1. Feb 14, 2015

### gracy

I have to draw a contact angle.
Actually I've to detect the edge of the droplet first. It looks like a semicircle. Then I've to draw a tangent which gives me the contact angle.But I am not getting how to draw a tangent.I know a tangent is a line or plane which touches a given curve or solid at a single point.I want to know what will be that single point in my case(i.e in drawing contact angle)?The image below will depict my problem more clearly

Why not theta in red contact angle rather than black one?

2. Feb 14, 2015

### Staff: Mentor

It looks to me like the droplet curves inward just before hitting the surface, so the angle wouldn't be 90 degrees.

3. Feb 14, 2015

### gracy

I have got some questions on this picture .

Vector AP is resultant adhesive force,why?Why it is in this direction?

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4. Feb 14, 2015

### A.T.

This can be very ambiguous, to do manually. A more robust method is to fit some analytic function to the entire shape of the drop:

http://www.kruss.de/services/education-theory/glossary/drop-shape-analysis/

Last edited by a moderator: May 7, 2017
5. Feb 14, 2015

### Bystander

"To a first approximation" (translation: we know it isn't quite this because gravitational forces distort droplet shapes, but the distortion is so small it isn't worth messing with for surface tension measurements) droplet shapes are spherical. The droplet given in the schematic is at "just the limit" of sphericity, that is, it has been formed by adding liquid slowly and has not formed a "flat top" which is taken as the "first approximation" indication of a departure from spherical shape. The horizontal diameter of the drop is the diameter of the "first approximation" sphere. The tangent angle then becomes the angle of a line perpendicular to a radius drawn from the center of the sphere (or its circular cross-section) to the intersection of the surface with the drop.

6. Feb 14, 2015

### gracy

7. Feb 14, 2015

### gracy

The contact angle then becomes the angle between line perpendicular to a radius drawn from the center of the sphere (or its circular cross-section) and the intersection of the surface with the drop.
Did you mean the same?

8. Feb 14, 2015

### zoki85

What does it mean "Solid surface free energy"?

9. Feb 14, 2015

### Bystander

Is there any sort of discussion, legend, labelling, explanation at all with the picture? As it is, it makes absolutely NO sense.

10. Feb 14, 2015

### Bystander

The surface tension of the solid substrate.

11. Feb 14, 2015

### gracy

:(Sorry.I thought it is enough,I have drawn this with really hardwork.I will try to give more information.

Last edited: Feb 14, 2015
12. Feb 14, 2015

### zoki85

Ok, but isn't the surface tension only relevant to the liquid in these considerations?

13. Feb 14, 2015

### Bystander

If the surface tension is less than that of the solid substrate, it wets the solid; if greater than that of the solid substrate, it does not. Think water in glass, and compare it to mercury in glass.

14. Feb 14, 2015

### gracy

It denotes a case of liquid(eg.kerosene)partially wets the solid,resultant adhesive force(vector AP)between liquid and solid acting on a molecule A is stronger than resultant cohesive force (Vector AQ)between liquid molecules.Therefore resultant force of vector APand vector AQ is vector AR which lies inside the solid.
In equilibrium state,the tangent AT to the liquid surface,must be perpendicular to resultant force.Therefore liquid molecules like molecule A creep upwards on the solid surface.

15. Feb 14, 2015

### gracy

16. Feb 14, 2015

### zoki85

I understand. I confused terms "solid surface" and "solid substrate"...

17. Feb 14, 2015

### Bystander

That's beautiful.

18. Feb 14, 2015

### gracy

19. Feb 14, 2015

### Bystander

You mean at an angle that intersects the glass-kerosene interface rather than parallel to it? That is a phenomenon characteristic of "partial wetting." I wouldn't expect to see that for glass-kerosene, but depending on the surface treatment of the glass (it may have an adsorbed film of water on it), it's possible.

20. Feb 14, 2015

### gracy

I wanted to ask how resultant adhesive and resultant cohesive forces have been given directions?