseline drawn on top
of a water droplet. The angle tool (in ImageJ) was used to
measure the contact angle of the right side of the drop
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3.3 Open-Access Contact Angle
Computer Programs
The three open-access programs of which the authors
are aware are all plugins for the ImageJ program. The
plugins include the Contact Angle Analysis routine
by Brugnara [13], the Low Bond Axisymmetric Drop
Shape Analysis (LB-ADSA) technique by Sage et. al.
[11], and the DropSnake method by Sage et. al. [14].
Brugnara’s routine supplies the circular and conical-
section models in Table 1. The DropSnake routine
is an implementation of the polynomial approach in
Table 1, and the LB-ADSA plugin uses the Young-
Laplace analysis (column 4 in Table 1).
4 Experimental
The purpose of this work was to compare the three
plugins noted above by measuring the contact angles
present in a common set of digital images. In order
to eliminate the many additional variables and errors
arising when liquid drops are used, the work was car-
ried out using simulated drops, as described below.
The drops used in this work were actually spheri-
cal lenses of known dimension. Three contact angle
conditions (acute, near-normal, and obtuse) were
selected to assess the software under a wide range of
conditions found in practice.
4.1 Standard Samples
A spherical ruby ball lens (Edmund Optics, NT43-830)
with a well-defined diameter (d = 6.000 ± 0.003 mm)
was placed in the 13/64 inch hole of a metallic drill
gage card (Grainger, 5C732) for the obtuse contact
angle standard. A sapphire half-ball lens (Edmund
Optics, NT49-556) was placed on a metal surface as
the near-normal contact angle standard. For the acute
contact angle standard, the ruby ball was placed in
the 15/64 inch hole of the gage card, and the portion
of the ball protruding through the other side of the
card was photographed.
The high sphericity of the ball lenses allowed us to
use the half-angle method (Eq. <1>) with variables
defined in Figure 1 to calculate the theoretical con-
tact angle (CA) of these samples. In all three cases, a
rectangle was drawn on the magnified image so that
the base width (b) and drop height (h) could be deter-
mined with an uncertainty of ±1 pixel.
CA = 2θ = 2tan-a(2h/b) <1>
These dimensionally-stable elements provided a
useful standard for refining the digital imaging tech-
niques and for comparing the accuracy of the three
contact angle plugins.
4.2 Imaging Apparatus
The image capture apparatus consisted of a light
source, a collimating mask, an adjustable stage, and
a USB microscope. The light source was a 60-W
incandescent light in a metal shroud (ACE Hardware,
Clamp Lamp) powered by a variable AC power
supply (Staco, 3PN1010) for brightness control. The
horizontal optical axis was approximately 16 cm
above the laser table. The collimating mask consisted
of an arch-shaped hole in a 8.5 x 11-inch piece of
fiberboard (inset of Fig. 3). The mask was placed
between the light source and the stage with the center
of the sample stage approximately 10 cm from the
collimating mask. The sample stage (DinoLite,
MS15X-XY-R) was adjustable horizontally in the
X and Y directions with a rotary platform on which
Fig. 3: Apparatus for capturing a high-contrast image of a sessile drop
= 2arctan(2h/b)
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the sample is placed. The microscope (DinoLite,
AM411T) was mounted on an adjustable microscope
mount (Edmund Optics, NT54-794) supported by a
¾ inch post.
4.3 Image Capture Settings
The Dino Capture software bundled with the Dino-
Lite microscope was used to photograph the drop.
The camera was placed in black-white mode to give
the image sharp and distinct contrast. The masked
backlighting also ensured a sharp drop edge. The
effects of room light and unmasked backlighting are
illustrated in the left image of Figure 4 where a thin
white or grey unfocused line appears around the edge
of the drop. The right image of Figure 4 shows the
desired drop edge contrast. The maximum available
resolution provided with the microscope (1280 x 1024)
was used.
Care was taken to keep the microscope as close as
possible to grazing angle incidence to the test sur-
face so as to view the drop in profile. However, some
elevation from the horizontal was required to view
the reflection of the drop on the surface. The reflec-
tion was critical for accurate location of the triphase
points by the plugins DropSnake and LB-ADSA. The
Brugnara plugin makes no use of the drop reflection,
although the reflection assists the operator in visually
selecting the triphase points.
The DinoCapture software automatically saves the
images in bitmap format. Before analyzing the images
in any of the plugins, the images were converted to
32-bit grayscale using ImageJ.
