A contact angle goniometer measures the contact angle of a liquid on a solid surface and can obtain surface energy of a solid. This instrument is used in all the major industries; especially where research is done in coming up with newer materials. Low values of contact angle indicate greater wettability and higher values mean that the solid doesn’t attract the liquid as much. This instrument already exists but with my design it costs over ten times less, which will make it more accessible to school labs and small-scale industries.

1. TEXAS A&M UNIVERSITY-CORPUS CHRISTI
SCHOOL OF ENGINEERING AND COMPUTING SCIENCES
MECHANICAL ENGINEERING AND ENGINEEERING TECHNOLOGY
ENTC 4370 – CAPSTONE PROJECTS
Spring 2013
Capstone Project Progress Report
Contact Angle Goniometer
by
Shehryar Niazi
Advisor: Dr. Dugan Um
Dr. Ruby Mehrubeoglu
April 15th, 2013
A contact angle goniometer measures the contact angle of a liquid on a solid surface and can
obtain surface energy of a solid. This instrument is used in all the major industries; especially
where research is done in coming up with newer materials. Low values of contact angle indicate
greater wettability and higher values mean that the solid doesn’t attract the liquid as much. This
instrument already exists but with my design it costs over ten times less, which will make it more
accessible to school labs and small-scale industries.

2. 1. INTRODUCTION
To determine the surface energy of a surface, the contact angles for reference liquids need to
be measured. Surface Angle Goniometer measures these angles that the liquid drops make
with the solid. Figure 1.01 shows what a contact angle is. The angle is dependent on the
interfacial tensions between the gas and solid, liquid and solid, and gas and liquid. Goniometers
measure the contact angle by assuming that the surface of the droplet can be modeled as the
geometry of an ellipsoid, a sphere, or the Young’s-Laplace equation.
Figure
1.1: A
schematic
of
a
solid-­‐liquid-­‐air
interface
Surface Angle Goniometers are expensive for schools and small-scale industries to afford.
“Ramé-hart,” a renowned company, that makes Surface Angle Goniometers, have a range of
instruments that cost from $10,000 - $50,000 as of April 12th, 2013. The design that this project
is proposing costs $800, which makes it easily affordable and performs exactly the same way.
The goal of this project is to approach schools and research facilities and make them realize
how cheap they can get hold of a Surface Angle Goniometer. The research that can be done
with this equipment has endless possibilities.
Recently a company, “Ultra Ever Dry”, which is based on their project in which they came up
with a liquid which on spraying on a material acts as a waterproof coating. Figure 1.02 shows
how the coat creates a barrier against water, oil and other liquids by decreasing the surface
energy thus resulting in less wettability of the surface. Researches like these are only possible
with Contact Angle Goniometer.
Figure
1.2
Untreated
glove
versus
Ultra
Ever
Dry
Treated
Glove
Equipment like this is necessary to have in high schools and schools where student’s should
learn about the concept of surface energy.
2

3. 2. BACKGROUND
Previously, for over years Ramé-Hart is one of the famous companies that make contact angle
goniometer. Two out of the eight parts ordered for this project are from that company too.
Details about the parts are listed later in the proposal. The company makes commercial contact
angle goniometers that range from between $10,000 - $50,000 and one of them is shown in
Figure 2.1. The pictures of the drops of the liquid they come up with are really clear and high
definition. A picture of a drop of liquid by one of their Contact Angle Goniometer is shown in
Figure 2.2.
Figure
2.2:
Image
from
a
Commercial
Contact
Angle
Goniometer
Figure
2.1:
Commercial
Contact
Angle
Goniometer
Ramé-hart’s Goniometer work is really impressive with the only draw back of the prices being
really high. This project came into idea just to over come that draw back. The price difference
from $10,000 to $800 is really significant which makes the goniometer really affordable for labs
at schools and industries. An image from the Goniometer from this project is shown in Figure
2.3.
Figure
2.3:
A
drop
of
liquid
on
a
CD.
Image
obtained
from
Contact
Angle
Goniometer
from
this
Project
3

