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Computerized Measurement of Contact Angles


Abstract and Figures

Measurement of contact angles often provides valuable information as to the cleanliness of a surface as well as the ease of wetting of a surface with a coating such as paint or other organic species. Previous methods based on use of a sessile drop were subject to considerable operator error. In order to minimise such errors, the computer-based analysis of drop shape has been developed. The use of such software which is Windows-compatible and easy to learn, is described, giving results where operator-error is minimised. The method has considerable potential for Quality Control in surface finishing.
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Eugen G. Leuze Verlag 108 Jahre
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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 drophas 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
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
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,
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-
Eugen G. Leuze Verlag108 Jahre
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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
10–100°  
100–180°  
Drop weight (volume·density)
Low  
High  
Very high  
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
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-
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
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
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
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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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.
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... Often the measurement of contact angles is cumbersome and needs post-processing after the image capture. There have been multiple methods reported for contact angle measurement by fitting the droplet profile using different geometrical curves like circles (Williams et al. 2010) and ellipses (Fitzgibbon et al. 1996) or, solving through mathematical functions like polynomial functions (Andersen and Taboryski 2017), or Laplace functions (axisymmetric droplet shape analysis or ADSA) (Rotenberg et al. 1983;Cheng et al. 1990;Lamour et al. 2010;Stalder et al. 2010). These methods have limitations, such as the necessity of precise capturing of the contact points in the image, the validity of the methods for a limited range of contact angles, the high sensitivity of the method to the chosen parameters, and the need to solve the equations numerically to achieve a precise fit for the droplet shape (Kabir and Garg 2023). ...
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We present a novel method of 3-dimensional surface fitting of a droplet using ellipsoids such that the droplet is a combination of segments of two to four distinct ellipsoids. Further, this fitting method has been used to develop an analytical model estimating the volume of a droplet resting over compliant as well as non-compliant substrate. Here, we have used Glass and Poly (methyl methacrylate) (PMMA) substrates as rigid, and Polydimethylsiloxane (PDMS) free-hanging thin membranes (with thickness ranging from 20–40 µm) as compliant substrates. The analytical model considers the base length, width, height, and contact angles of the droplet captured from the experiment and estimates the droplet volume. The proposed analytical model could predict the volume correctly for droplets resting over compliant as well as non-compliant substrates with a maximum deviation of 16.6% for the volume range of 5–70 µL. Further, the predictions from the proposed analytical model are compared with the spherical cap-based model for droplets placed over compliant as well as non-compliant substrates. While the spherical cap-based model failed to accurately estimate droplet volume over a compliant substrate with an error of over 50%, the ellipsoid-based model proposed in this study could predict droplet volume accurately with a maximum error of 16.6%. Also, the proposed analytical model estimates the volume of droplets even at high contact angle hysteresis (> 50°) where the droplet has high azimuthal asymmetry. Further, the study also illustrates how Artificial Neural Networks (ANNs) can be used to forecast droplet width and contact angle hysteresis (CAH). The droplet width predicted from ANN could be used to eliminate the requirement of measuring droplet width from the top view experimental image. The volume of the droplet can thus be predicted from its side profile alone when utilized in conjunction with the theoretical model. Further, we developed an ANN model which predicts the CAH of the droplet by considering the length scales of the droplet. The developed ANN models performed a very good prediction with an R-value of >0.98\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$>0.98$$\end{document}.
... The contact angle measurements were performed by recording an image of a water droplet (which acted as the probe) on the solid polymer particles. These images were then analyzed using an online protractor to determine the contact angle [62]. In addition, octanol-water partitioning was studied by placing a drug sample onto a 1:1 ratio of water (aqueous phase) and octanol (organic phase). ...
