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When discussing about surface tension, it is said that the surface water molecules experience a net downward cohesive force. If they experience such a force, then why don't the surface water molecules get pulled down into the liquid/ to the bottom of the liquid? How can they still stay at the surface?

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I assume that the 'cohesive force' is a long-range attractive force, or at least longer range than the repulsive force that also acts between molecules when they are close. Equilibrium occurs when the attractive and repulsive forces balance, so the molecule is not pulled down into the liquid.

It seems to me to be clearer to consider just a single resultant force between molecules that varies with molecular separation in a well-known ladle-shaped curve and is zero roughly where the handle of the ladle meets the bowl. You might care to look up intermolecular force curve.

[Not what you're asking, but I believe that surface tension is a tension parallel to the surface, arising from molecules in the surface layer being further apart than those in the bulk of the fluid...]

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