4.4 Brugnara Plugin
When using the Brugnara plugin, the image must be
rotated and saved such that the drop appears to be
hanging from the surface. Upon opening this plugin, a
cross hair appears as the cursor. One must first define
the base of the drop by selecting the left triphase point
and then the right triphase point. One completes the
definition of the drop edge by placing three more
points around the drop edge. All five points should
be in order and in a clockwise direction. Figure 5
shows the multi-colored selection points on the edge-
detected image of the half-ball sample.
The fourth button on the plugin toolbar (document
icon) opens the Point List dialog box. One has a
choice of a manual points procedure which fits a
circle and ellipse to the five points just defined. One
also has a choice of Circle, Ellipse, or Both BestFits.
These options use an edge detection algorithm to find
the drop edge. This edge detector greatly increases
Fig. 4: The left image was taken with the room lights on and no collimating mask. The drop edge is not well-defined. The
right image was taken in a dark room with the collimating mask on the light source. The drop edge is sharp and distinct
Fig. 5: The edge-detected image of the half-ball sample
during the threshold operation in the Brugnara plugin.
The multi-colored points define the baseline and edge. The
threshold-defined edge is shown in red. The plugin toolbar
is shown at the top of the figure
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the number of points used to define the circle or
ellipse.
This work used the Both BestFits procedure which
automatically detects the drop profile using the edge
detection algorithm included in ImageJ. The edge
detection algorithm uses a first derivative function
of image intensity and a process known as Canny-
Deriche Filtering [15]. A highlighted edge image is
displayed with a Removing Points dialog box as seen
in Figure 5. One should adjust the minimum and
maximum threshold values (from 0 to 255) so that
the most precise (thin) definition of the edge of the
drop is obtained. The Set Threshold button updates
the edge image using the new threshold values. Once
the settings are accepted, a results window gives the
circle contact angle (θ C), left, right, and average
contact angle of the ellipse (θ E) in a format that is
amenable to copying and pasting into a spreadsheet
program. This report window can also be saved as a
text file.
The Manual Points procedure is very robust in that
it will work with any image contrast. However, it
depends completely upon the accuracy of point place-
ment by the user. No edge detection or optimization
routines are used for this procedure.
4.5 DropSnake Plugin
The DropSnake plugin utilizes the drop’s reflection
to get a more accurate measurement of the triphase
points. This plugin is ideal for measuring asymmetric
drops since no shape assumptions are used. This is
particularly useful if the drop is on a tilted surface or
in contact with a syringe needle for the measurement
of advancing and receding contact angles.
Initially, seven knots are placed along the contour of
the drop beginning at the lower-left triphase point,
continuing clockwise around the drop, and ending at
the lower-right triphase point. After the seventh knot
is placed, a double-click anywhere in the image will
signal that the definition of the drop edge is complete.
A blue snake curve will appear around the drop edge
with a symmetric reflection of the snake below the
drop (Fig. 6).
The knots along the drop may be adjusted using the
mouse so that the blue curve follows the drop edge
closely. The snake should be refined by clicking the
Fig. 6: The DropSnake plugin toolbar is shown at the top. The contact angles are displayed in the
upper-left portion of the image (Sample 3 (120°)) and in the “Final curves” result window. The
initial (blue) and refined (red) snakes drawn by the DropSnake plugin are shown on the image
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green snake toolbar button. The final snake is com-
puted, and the angle measurements are displayed in
the Final curves dialog box. A red snake appears on
the drop that contains many more knots. One accepts
the red snake by clicking the green arrow toolbar
button, thus ending the analysis. The results can be
cut and pasted into other documents or saved as a
text file.
Close inspection of the snake around the triphase
points is a necessity. If the plugin has difficulty iden-
tifying the triphase points on a particular drop image,
one may have to change the default settings by click-
ing the heart toolbar button. The Preferences dialog
is displayed with numerous options – each defined in
the plugin documentation.
Two terms require some explanation. The image
energy (Eimage) is related to the gradient of pixel
intensity and allows the snake to find the drop edge
[14]. The internal energy is related to the flexibility of
the snake and allows the snake to ignore image arti-
facts (or otherwise) that may occur near the triphase
points. The Eint/Eimage term is the relative weight
that is given to each of these terms in the snake opti-
mization.
The most rewarding preference changes, in our
experience, were the smoothing radius of 1 pixel,
and adjustment of the Knot spacing at the interface,
where a smaller number places more knots near the
triphase points. Changes to the preferences should be
accepted using the OK button, and the curve should
be refined again using the green snake toolbar button.
This plugin required some practice before confidence
was obtained in the results.
