Hello, I am wondering how much weight can a liquid (like a drop of water or some amount of water) support thanks to its surface tension.
I attached a simple draft of the problem.
The question seems simple ; a lot of books give cases of objects floating on such liquid but I did not manage to find any information on why in terms of mathematical formulas leading to the physical effect.
Does anyone have a clue ?
Thanks in advance!
Dear Robert Doe :
Regards !:)
It is not difficult to work it out (if you know the most relevant geometrical parameters of the liquid).
The Surface Tensión of the Liquid (gamma) is equal to :
gamma = (1/2)* (F/L)
where gamma should be in units of [N/m] or [J/m^2]
"L" is the Lenght of the portion of the liquid which is experiencing the stress. In your problem this would be the lenght of the box.
and "F" would be the force with the liquid is trying to push/support the whole weight of the object.
Hope it helps !
Best Regards !
Hello, in the question (and in the previous answer), the surface tension of the solid is missing... in my opinion it plays a crucial role.
Hello, thank you for your answers. However, shouldn't the thickness of the liquid be taken into account ?
This was my first approach :
I was thinking that the equation should take into account the downward weight force of the object onto the liquid.
If the liquid normal force is higher than the weight, then, the liquid could support the said object.
The problem is : in the end, I could have asked what was the equation of the normal force exerced by a liquid onto an object placed above the liquid
Also, I was thinking that the pressure inside the liquid should have an important place in the problem but we did not mention it so far
Dear Didier Lairez :
You are right. What I said to Robert only follows the basic definition of the property of liquids: Surface Tension. So as you can see with the attached image, is a very simplified case. And the equation to model that case is the definition I gave in my first reply : (1/2)*(F/L) (see second attached image)
So, this is only the case when you have a liquid, and the interphase between the liquid and the gas in uniform and homogeneous, and a constant Force is applied in the direction of the liquid medium or in the opposite direction.
But in Robert's problem the interphase is not between a liquid and a gas, but between a liquid and a solid.
In this case, instead of refering to the Surface Tension of the liquid we have to refer to the "Interfacial Energy". Which in reality have the exact same meaning as the Surface Tension: The amount of Energy needed to "create" a m2 of Surface.
So, Yes. the property that we would have to use in this problem technically is not the Surface Tension, but the Interfacial Energy between the two media.
This number has to be computed, or experimentally determined using some model like the Young Equation.
Normally these models involve the three Interfacial Energies :
- between the Liquid and Gas
- between Gas and Solid
- and between Liquid and Solid
and it also involves the Contact Angle.
Regards !
Dear Robert Doe :
Not really, the property of Surface Tension (or Interfacial Tension, or Interfacial Energy) does not depends on the bulk of the medium.
It only depends on the characteristics of the surface; like the 2D lattice of the structure in the surface, the lenght of the bonds between the atoms in the surface, the magnitude of the Cohesive Forces (in the Surface), the Surface density of Atoms, etc. these kind of parameters. It is a Surface property, independent of the Bulk characteristics of the material/medium.
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