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The definitions offered seem contradictory. The first paragraph indicates that a "free surface" is a stress free surface, while the second allows for normal stresses. I would add that in the study of the dynamics of liquid drops, jets and films, it is quite common to describe a liquid/liquid or liquid/gas interface as a "free surface", and in such studies a variety of normal and tangential stresses can of course be present (e.g. capillary stresses, Marangoni stresses, electrostatic or Maxwell stresses, etc.). Also, the equation from reference 9 is a simplification of the more general "traction boundary condition", that requires the "jump" in stress across a free surface be balanced by capillary and Marangoni stresses arising from the presence of the phase boundary. Typically in solving such problems using the methods of computational fluid dynamics, a "kinematic" boundary condition is also required.
I'm considering a major rewrite of this article, but don't want to step on any toes. Anyone opposed to an expansion? --22.214.171.124 (talk) 03:33, 25 March 2009 (UTC)
I think some major improvements are very desirable. Please go ahead with your plans. I strongly recommend that before you go too far you create a user account so that you can work under a recognisable name, and we can communicate directly with you. Creation of a user account is free and there are many advantages, both to the user and to the Wikipedia community. Best wishes. Dolphin51 (talk) 05:08, 25 March 2009 (UTC)
Please feel free to improve. The notion that "free" in "free surface" refers to "stress free" is incorrect. "Free" refers to the fact that the surface is free to move under the action of the fluid motion and forces on both sides. Free surfaces, as encountered in nature, are very often not stress free, which gives rise to many phenomena, e.g. wind waves, storm surges, Ekman layers, terminal velocity in rising bubbles and falling water drops. -- Crowsnest (talk) 07:58, 25 March 2009 (UTC)
Also the second sentence in the intro does not seem to be true (so the whole 1st paragraph is misleading): as far as I can remember I have seen experiments with a lighter gas on top of a heavier one, with the interface behaving as a free surface. A free surface is just an interface between two fluids, which may be a gas-gas, liquid-liquid, or liquid-gas interface. Or, in mathematics and probably astrophysics, an interface between a fluid and a vacuum. I do not know about plasmas, but there probably as well free surfaces may occur.
One of the core elements on Wikipedia is verifiability by reliable sources. The nice thing of the article as it is now, is that there are quite some footnotes to sources used (although unfortunately either unreliable or misinterpreted by the authors of the opening paragraph). So accompanying your edits with sufficient inline citations to journals and pages in books will be of great help. -- Crowsnest (talk) 08:14, 25 March 2009 (UTC)
I am doubting about what I wrote above, about qualifying liquid-liquid, gas-liquid and gas-gas interfaces as free surfaces (provided being 'sharp' enough). Perhaps I am mixing up interfaces and free surfaces, see e.g. "An Introduction to Fluid Mechanics and Transport Phenomena", G. Hauke, p. 108, who restricts the term free surface to the liquid-gas interface. "Advanced Transport Phenomena", L. Gary Leal, pp. 357-358 gives the interfacial conditions ("tractions"). See also Batchelor pp. 148-151. -- Crowsnest (talk) 13:01, 25 March 2009 (UTC)