4.6 LB-ADSA Plugin
The Low Bond Axisymmetric Drop Shape Analysis
(LB-ADSA) plugin is interactive using five variables
(b, x, y, h, and d) to manipulate a green Young-
Laplace drop shape that is superimposed upon the
drop image (Fig. 7). Manipulation of these variables
by moving their respective sliders will allow a close
fit of the drop shape to the drop image.
The preferred sequence is to first manipulate the x
and y settings until the highest point of the green drop
shape lies directly on the highest point of the drop
image. Use of the mouse to move the sliders serves
as a coarse adjustment. The right and left arrow keys
on the keyboard act as fine adjustments. The b vari-
able is adjusted next to refine the horizontal width of
the drop shape. Iterative adjustment of x and y may
be necessary. Finally, the h variable is adjusted until
the drop shape accurately matches the triphase points
on the drop image. If desired, the d variable may be
adjusted to cut the reflection portion, although this
did not appear to impact the results.
At this point, the superimposed drop shape is a
manual fit to the drop image. One may record the
contact angle reported by the Contact angle (Canvas)
Fig. 7: Screen-shot of a completed LB-ADSA contact angle analysis showing the drop photo (Sample 1 (52°)) with the
adjusted drop shape outline (right), the drop characteristics table output (lower-left), and the L dialog box (upper-left)
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line in the dialog box. With the outline correctly ori-
ented around the drop image, an optimization of the
drop shape may be initiated by clicking the Gradi-
ent Energy button. The b, x, y, and h variables have
checkboxes labeled Optimize next to them. Check
marks indicate that these variables are active for opti-
mization using the contrast between the drop and the
background.
In like manner to DropSnake, this plugin uses the
gradient-based edge detection that locates the point
of greatest contrast along the drop edge. Thus, the
optimization procedure is more likely to find the
exact drop edge if the drop image under analysis pos-
sesses a stark black and white contrast.
Post-optimization inspection of the drop shape is nec-
essary, because the optimization may shift the drop
shape substantially. If the refinement is acceptable, a
click of the Table button will display the results in a
window labeled Drop characteristics.
The LB-ADSA plugin should not be used when ana-
lyzing drops lacking symmetry or images that are not
level. Image tilt can introduce significant error, and
this plugin will not provide individual values for the
left and right contact angles of an asymmetric drop.
While the purpose of this work concerns LB-ADSA’s
ability to measure contact angle, it is worth noting
that the plugin also reports other geometric values of
the drop such as drop volume, drop-air surface area,
and drop-solid interface area. To display these, the
user must input the proper pixel/millimeter conver-
sion factor under the Settings button to the right of
Table (Fig. 7). Additionally, input of the liquid’s cap-
illary constant, which appears as the variable c in the
LB-ADSA dialog box, allows for accurate correction
for gravitational deformation of the drop. This was
set to zero for our spherical ball lenses.
5 Results and Discussion
The spherical samples used in this work allowed a
very accurate measurement of the contact angle using
the half-angle method. In ImageJ, a rectangular box
was drawn that connected the apex of the circle to the
two triphase points. The dimensions of this rectangle
were recorded in pixels. The procedure was repeated
three times to compute the uncertainty in the contact
angle measurement. The range of uncertainty in the
selection of height and width was less than 5 pixels.
These height (h) and width (b) values were used with
Equation <1> to produce the accepted contact angle
values in Table 2.
Six of the listed authors participated in the study.
Each participant (labeled operator in the statistical
analysis) used all three plugins to measure the contact
angle of all three samples. These three samples are
labeled Sample 1 (52°), Sample 2 (92°) and Sample
3 (120°) in the statistical analysis. The Brugnara
plugin uses two methods (circle and ellipse) which,
together with DropSnake and LB-ADSA, yields
four methods of contact angle determination. These
(B-Circle, B-Ellipse, DropSnake, and LB-ADSA) are
labeled method in the statistical analysis.
The statistical software package Minitab [16] was
used to evaluate the data. One useful tool avail-
able in Minitab is the multi-variable chart (Fig. 8).
The response variable is absolute error (labeled
Error(deg)) which is computed as measured CA
minus accepted CA. Of course, the desired response
is zero. Negative responses indicate that the mea-
surement is less than the accepted value and vice
versa. The abscissa is divided into three panels by
sample. The center of each panel contains a green
datum which is the average of all measurements for
that sample. Each sample panel is divided into the
four methods with red data indicating the average of
that method for that sample. The individual opera-
tor results are clustered within each method region.
One can see the scatter (or otherwise) of the operator
using each method on any given sample.