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The low solubility and slow dissolution of hydrophobic drugs is a major challenge for the pharmaceutical industry. In this paper, we present the synthesis of surface-functionalized poly(lactic-co-glycolic acid) (PLGA) nanoparticles for incorporation into corticosteroid dexamethasone to improve its in vitro dissolution profile. The PLGA crystals were mixed with a strong acid mixture, and their microwave-assisted reaction led to a high degree of oxidation. The resulting nanostructured, functionalized PLGA (nfPLGA), was quite water-dispersible compared to the original PLGA, which was non-dispersible. SEM-EDS analysis showed 53% surface oxygen concentration in the nfPLGA compared to the original PLGA, which had only 25%. The nfPLGA was incorporated into dexamethasone (DXM) crystals via antisolvent precipitation. Based on SEM, RAMAN, XRD, TGA and DSC measurements, the nfPLGA-incorporated composites retained their original crystal structures and polymorphs. The solubility of DXM after nfPLGA incorporation (DXM–nfPLGA) increased from 6.21 mg/L to as high as 87.1 mg/L and formed a relatively stable suspension with a zeta potential of −44.3 mV. Octanol–water partitioning also showed a similar trend as the logP reduced from 1.96 for pure DXM to 0.24 for DXM–nfPLGA. In vitro dissolution testing showed 14.0 times higher aqueous dissolution of DXM–nfPLGA compared to pure DXM. The time for 50% (T50) and 80% (T80) of gastro medium dissolution decreased significantly for the nfPLGA composites; T50 reduced from 57.0 to 18.0 min and T80 reduced from unachievable to 35.0 min. Overall, the PLGA, which is an FDA-approved, bioabsorbable polymer, can be used to enhance the dissolution of hydrophobic pharmaceuticals and this can lead to higher efficacy and lower required dosage.
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Despite the great potential of 3D printing technologies coupled with nanotechnologies, just few studies are present in the scientific literature. Application of nanocomposites materials for 3D printing in the field of cultural heritage restoration, is a promising approach to obtain novel and functionalized materials for the artworks element to be recreated. In this context, the present work aims to study innovative nanocomposites materials suitable for the considered application. A commercial PLA filament was additivated with SiC, SiO 2 and TiO 2 nanoparticles, synthetized by CO 2 laser pyrolysis. Nanocomposite filaments were produced by a co-rotating twin-screw extruder and specimens were produced by 3D printing and analysed against their mechanical and hydrophobic properties by means of tensile tests and water absorption and contact angle measurements, respectively.
Lubricants are excipients used in tablet formulations to reduce friction and adhesion forces within the die or on the punches surface during the manufacturing process. Despite these excipients are always required for the tablets production, their amount must be carefully evaluated since lubricants can negatively impact on mechanical strength, disintegration and dissolution behavior of solid dosage forms. Alternative compounds have been suggested to overcome the issues of conventional lubricants and sodium lauryl sulfate (SDS) is one of the most promising one. Despite SDS has been object of several investigations, a definitive conclusion on its effectiveness cannot still be drawn. Particularly, its efficacy on tablets disaggregation and API dissolution is still unclear. Here, the effect of SDS on all the relevant features of tablets and tableting process has been evaluated on immediate release hydrophobic tablets formulations in comparison with conventional lubricants. The results of this investigation are quite outspoken: SDS has a low lubricant power while it determines only a limited improvement on tablets hardness. It greatly improves the tablets wettability but only on model formulations, the presence of superdisintegrants resets its effectiveness and any possible effect on tablets disaggregation. None of the tested formulations showed improvement on the API dissolution rate.
A new method of measuring material properties such as thickness or contact angle from recorded images is presented. A usual inspection of the image largely depends on the human decision for the boundary determination, which could induce the result to be biased. The present study proposes to use “k-means clustering”, which is a method of vector quantization. The image was digitized, and the digitized data were categorized into several clusters (three in case of the thickness measurement, two in case of the contact angle measurement) as objective as possible. It was shown that this method is reliable and does not require any human decision, except for the number of clusters. The low-resolution image was well treated by the present method, which was not possible in other conventional methods.
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Characterization of surface wettability plays an integral role in physical, chemical, and biological processes. However, the conventional fitting algorithms are not suitable for accurate estimation of wetting properties, especially on hydrophilic surfaces, due to optical distortions triggered by changes in the focal length of the moving drops. Therefore, here we present an original setup coupled with Convolutional Neural Networks (CNN) for estimation of Contact Angle (CA). The developed algorithm is trained on 3375 ground truth images (at different front-lit illuminations), less sensitive to the edges of the drops, and retains its stability for images that are synthetically blurred with higher Gaussian Blurring (GB) values (GB: 0–22) if compared to existing goniometers (GB: 0–12). Besides, the proposed technique can precisely analyze drops of various colors and chemistries on different surfaces. Finally, our automated orthogonal camera goniometer has a significantly lower average standard deviation (6.7° vs. 14.6°) and coefficient of variation (14.9 vs. 29.2%) than the existing techniques and enables wettability assessment of non-spherical drops on heterogeneous surfaces.
