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.

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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.

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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.              

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  

Figure  2.2:  Image  from  a  Commercial  Contact  Angle  Goniometer  

Figure  2.1:  Commercial  Contact  Angle  Goniometer  

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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 sγ can be expressed as a function of contact angle θ , lubricant-reference liquid interfacial

energy slγ , and surface energy of the reference liquid lγ , using Young’s equation,

θγγγ coslsls += . (6)

All  the  symbols  in  the  equation  6  are  labeled  in  Figure  1.01.  

The dispersive component of the surface energy dslγ between lubricant and reference liquid when

the liquid only interacts with dispersive forces is given by dl

ds

dl

ds

dsl γγγγγ 2−+= (7)

where dsγ and d

lγ 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

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4)cos1( 2θγ

γ+

=dld

s (8)

where θ is the measured contact angle from methylene iodide, and dlγ 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,

pl

ps

dl

dslssl γγγγγγγ 22 −−+= . (9)

The polar component of the surface energy of the lubricated disks can be obtained by combining Equations 6 and 9 as

[ ]pw

dw

ds

pw

dwp

s γ

γγθγγγ

42)cos1)((

2−++

= (10)

where θ is the measured contact angle from DI water, and dwγ and p

wγ 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 t

sγ of the lubricated disk can be expressed as the sum of polar and

dispersive components as ps

ds

ts γγγ += .

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 high-resolution 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.

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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 1P , 2P , and 3P are given on a plane. A line (a) can be drawn between 1P

and 2P , and line (b) can be drawn between 2P and 3P . The slopes of the two lines can be determined using

12

12

xxyyma −

−=    and                                                                                                                                                                                                                        (11)  

23

23

xxyy

mb −

−=                                                                                                                                                                                                                                    (12)  

where ),( 11 yx , ),( 22 yx , and ),( 33 yx are the components of 1P , 2P , and 3P respectively. am and bm 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

( ) ( ) ( )( )ab

abba

mmxxmxxmyymm

h−

+−++−=

2322131  and                                                                                                            (13)  

221 2121 yyxxhm

ka

++⎟⎠

⎞⎜⎝

⎛ +−−= .                                                                                                                                                                                (14)  

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From the calculated values of the coordinates of the midpoint of the circle, and the x and y coordinates of 3P , the slope of the tangent line 3Pm at 3P can be found using

kyxh

mP −

−=

3

33 .                                                                                                                                                                                                                                              (15)  

The inverse tangent of the slope of the tangent line at 3P provides the contact angle as

( )311 tan)(tan Pmslope −− ==θ                                                                                                                                                                                (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

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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);

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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);

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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! =(

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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