It is evident from Figure 8 that DropSnake is very
operator-dependent. The tightest distribution was the
use of LB-ADSA on Sample 3 (120°), but LB-ADSA
showed the most operator variation on Sample 2
(90°). In general, Brugnara’s plugin was least depen-
dent upon operator with errors well within the range
Tab. 2: The accepted values (Half-Angle CA) for the
three standard samples
Sample Half-Angle
CA
Standard
Deviation
Obtuse (ruby ball in
13/64” hole)
119.58° 0.14°
Near-normal (sapphire
half-ball lens)
91.75° 0.46°
Acute (ruby ball protrusion
through a 15/64” hole)
51.91° 0.72°
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Fig. 8: The multi-variable chart from Minitab shows the operator results, the average value
of each method (red), and the average value for each sample (green). The connecting lines
are included for clarity
of ± 2.5° across all operators. The ellipse results were
somewhat low for samples 2 and 3 on average. It is
unsurprising that the circle gave the most consistently
accurate results, because our spherical samples are
exactly circular in profile.
The Gage R&R analysis tool in Minitab examines the
repeatability and reproducibility (R&R) of a particu-
lar measurement system. The Gage R&R is typically
used to evaluate several operators measuring similar
parts multiple times. The repeatability component
is the variability of a single operator measuring the
same part. The reproducibility component is the vari-
ability of multiple operators measuring the same part.
The response variable in this study is Error(deg), and
this variable should be zero in all cases. Therefore,
no difference should exist between Samples 1, 2, or
3. The differences that occur are due to the measure-
ment system – different operators using different
plugins.
Using a response variable that should be zero in all
cases allows a great deal of flexibility in the Gage
R&R routine. One may perform the analysis in the
traditional way of operator (Amann, Hausinger, etc.)
and part number (Sample 1, 3, and 3) as seen in Figure
9. In this case the variability due to method was aver-
aged into the operator’s repeatability term. Thus, the
repeatability term dominates the components of vari-
ation chart. The distribution of the method results by
each operator is found in the By Operator box plot of
Figure 9. The outliers indicate non-randomly distrib-
uted measurements. This is expected, because each
datum was obtained by a different plugin method.
The part-to-part component of variation is negligible
which is evident in the similarity of sample means in
the By Sample box plot of Figure 9.
Another option for the Gage R&R routine is to compare
the plugin method performance against part number
(Sample 1, 2, and 3). This is shown in Figure 10. In
this case, the variability due to operator (Amann,
Hausinger, etc.) is averaged into the method’s repeat-
ability term which is 41 % of the total variation.
The reproducibility component (different plugin
methods on the same sample) accounts for 59 % of
the total variation. A significant interaction exists
between method and sample (lower-right chart of
Figure 10), where it is evident that the students had
difficulty (on average) using DropSnake on the 52°
and 92° samples.
In order to explore the possibility of an operator-
method interaction, the Gage R&R routine can be
configured to measure the accuracy of each opera-
tor’s results against plugin method (Fig. 11). The
variability due to sample 1, 2, and 3 is averaged into
the operator’s repeatability term. The most important
chart in Figure 11 is the Operator-Method Interac-
tion chart where it is seen that DropSnake and LB-
ADSA are more operator-dependent than the circle or
ellipse fitting methods.
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Fig. 9: Minitab Gage R&R report of Error (deg) where each operator is compared by sample. The method variation is pres-
ent in the operator range and mean
Fig. 10: Minitab Gage R&R report of Error (deg) where each method is compared by sample. The operator variation is
present in the method range and mean
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6 Conclusions
The primary purpose of this work was to demonstrate
that contact angles of sessile drops can be accurately
measured using very low-cost equipment in conjunc-
tion with open-access computer programs. Three
such programs, each based on a different drop model
were used and their results compared, using statisti-
cal analysis. The results obtained were discussed in
terms of the quality of the droplet image required in
each case, susceptibility to operator error and limita-
tions such as angle of tilt or drop symmetry, which
some programs handle, while others do not.
Each of the three models has strengths and weak-
nesses. The Brugnara plugin was the easiest to learn
and the least susceptible to image tilt. DropSnake
was difficult to use at first, but became quite easy
once high-contrast image illumination was achieved
via the apparatus presented in Figure 3. DropSnake
was able to accommodate image tilt, and is the only
option for highly asymmetric drops such as those
used in advancing-receding contact angle studies.
Precision was addressed throughout the Gage R&R
figures, and the multi-variable chart of Figure 8. The
least precise method was the DropSnake plugin (cf.