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A literature review of the five main theories describing the interaction mechanisms in the bitumen/aggregate system was conducted: theory of weak boundary layers, mechanical theory, electrostatic theory, chemical bonding theory, and thermodynamic theory (adsorption theory). The adhesion assessment methods in the bitumen/aggregate system are described, which can be divided into three main groups: determination of adhesion forces for bitumen with different materials, determination of bitumen resistance to the exfoliating action of water with different materials, and determination of adhesion as a fundamental value (contact angle measurements, interfacial fracture energy, adsorption capacity and others). It is proposed to evaluate the quality of adhesive interaction in the bitumen/aggregate system in two stages. The authors recommend using the adhesion determination methods for these two stages from the second group of methods the determination of bitumen resistance to the exfoliating action of water with different materials. In the first stage, the adhesion in the bitumen/aggregate system is determined by an accelerated technique in which the used bitumen binder and mineral material are considered as test materials. After the first stage, there are positive results in the second tests on compacted mixtures (indirect tensile strength test, Modified Lottman indirect tension test, immersion-compression test, and Hamburg wheel tracking test).
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Governing the physical and chemical characteristics of contact area among solid substrate and liquid droplets is a widely used strategy to fabricate superhydrophobic and superhydrophilic surfaces. While both surface morphology and surface free energy of a solid substrate conclude its wettability, designing the surface with right topology has reserved immense focus by researchers in last few decades. In the pursuit to achieve such goals of immaculate surfaces, some intriguing question need to be answered, for instance, what will happen if one takes same material for the solid substrate but having different morphological features? Irrespective of chemical nature, how the physical appearance of a rough surface controls the wettability? To unravel these questions, we examine the wettability of different surrogate models using coarse-grain (CG) simulations. Interesting results were obtained for apparent contact angles on varying the morphology of a particular surface with different geometrical shapes. Different surface geometries such as square, nail, solid sphere, hollow sphere, rod, and hollow sphere of hydrophobic (poly(dimethylsiloxane)) (PDMS) and hydrophilic (poly (vinyl alcohol)) (PVA) polymers were created. In hydrophobic case, the square followed by nail shape corrugated surface demonstrated least wettability by restricting the penetration of water beads inside the grooves. Whereas, for hydrophilic case, the shell shaped surface showed excellent wetting condition due to maximum availability of unoccupied volume. It was concluded from the present study that hollow cylinder and square shaped corrugated surface could be respectively used to obtain the maximum and the least surface wettability possible. This investigation, through the evolved understanding of the role of surface geometry at the nano level could guide researchers and materials scientists to develop effective materials with desired wetting conditions.
To rationally design intranasal drug delivery systems, i.e., for the assessment of the administered formulation properties, ex vivo porcine nasal mucosa (PNM) explants are one modern but complex standard. Therefore, the development of artificial mucosa substrates as straight-forward PNM analogs is important. The mucosa analog (MA; 5 wt% mucin and 1 wt% agarose coating on glass) was found to be a sufficient substitute of PNM. It exhibited similar mucoadhesive properties as determined by detachment force measurements (MA: 0.04±0.01 N mm; PNM: 0.03±0.01 N mm) and its’ topological surface properties (i.e., roughness ratio r, and mean arithmetic surface height Sa) were in good agreement with the natural tissue (rMA: 1.12, rPNM: 1.17; Sa,MA: 7.80±1.95 µm, Sa,PNM: 7.61±0.72 µm). Using this MA, the present study describes an experimental and theoretical spreading approach using hyaluronic acid (HA) in various concentrations (10-30 mg mL⁻¹), molecular weights (280-1260 kDa), and tyramine modifications (HA-Tyr). The spreading behavior of HA and HA-Tyr was determined in different environments (laboratory conditions, climatic chamber) on specific substrates (PNM, artificial mucosa, and glass). An exponential relationship between HA concentration and viscosity was determined. Higher humidity, use of HA-Tyr, and sessile droplet orientation improved spreading. The dynamic spreading model was then developed mathematically and validated experimentally. Parameters such as molecular weight, droplet volume, and surface tension are also covered by this mathematical model. The present study demonstrates that this MA combines attractive features such as broad availability, good reproducibility, high stability under physiological conditions, ease of fabrication and low production cost.