4. 3. HOW IT WORKS
3.1 Surface energy
The surface energy of a body quantifies the disruption of intermolecular bonds that occurs when
a surface is developed. Surface energy of a solid surface can be found using the contact angle
technique. The contact angle of a liquid on the surface is a function of the surface energies of
the system. It is a quantitative measure of the wetting of a solid by a liquid. It is defined
geometrically as the angle formed by a liquid at the boundary where a solid, gas and liquid
intersect. Low values of contact angle indicate greater wettability and surface energy of the
substrate. Converse is true for higher contact angles.
The surface energy can be divided into two components – dispersive and polar. The dispersive
component of the surface energy interacts with just the van der waals forces, which are caused
by the random motion of electrons about a molecule or an atom. The polar component of the
surface energy consists of all the other types of interactions such as covalent bonds, hydrogen
bonds, and dipole dipole-forces. Usually, two reference oils are used to find the surface energy
of a surface. The first liquid interacts with the dispersive forces only, and the second liquid
interacts with both the dispersive and the polar components. Liquids such as hexadecane and
methylene iodide can be used to find the dispersive component, while deionized water can be
used as the second reference liquid. The polar and dispersive components of the surface
energies for the reference liquids are known values. The dispersive components of the surface
energy for hexadecane and methylene iodide are 27.5 mJ/m² and 51.0 mJ/m², respectively. The
polar and dispersive components of deionized water are 51.0 mJ/m² and 21.8 mJ/m². In these
experiments, methylene iodide and deionized water were used as the two reference liquids. The
dispersive and polar surface energies of the disk sample were obtained using the measured
contact angles from these reference liquids.
Neglecting foreign vapor effects on the measurements, the surface energy of the lubricated disks
γ s can be expressed as a function of contact angle θ , lubricant-reference liquid interfacial
energy γ sl , and surface energy of the reference liquid γ l , using Young’s equation,
γ s = γ sl + γ l cosθ .
(6)
All
the
symbols
in
the
equation
6
are
labeled
in
Figure
1.01.
d
The dispersive component of the surface energy γ sl between lubricant and reference liquid when
the liquid only interacts with dispersive forces is given by
d
γ sl = γ sd + γ ld − 2 γ sd γ ld
(7)
where γ sd and γ ld are the dispersive components of surface energy for the solid and liquid
respectively.
The dispersive component of surface energy of the lubricated disk is determined by combining
Equations 6 and 7 as
4

5. d
s
γ =
γ ld (1 + cosθ ) 2
(8)
4
where θ is the measured contact angle from methylene iodide, and γ ld is the known value of
methylene iodide. In cases where the reference liquid interacts with both dispersive and polar
forces, the interfacial energy can be determined by applying the generalization of the Dupre
equation,
γ sl = γ s + γ l − 2 γ sd γ ld − 2 γ sp γ lp .
(9)
The polar component of the surface energy of the lubricated disks can be obtained by combining
Equations 6 and 9 as
γ sp
[(γ
=
d
w
p
d
+ γ w )(1 + cosθ ) − 2 γ sd γ w
p
4γ w
]
2
(10)
d
p
where θ is the measured contact angle from DI water, and γ w and γ w are the known values of
DI water.
The polar and dispersive surface energies could be determined by using equations 3 and 5. The
total surface energy γ st of the lubricated disk can be expressed as the sum of polar and
dispersive components as γ st = γ sd + γ sp .
3.2 Contact angle goniometer
The contact angle is dependent on the interfacial tensions between the gas and solid, liquid and
solid, and gas and liquid. Goniometers measure the contact angle by assuming that the surface
of the droplet can be modeled as the geometry of an ellipsoid, a sphere, or the Young’s-Laplace
equation.
Another way of describing contact angle is by using adhesion vs. cohesion. Adhesion is the
force between solid molecules and liquid molecules. Cohesion force exists between the liquid
molecules that hold them together. Contact angle is a measure that tells a person the ratio of
adhesion vs. cohesion. If the contact angle is near zero, then the adhesion forces are
dominating. And if the contact angle is very high, cohesive forces are dominating.
A goniometer consists of a stage, an illumination system, a microsyringe assembly, and a highresolution camera. The stage is used to hold the sample, and the microsyringe is used to pour a
drop of liquid on the sample surface. To illuminate the drop, the illumination system is used
which consists of a fiber optic illuminator. Images are captured using the high-resolution
camera.
5

6. 3.3 Image processing
Once the images of a drop are obtained using the camera, the contact angle can be determined
using three points on the surface of the drop. The surface is assumed to be spherical; therefore,
equations of a circle can be applied. As shown in Figure 3.1, to find the characteristics of a
circle, three points P1 , P2 , and P3 are given on a plane. A line (a) can be drawn between P1
and P2 , and line (b) can be drawn between P2 and P3 . The slopes of the two lines can be
determined using
ma =
y 2 − y1
and
(11)
x2 − x1
mb =
y3 − y 2
(12)
x3 − x 2
where ( x1 , y1 ) , ( x2 , y 2 ) , and ( x 3 , y 3 ) are the components of P1 , P2 , and P3 respectively. m a
and mb are the slopes of lines a and b respectively. Once the slopes
Figure
3.1:
Three
points
to
find
properties
of
a
circle
have been calculated, the x (h) and y (k) components of the midpoint of the circle can be
calculated using
h=
ma mb ( y1 − y3 ) + mb (x1 + x2 ) − ma (x2 + x3 )
and
(13)
2(mb − ma )
k=−
x + x 2 ⎞ y1 + y 2
1 ⎛
.
(14)
⎜ h − 1
⎟ +
ma ⎝
2 ⎠
2
6