Error(deg) by Method in Fig. 10). The LB-ADSA
Fig. 11: Minitab Gage R&R report of Error(deg) where each operator is compared by method. The sample variation is
present in the operator range and mean
plugin exhibited sample-dependent precision (cf. R
Chart in Fig. 10). Brugnara’s plugin exhibited the
least amount of sample-dependent variability in pre-
cision (cf. R Chart in Fig. 10).
The evaluation of accuracy required stable standard
samples – a spherical ball in a hole and a half-ball lens
on a surface. The accepted value (i.e. Error(deg) =
0°) was contained within the range of values for each
plugin with the exception of the DropSnake method
on Sample 2 (92°) (Fig. 9). The plugins in aggregate
erred towards underestimation of the contact angle,
with an overall mean of Error(deg) equal to -1.1°.
Finally, successful training (or otherwise) was very
easy to assess using these standard samples and the
Gage R&R analysis. Once a participant had been
trained in each of the plugins, their work could be
evaluated for its reliability and whether the expected
range of variability was achieved. Any problems were
evident on the R chart. If an operator did not under-
stand how to use the plugins properly, the R Chart
showed repeatability problems for that operator. If
the operator consistently obtained the wrong answer,
the XBar Chart indicated that the mean of their mea-
surements stood apart from the group. This analysis
quickly identified who needed refresher training on
the measurement techniques.
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Acknowledgements
The previous research students of the Williams Group at Sam Houston
State University (Trisha O’Bryon, Nelson Sheppard, Blake Howard, and
Bryan Crom) are acknowledged for their hard work, curiosity, and cre-
ative ideas related to this project. Dustin Palm is also acknowledged for
his participation in the statistical study.
References
[1] T. Phil. Young; Trans R Soc Lond 1805, 95, 65–87
[2] ASTM Standard D 7334, 2008: Standard Practice for Surface Wet-
tability of Coatings, Substrates and Pigments by Advancing Contact
Angle Measurement; ASTM International, West Conshohocken, PA,
2008, DOI: 10.1520/D7334-08, http://www.astm.org. (and included
references)
[3] A. W. Adamson, A. P. Gast: Physical Chemistry of Surfaces; 6th Ed.,
Wiley-Interscience, New York, NY, 1997
[4] C. M. Hansen: Hansen Solubility Parameters – A User’s Handbook;
2nd Ed. CRC Press LLC, Boca Raton, FL, Chapter 6, 2007
[5] M. E. Schrader, G. I. Loeb: Modern Approaches to Wettability –
Theory and Applications; Plenum Press, New York, NY, 1992
[6] R. Wright, M. Blitshteyn: Method and Apparatus for Measuring
Contact Angles of Liquid Droplets on Substrate Surfaces; U.S. Patent
5,268,733, Dec. 7, 1993
[7] P. G. Wapner, W. P. Hoffman: Liquid to Solid Angle of Contact
Measurement; U.S. Patent 6,867,854, Mar. 15, 2005; and referenced
patents therein
[8] CorelDraw, version X5, Corel Corp., Mountain View, CA 2010
[9] Adobe Photoshop, version CS5, Adobe Systems Inc., San Jose,
CA 2010
[10] W. S. Rasband: ImageJ, U. S. National Institutes of Health, Bethesda,
Maryland, USA, http://rsb.info.nih.gov/ij/ (accessed July 2010),
1997–2010
[11] A. R. Stalder, T. Melchior, M. Muller, D. Sage, T. Blu, M. Unser:
Low-Bond Axisymmetric Drop Shape Analysis for Surface Tension
and Contact Angle Measurements of Sessile Drops; Colloids Surf A,
2010, 364, 72–81
[12] F. Thomsen: Practical Contact Angle Measurement – Measuring
With Method – But With Which One?; KRÜSS Newsletter, 2008,
19, [Online] KRÜSS GmbH, Hamburg, Germany http://www.kruss.
de/en/newsletter/newsletter-archives/2008/issue-19/application/
application-02.html (accessed July 2010)
[13] M. Brugnara: Contact Angle Plugin; University of Trento, Trento,
Italy 2010
[14] A. F. Stalder, G. Kulik, D. Sage, L. Barbieri, P. Hoffmann: A Snake-
based Approach to Accurate Determination of Both Contact Points
and Contact Angles; Colloids Surf A, 2006, 286, 92–103
[15] R. Deriche: Using Canny’s Criteria to Derive a Recursively Imple-
mented Optimal Edge Detector; Int. J. Computer Vision, 1987, 1,
167–187
[16] Minitab, version 14, Minitab Inc., State College, PA 2010
