How Do You Determine the Tangent Point for Contact Angle in Droplet Analysis?

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In summary, the contact angle is the angle between the surface of the droplet and the surface of the substrate.
  • #1
gracy
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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

upload_2015-2-14_12-29-12.png

Why not theta in red contact angle rather than black one?
 
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  • #2
It looks to me like the droplet curves inward just before hitting the surface, so the angle wouldn't be 90 degrees.
 
  • #3
I have got some questions on this picture .
upload_2015-2-14_13-34-3.png

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

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  • #4
gracy said:
But I am not getting how to draw a tangent.
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/
http://www.researchgate.net/profile/Sjoerd_Rienstra/publication/226994659_The_shape_of_a_sessile_drop_for_small_and_large_surface_tension/links/0c960524954aa24f2f000000.pdf
 
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  • #5
gracy said:
Why not theta in red contact angle rather than black one?
"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
Can you Please answer post 3 also.
 
  • #7
Bystander said:
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.
It was extremely helpful.
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
gracy said:
View attachment 79043
Why not theta in red contact angle rather than black one?

What does it mean "Solid surface free energy"?
 
  • #9
gracy said:
post 3 also.
Is there any sort of discussion, legend, labelling, explanation at all with the picture? As it is, it makes absolutely NO sense.
 
  • #10
zoki85 said:
What does it mean "Solid surface free energy"?
The surface tension of the solid substrate.
 
  • #11
Bystander said:
As it is, it makes absolutely NO sense.
:(Sorry.I thought it is enough,I have drawn this with really hardwork.I will try to give more information.
 
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  • #12
Bystander said:
The surface tension of the solid substrate.
Ok, but isn't the surface tension only relevant to the liquid in these considerations?
 
  • #13
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
upload_2015-2-14_13-34-3-png.79048.png

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.
 
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  • #15
Now can you please answer post 3?
 
  • #16
Bystander said:
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.
I understand. I confused terms "solid surface" and "solid substrate"...
 
  • #17
gracy said:
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.
That's beautiful.
 
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  • #18
Now can you please answer post 3?
 
  • #19
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
I wanted to ask how resultant adhesive and resultant cohesive forces have been given directions?
 
  • #21
gracy said:
adhesive and resultant cohesive forces have been given directions?
You get the direction of the cohesive force from the contact angle; it also lies in the plane of the liquid surface. The adhesive force appears to be normal (perpendicular) to the solid surface. It's a measure of how much the two materials want to stick to each other, and since the solid surface has the only permanent "shape," we have to look at forces normal to that surface as far as its attraction to/by liquids.
 
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  • #22
gracy said:
In equilibrium state,the tangent AT to the liquid surface,must be perpendicular to resultant force.
Why?
 
  • #23
"... must be perpendicular ..." Must? Now you're making me go read Adamson (surface chemistry "bible"). I've never actually done any work that required me to look at this specific question. Take a break --- this is going to take me a while --- get back to you tomorrow, hopefully with an answer rather than, "Wow, I have no clue."
 
  • #24
ok can you please explain me what it it means'the pressure n concave side is greater than the pressure on the convex side.
upload_2015-2-14_17-14-27.png

Why pressure at point A is greater than at point B?
 
  • #25
Here T1=Force due to surface tension at the liquid-solid interface
T2=Force due to surface tension at the air-solid interface
T=Force due to surface tension at the air-liquid interface
upload_2015-2-14_17-36-16.png

How direction of T1,T2 and T3 is obtained?
 
  • #26
Sir,what is the direction of surface tension?Is it same as direction of contact angle?
 
  • #27
gracy said:
Why pressure at point A is greater than at point B?
Pressure inside a balloon is greater than that outside, and the same case holds for distortion of an interfacial surface. The concave side of the surface is always at higher pressure.
gracy said:
How direction of T1,T2 and T3 is obtained?
T1, and T2 are interfacial (surface) tensions between the solid and liquid (which is not wetting in the illustrated case), and the solid and air, and both are parallel to the solid surface (if the liquid were to wet the surface, direction of T1 would be different). T3 is the surface tension between the air and the liquid, and the direction is determined by any of several relationships that are not obvious from the drawing.
gracy said:
direction of contact angle?
Yes.
 
