A Study of the Contact Angle of Drops on a Solid
Silicon Surface That Has Been Treated to Produce
a Wettability Gradient
Christopher Gilbert1, Nadjoua Moumen2, and R. Shankar
Subramanian3
Department of Chemical Engineering, Clarkson University
Whenever a liquid rests on a solid, it will either completely wet the solid or only partially wet
it. If the liquid only partially wets the solid, then there is a measurable contact angle between the
liquid and solid. This contact angle is measured at the point where the drop has spread the furthest
along the solid. The angle (  ) is measure tangentially to the surface to the drop, as shown in the
diagram below.
Drop of liquid

Solid surface
When the contact angle changes with position along a surface, a drop can move. The issue of
how contact angles of drops of liquid change on a surface with a wettability gradient and how
drops move on such surfaces is not well understood. It would be advantageous to develop a
model for these situations that could be used to predict the movement and contact angles of drops
because there are several applications where this model would be put to good use. These include:
eliminating the need for pumps when moving extremely small amounts of liquid on a surface, the
1
Class of 2009, Department of Chemical Engineering, Clarkson University, Honors Program, Oral
Presentation
2
Doctoral Student, Department of Chemical Engineering, Clarkson University
3
Professor and Mentor, Department of Chemical Engineering, Clarkson University
possibility of the use of a gradient in a microgravity environment, and the removal of debris in an
inkjet printer.
Developing a comprehensive model of this phenomenon would be quite complicated and
require considerably more time than is available during the summer, since it is a thesis project in
itself and is, therefore, outside the scope of summer research. Because of this, the focus for the
summer research was placed upon the analysis of images taken of the drops on placed on a
rectangular silicon strip using digital cameras.
The preparation of these rectangular strips started with cutting a silicon wafer into small
30mm x 40mm rectangles. These strips were then thoroughly cleaned, rinsed, and dried. They
were then placed in a Plexiglas box where the humidity was decreased to about 15%, and the
surfaces of the wafers were treated with trichlorododecylsilane to produce a wettability gradient.
After the strips were prepared, they were placed on a movable stage that could be
photographed from three orthogonal directions. The drops of liquid (tetraethylene glycol was
used for this phase) were delivered onto the surface using a nanoliter pump. The images of the
drop were captured digitally by the cameras and were processed using a computer.
Once the images were captured, they were analyzed with special software that was capable of
determining the profile of each drop. This produces a number of data points that can be fitted with
a third order polynomial. This fitting produces different coefficients when different numbers of
pixels (picture elements) are used. When the fitting procedure with different numbers of pixels
yields a consistent value of the contact angle, as suggested by Bateni et al (2003), that angle is
taken to be the true contact angle. One example follows, with the graph on the left representing
the digitized contour of the drop and the graph on the right is produced by fitting the polynomial
to varying numbers of pixels:
Edge Profile Plot
30 Degree Sample Angle Analysis
50
40
20
Edge Profile Plot
10
0
0
50
100
150
200
250
300
350
400
Angle
Pixel #
30
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
Values Obtained Fitting
Polynomial to Profile
0 10 20 30 40 50 60 70 80 90 10 11 12 13 14 15 16 17 18 19
0 0 0 0 0 0 0 0 0 0
-10
Pixel #
# of Pixels Fitted to Polynomial
The manner by which the angle is calculated from the polynomial involves thinking of the
curve as nothing more than a series of small right triangles, whose legs are dx and dy, and whose
hypotenuses approximates the curve. It follows that the angle,  , is given by the formula
 dy 
 . Since the contact angle is the goal of this analysis, the derivative of the
 dx 
  tan 1 
polynomial is evaluated at x=0.
During the time spent analyzing data this summer, several problems worth investigating
presented themselves. Firstly, the influence of the resolution of the monitor on the edge detection
software, particularly whether to use 256 colors (8-bit) or true color (16-bit), was studied. Next,
the ideal illumination conditions for the images were investigated. In the process of analyzing the
data the issue of whether optical distortion may have affected the image close to the contact line
was studied. Also, the variation of the acquired images from one picture to the next was studied.
It was determined that the images are best analyzed using 256 colors and are best captured at
medium dark light levels. The pixels corresponding to within about 10µm from the contact line
should be removed to counteract the effects of optical distortion. It was also discovered that when
using less than 60 pixels, the data may be more precisely fitted with a straight line or a quadratic
function, but the results are obtained using less than about 60 pixels still are scattered too much to
be considered useful. These results helped to find solutions to several problems regarding the
analysis of the images of the drops. It is hoped that the results from this summer research will
help in the search to develop a model for the motion of drops on a wettability gradient.
References:
Bateni, A., S. S. Susnar, A. Amirfazli, A. W. Neumann. “A High-Accuracy Polynomial Fitting
Approach to Determine Contact Angles.” Colloids and Surfaces A: Physiochem Eng.
Aspects 219, 215-231 (2003).
“Motion of a drop on a Horizontal Solid Surface with a Wettability Gradient.” A Doctoral
Research Proposal by Nadjoua Moumen. Jan 2004.
National Center for Biotechnology Information. July 7, 2005 http://www.ncbi.nlm.nih.gov