7. From the calculated values of the coordinates of the midpoint of the circle, and the x and y
coordinates of P3 , the slope of the tangent line m P 3 at P3 can be found using
mP 3 =
h − x3
.
(15)
y3 − k
The inverse tangent of the slope of the tangent line at P3 provides the contact angle as
θ = tan −1 ( slope ) = tan −1 (m P 3 )
(16)
where θ is the contact angle.
4. PARTS
Parts ordered to assemble the project were:
1. Dino-Lite Stand MS36B Tabletop Boom Stand
2. Dino-Lite AM311S 0.3MP Digital Microscope USB 2.0
3. Dino-Lite MS15X XY+R Base with Removable Rotating Table
4. 4X6 Cast Iron Lab Support Stand and Burette Clamp
5. 214B2 Karter Scientific Stainless Steel Lab Jack
6. Spare Microsyringe Assembly
7. Straight Stainless Steel Needle; Needle Gauge: 33
8. Diiodomethane
9. Deionized Water
10. Table Lamp
7

8. 5. RESULTS
Some of the Images Obtained:
Once the images from the camera were obtained, the coordinates of the three points labeled in
Figure 3.1 were picked for every image. Then a self generated MATLAB code was used to run
all the calculations. All the equations mentioned earlier were programmed and run as shown
below.
%…………………………………………………………………………………………………………………………………………………………………………………………
% Method for determining the contact angle of a liquid sample
% using three points. (x,y) are the coordinates of the circle's
% center. slope is the gradient at the interface, and theta is the
% contact angle. Points (x1,y1), (x2,y2), and (x3,y3) are the
% left, top, and right corners of the liquid surface respectively
function z=command(x1,y1,x2,y2,x3,y3)
m1=(y2-y1)/(x2-x1);
m2=(y3-y2)/(x3-x2);
8

9. x=((m1*m2)*(y1-y3)+m2*(x1+x2)-m1*(x2+x3))/(2*(m2-m1));
y=-(1/m1)*(x-((x1+x2)/2))+(y1+y2)/2;
slope=-(x3-x)/(y3-y);
theta=atand(-slope);
disp('
x
y
slope
theta ')
disp(sprintf(' %10.5f %10.5f %10.5f %10.5f',x,y,slope,theta));
return
……………………………………………………………………………………………………………………………………………………………………………………………
Using the contact angle values, surface energy values for the polar and dispersive components
were found by using the following code:
% ………………………………………………………………………………………………………………………………………………………………………………
% To determine the polar and dispersive components of
% the surface energy of the sample. Methylene iodide
% and deionized water are the test liquids. Angles are
% in degrees, and all other terms have the units mJ/m^2.
% thetam = contact angle of methylene iodide
% thetaw = contant angle of deionized water
% sd = dispersive surface energy of the surface
% md = dispersive surface energy of methylene iodide
% sp = polar surface energy of the surface
% wd = dispersive surface energy of deionized water
% wp = polar surface energy of deionized water
% w = total surface energy of deionized water
% t = total surface energy of the surface
function z=suen(thetam,thetaw)
wd=21.8;
wp=51.0;
md=51.0;
w=wp+wd;
sd=(md*(1+cos(thetam*pi/180))^2)/4;
sp=(w*(1+cos(thetaw*pi/180))-2*(sd*wd)^0.5)^2/(4*wp);
9

10. t=sd+sp;
dispersive=sd;
polar=sp;
total=t;
disp('
dispersive
polar
total ')
disp(sprintf(' %12.5f %12.5f %12.5f',dispersive,polar,total));
return
……………………………………………………………………………………………………………………………………………………………………………………………
Conclusion:
Everything went well.. Still have to write this and some more editing to do like appendices,
contents and some more details. Running late for class! =(
10

11. Sources:
Chang-Dong Yeo, “Adhesion,” ME 6330 Contact Mechanics, (2010).
Chang-Dong Yeo, M. Sullivan, Sung-Chang Lee, and A. A. Polycarpou, “Friction Force
Measurements and Modeling in Hard Disk Drives,” IEEE Transactions on Magnetics, 44, pg.
157 (2008).
F. Thomsen, “Practical Contact Angle Measurement (3): All that meets the eye,” Kruss Surface
Science Newsletter, 18, (2007).
P. Bourke, “Equation of a Circle from 3 Points”, paulbourke.net (1990).
www.ramehart.com
www.foreverdry.net
11