How Do Forces Influence the Shape of Water and Mercury Drops on Glass?

[pranjal verma]

I am trying to understand how fluids form particular shapes when put on a solid.

1. In the two figures,what are we taking as a system for the forces?
2. How the resultant of the forces influences the shape of the different fluids?

 

[BvU]

Hi,

Do not erase the template ! You have already found something, so start from there!

 

[haruspex]

I am trying to understand how fluids form particular shapes when put on a solid.

There are two parts to this:
- the forces that result in the contact angle
- the forces that control the shape of the surface elsewhere
Are you interested in analysing both of those or just one?
For the latter, consider a horizontal slice at some height. Can you relate the surface tension, the curvature and the internal pressure? (Are you familiar with the analysis of pressure in bubbles?)

 

[pranjal verma]

There are two parts to this:
- the forces that result in the contact angle
- the forces that control the shape of the surface elsewhere
Are you interested in analysing both of those or just one?
For the latter, consider a horizontal slice at some height. Can you relate the surface tension, the curvature and the internal pressure? (Are you familiar with the analysis of pressure in bubbles?)

I am Interested in determining the system on which the forces are acting and how the forces influence the contact angle of the drop.(I.e why liquid forms a specific contact angle due to resultants of all forces acting on it?)

 

[haruspex]

I am Interested in determining the system on which the forces are acting and how the forces influence the contact angle of the drop.(I.e why liquid forms a specific contact angle due to resultants of all forces acting on it?)

I might have been of help with the shape elsewhere but I know little about contact angles.
Have you read this https://en.m.wikipedia.org/wiki/Contact_angle?

 

[pranjal verma]

I might have been of help with the shape elsewhere but I know little about contact angles.
Have you read this https://en.m.wikipedia.org/wiki/Contact_angle?

You can write what ever you know about shape of drops,I will like to learn it as well.

 

[haruspex]

You can write what ever you know about shape of drops,I will like to learn it as well.

Consider a horizontal disc of the drop, height y, thickness dy, radius x.
What equations can you write relating the these to y', y", density, surface tension etc?