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I was solving question 2.07 from MIT's advanced FM and it was asked to find the force required to hold to glass plates in place when water is placed between them.

I solved by showing that due to the lower pressure in the region inside the squeezed droplet, the plates are squeezed inwards. So I found the force of the squeeze.

This was also how they solved it, but on looking at the solution and the diagrams I wondered why would surface tension not provide an "extra" force?

I will give any further clarifications if required.

Hope my question was understandable, I will link the solution.

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I assume that you mean "why is there no force propertional to the perimeter of the water droplet in addition to the force proprotional to the area from the pressure difference."

I think that there are two things to consider: 1) The wetting condition means that the surface tension at the edge is pulling inwards and has no vertical component; 2) If the droplet is circular of radius $\rho$ then the pressure difference formula is not just $+\sigma/R$ but also has a contribution $-\sigma/\rho$. I think that this is being neglected becuse $\rho\gg R$.

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  • $\begingroup$ Yes sir that is what I mean sorry for my bad articulation, but it is given that the contact angle is alpha therefore a component exists $\endgroup$
    – Logan
    Jun 6, 2021 at 13:42
  • $\begingroup$ Yes. I misread the problem. There will be a perimeter contribution then. I guess that they are just ignoring it. This is the usual issue with any exam/homework problem: in addition to knowing the physics, you have a make a model of what is in the question-creator's mind. This is often harder than the physics. $\endgroup$
    – mike stone
    Jun 6, 2021 at 13:51

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