Striking a balance between applied and theoretical research, this work details many of the uses of wettability and interprets experimental data from a variety of viewpoints, including the 'separation of forces' and the 'equation of state approaches.'
An overview of various methods of measuring contact angle by Krüss drop shape analysis programs (DSA) with different application and validity ranges is presented. The sessile drop is the standard arrangement for contact angle measurement in which the drop lying on the solid surface forms a characteristic contact angle with the surface at the three-phase contact point. The circle method is a method, in which height and width of the rectangle enclosing the arc are determined. The Young-Laplace method is suitable for symmetrical drop shapes that are not affected by interferences such as tilting or contact with deposition needle. Dynamic and static drop method uses advancing or retreating angles such that the distortion of the drop shape by contact with the needle does not stretch out to the three-phase contact point.
A new method based on the Young–Laplace equation for measuring contact angles and surface tensions is presented. In this approach, a first-order perturbation technique helps to analytically solve the Young–Laplace equation according to photographic images of axisymmetric sessile drops. When appropriate, the calculated drop contour is extended by mirror symmetry so that reflection of the drop into substrate allows the detection of position of the contact points. To keep a wide range of applicability, a discretisation of the drop’s profile is not realised; instead, an optimisation of an advanced image-energy term fits an approximation of the Young–Laplace equation to drop boundaries. In addition, cubic B-spline interpolation is applied to the image of the drop to reach subpixel resolution. To demonstrate the method’s accuracy, simulated drops as well as images of liquid coal ash slags were analysed. Thanks to the high-quality image interpolation model and the image-energy term, the experiments demonstrated robust measurements over a wide variety of image types and qualities. The method was implemented in Java and is freely available [A.F. Stalder, LBADSA, Biomedical Imaging Group, EPFL,].
We present a new method based on B-spline snakes (active contours) for measuring high-accuracy contact angles. In this approach, we avoid making physical assumptions by defining the contour of the drop as a versatile B-spline curve. When useful, we extend this curve by mirror symmetry so that we can take advantage of the reflection of the drop onto the substrate to detect the position of the contact points. To keep a wide range of applicability, we refrain from discretizing the contour of the drop, and we choose to optimize an advanced image-energy term to drive the evolution of the curve. This term has directional gradient and region-based components; additionally, another term—an internal energy—is responsible for the snake elasticity and constrains the parameterization of the spline. While preserving precision at the contact points, we limit the computational complexity by constraining a non-uniform repartition of the control points. The elasticity property of the snake links the local nature of the contact angle to the global contour of the drop. A global knowledge of the drop contour allows us to use the reflection of the drop on the substrate to automatically and precisely detect a line of contact points (vertical position and tilt). We apply cubic-spline interpolation over the image of the drop; then, the evolution procedure takes part in this continuous domain to avoid the inaccuracies introduced by pixelization and discretization.We have programmed our method as a Java software and we make it freely available [A.F. Stalder, DropSnake, Biomedical Imaging Group, EPFL, [ON LINE] visited 2005.]. Our experiments result in good accuracy thanks to our high-quality image-interpolation model, while they show applicability to a variety of images thanks to our advanced image-energy term.
A highly efficient recursive algorithm for edge detection is presented. Using Canny's design [1], we show that a solution to his precise formulation of detection and localization for an infinite extent filter leads to an optimal operator in one dimension, which can be efficiently implemented by two recursive filters moving in opposite directions. In addition to the noise truncature immunity which results, the recursive nature of the filtering operations leads, with sequential machines, to a substantial saving in computational effort (five multiplications and five additions for one pixel, independent of the size of the neighborhood). The extension to the two-dimensional case is considered and the resulting filtering structures are implemented as two-dimensional recursive filters. Hence, the filter size can be varied by simply changing the value of one parameter without affecting the time execution of the algorithm. Performance measures of this new edge detector are given and compared to Canny's filters. Various experimental results are shown.
Liquid to Solid Angle of Contact Measurement
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