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  • #28
surface tension induces reduction in surface area.
upload_2015-2-15_2-15-45.png

Here in these pictures,direction of surface tension shows that it wants a flat surface.Does flat surface have smaller surface area than curved one?
 
  • #29
Bystander said:
T1, and T2 are interfacial (surface) tensions between the solid and liquid (which is not wetting in the illustrated case), and the solid and air,
T1, and T2 are interfacial (surface) tensions between the solid and liquid (which is not wetting in the illustrated case), and the solid and air Respectively?
 
  • #30
It is (the picture in 25th post)actually like this
upload_2015-2-15_2-27-46.png

gracy said:
How direction of T1,T2 and T3 is obtained?
Bystander said:
T1, and T2 are interfacial (surface) tensions between the solid and liquid (which is not wetting in the illustrated case), and the solid and air, and both are parallel to the solid surface (if the liquid were to wet the surface, direction of T1 would be different).
After this correction of my picture will your answer be still same?
 
  • #31
gracy said:
Here in these pictures,direction of surface tension shows that it wants a flat surface.Does flat surface have smaller surface area than curved one?
Yes.
gracy said:
T1, and T2 are interfacial (surface) tensions between the solid and liquid (which is not wetting in the illustrated case), and the solid and air Respectively?
Yes.
gracy said:
After this correction of my picture will your answer be still same?
Yes. I think, not certain, the angle for T3 is exaggerated. My suspicion is that T3 will have a direction very close to that of T2.
 
  • #32
gracy said:
Sir,what is the direction of surface tension?Is it same as direction of contact angle?
Bystander said:
Yes.
Sir,how?As angle has two directions,contact angle also has two directions.One is direction of the cohesive force and direction of the adhesive force.
 
  • #33
Direction for a surface or interface is going to be in the plane that is tangent to the interface. You've already seen that it has to be specified which two phases are in contact, solid-liquid, solid-vapor, liquid-vapor. The contact angle for total wetting is 0 degrees, total repulsion (water on waxed paper, mercury on glass) is 180 degrees, and this is for solid-liquid interfaces. Partial wetting contact angles indicate the angle between the air/vapor-liquid interface/surface, and the air-solid interface or surface.
Now, which of these is the cohesive direction, and which the adhesive direction?
 
  • #34
Adhesion: perpendicular to the solid surface, the force of attraction holding either the liquid or the vapor phase to the solid surface.
Cohesion: parallel (tangent) to the solid surface (the cohesion of the solid surface), or parallel (tangent) to the liquid surface (the cohesion of the liquid surface).
 
  • #35
[
Bystander said:
Now, which of these is the cohesive direction, and which the adhesive direction?
Here T1=Force due to surface tension at the liquid-solid interface
T2=Force due to surface tension at the air-solid interface
T=Force due to surface tension at the air-liquid interface
All forces are adhesive.No cohesive force.Because the force of attraction between two molecules of the same substance is called cohesive force.
 
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Related to How Do You Determine the Tangent Point for Contact Angle in Droplet Analysis?

1. What are adhesive and cohesive forces?

Adhesive and cohesive forces are types of intermolecular forces that determine the attraction between molecules. Adhesive forces refer to the attraction between molecules of different substances, while cohesive forces refer to the attraction between molecules of the same substance.

2. What are some examples of adhesive and cohesive forces?

Examples of adhesive forces include water sticking to the surface of a leaf or a paper towel, or the adhesion of a gecko's feet to a wall. Cohesive forces can be seen in the formation of water droplets, or the cohesion of molecules in a glass of water.

3. How do adhesive and cohesive forces affect the properties of liquids?

Adhesive and cohesive forces play a significant role in determining the surface tension and viscosity of liquids. Stronger adhesive forces result in a higher surface tension, while stronger cohesive forces lead to higher viscosity.

4. How do adhesive and cohesive forces affect the behavior of fluids in capillary tubes?

Adhesive and cohesive forces are responsible for capillary action, where a liquid rises or falls in a narrow tube due to the balance between the two forces. If adhesive forces are stronger, the liquid will rise, while if cohesive forces are stronger, the liquid will fall.

5. How can adhesive and cohesive forces be manipulated for practical applications?

Adhesive and cohesive forces can be manipulated through the use of different surface materials or by adding substances that alter the strength of these forces. This can be used in various applications such as adhesives, coatings, and detergents.

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