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I have read through several junior undergraduate level explanations of surface tension. Here is a typical presentation at that level:

Molecules at the surface of a fluid experience approximately half of the force that molecules in the bulk of the fluid experience, thus putting surface molecules in an energetically unfavourable position. Thus the liquid tries to minimize surface area (in order to minimize the molecules at the surface) and macroscopically this is evidenced by the presence of a "surface tension" that resists deformation of the surface from its energetically favourable conformation.

There are several finer points that are not really explained in such an explanation:

  • What really is the difference between the force felt by a molecule in the bulk, versus a molecule at the surface? Is it that a molecule at the surface experiences a net force pulling it towards the bulk, while a molecule in the bulk feels zero net force?
  • How can such an intuition be properly connected with an intuition of "energetically favourable"? How should one develop an understanding of "energetically favourable"?
  • What is the nature of these intermolecular forces?

Simplistic explanations also leave the reader without enough of an understanding to definitively answer questions like:

  • Do elastic solids return to their original shape after deformation due to similar reasons?
  • What is the general mathematical framework that connects behaviours all the way from elastic solids, to capillarity in fluids?
  • Does the Earth's atmosphere have a surface tension?

Can you recommend resources that can help one develop a well-grounded understanding of surface tension?

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An excellent resource for a theoretical foundation in capillarity and wetting (i.e. surface tension dominated phenomena) is the book by de Gennes et al.:

P.G. de Gennes, F. Brochard-Wyart and D. Quéré, Capillarity And Wetting Phenomena - Drops, Bubbles, Pearls, Waves, 2003, Springer

In the first chapter it deals with the first three questions you pose. You need to go deeper in the book to get a feeling for the other three questions, but you will not find direct answers. For the fourth and fifth question you pose (and for a deeper understanding of the second question as well) you need to look into variational calculus (see this wolfram page and many useful references over there). As for the sixth question: surface tension is only well defined for immiscibles fluids so for gas-gas interfaces (if you can even specify a gas-gas interface) I don't think you can speak of a surface-tension.

P.S. I could answer most of the questions you pose, so if you are particularly interested in any of them, feel free to ask them in a separate (non reference-request) question.

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