Why are the three different surface tensions in the directions shown?

[vcsharp2003]

Homework Statement

I am trying to understand the paragraph mentioned below in my textbook. However, it doesn't make sense to me. The figure shown is Fig 10.19 (b) ( the other figure i.e. Fig 10.19 (b) is not shown).

Relevant Equations

None

I think in the explanation below a very small element of the liquid at the line of contact between the horizontal solid surface, air outside the liquid and the liquid itself is being taken, and forces acting on such a small element are being shown. This very small element is to the left of shown diagram. The liquid is going to have a circular area of contact with the solid surface and we have taken a very small arc element on the periphery of the liquid that is touching all three i.e. solid, liquid and air. I guess this part of my understanding is correct?

I cannot figure out how the liquid air force ($S_{la}$), solid air force ($S_{sa}$) and solid liquid force ($S_{la}$) point in the directions shown in the figure.

 

[haruspex]

The notion is that a contact area between media embodies some energy. If the area is allowed to shrink then energy is released. This implies forces tending to reduce those contact areas, and a movement of the boundary along one of those lines does just that.

 

[vcsharp2003]

The notion is that a contact area between media embodies some energy. If the area is allowed to shrink then energy is released. This implies forces tending to reduce those contact areas, and a movement of the boundary along one of those lines does just that.

Ok. But, I cannot explain the forces shown in textbook.

I tried to explain these forces via the hand sketched diagram and I was able to identify the surface tension acting tangentially to the small arc of contact from liquid above it on surface i.e. $S_{la}$ and also by liquid surface that is in contact with solid i.e. $S_{sl}$. But I cannot pinpoint the surface tension at the line of contact due to $S_{sa}$. Look at the hand sketched diagram I uploaded a few moments ago. The question is what part of the liquid's line of contact is in contact with both air and solid? It seems no part of the line of contact is in contact with both air and solid; its either in contact with only solid (bottom part of liquid drop) or with only air ( the top part of liquid drop i.e. the curved part of the drop).

 

[haruspex]

what part of the liquid's line of contact is in contact with both air and solid?

That's not the point. If there is an energy per unit area associated with the contact between air and glass then a movement of the liquid which reduces that area will reduce the energy. Therefore there is a force tending to do that.

 

[Lnewqban]

Your understanding seems correct to me.
The diagram of forces is for one molecule of liquid located in the peripherical line and which is simultaneously in close contact with molecules of air and molecules of solid.

Please, see:
https://courses.lumenlearning.com/a...liquids-surface-tension-and-capillary-action/

https://media.eurekalert.org/multimedia_prod/pub/web/141315_web.jpg

https://en.m.wikipedia.org/wiki/Contact_angle

The adhesive force between the solid surface and the liquid causes the drop to spread and wet the surface, and the cohesive force within the liquid drop causes it to try to adopt the shape of a sphere and avoid contact with the surface.