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So, I'm trying to find the largest radius of a needle before it ends up sinking, and I know that it's a balance of needle weight vs surface tension. However, I'm not really sure how the surface tension force is defined.

In a lot of resources, I see the surface tension force define as gamma, which is the force / length. Also, I am seeing surface tension defined in terms of curvature give by the Young-Laplace equation. Which one am I supposed to use?

If I can use the gamma one, it would be straightforward, but I'm not clear on what length to use. Obviously, it's the portion of the circumference in contact with the needle, but this length can vary based upon a lot of factors. Aside from that, I'm thinking that I would have to set the contact angle equal to zero (for the maximum surface tension force), but does that mean that I use gamma*2*pi*r? Wouldn't that imply that the needle is completely submerged?

Any help would be appreciated!

user108149
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  • You better have the total contact perimeter in your equation somewhere! – Carl Witthoft Feb 10 '14 at 12:48
  • Is that what the length is? Why? – user108149 Feb 10 '14 at 15:24
  • Because (and I'm not an expert here, so be cautious) the force due to surface tension depends on the total interface where tension exists. I suspect it's the total length, but I'd dig into some refn'ce material to be certain. – Carl Witthoft Feb 10 '14 at 15:49
  • Do I have to consider Laplace pressure? – user108149 Feb 10 '14 at 20:55
  • @CarlWitthoft is right, you should work with the contact perimeter, but for a thin needle it is safe to assume that it is just twice the length. Check out http://en.wikipedia.org/wiki/Surface_tension#Floating_objects – Michiel Feb 12 '14 at 09:07

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