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I understand that there is an imbalance of forces between molecules that lie on the surface of a fluid compared to those that lie within. This results in the surface area is minimised. However, I can't understand why this creates a layer of tension that allows objects like paper clips to float. When the surface area is minimised, does the strength of the intermolecular forces of molecules at the surface increase? I can't see the direct relationship between a layer of tension formed when the surface area is minimised.

Furthermore, why does an object not experience some sort of tension within the fluid? Could someone please give me an explanation or material to read to understand why this is the case?

Edit: The explanations I've seen so far state that when the surface area is minimised, those molecules on the surface exhibit stronger cohesive forces than their neighbours. If this is the case, why does this occur? I see no relationship between the minimisation of surface area and a layer of tension on the surface.

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Surface Tension

(image source: here)

This picture clearly depicts the situation. Consider a beaker of water; now if you consider molecules at two positions in the water, one is beneath the water, and the another one is on the surface. Since there are no molecules above the upper molecule (in the picture), the molecules at the water’s surface are unbalanced. As a result, only the molecules below will be attracted. This creates the surface tension.

Also the molecules on the surface cohere more closely to those specifically aligned with them on the surface creating a surface film that makes moving an object across the surface more difficult than moving it while fully submerged. As a result, a thin crust will form on the liquid’s upper surface and because of this thick layer, a form of stress is generated which helps the lighter objects (like, dry needle or spider) to float there. 

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The reason surface tension wants to minimize the shape of water comes down to the molecular level. If the surface of water is increased, the number of particles on the surface increases, and the molecular energy as well. Increasing energy takes work, so this is why the fluid wants to minimize the energy involved. The incremental energy (Gibb's free energy) $\Delta \mathbf G$ of the surface is proportional to its area $\Delta \mathbf A$, so $\Delta\mathbf G = \gamma \Delta \mathbf A$. Here, $\gamma$ refers to the surface tension (Newtons/meter) of the liquid.

Therefore, given a potential energy, a force exists vice versa. Suppose you have a square film of sidelength $a$. If you pull it so the sidelength changes by $\Delta a$, the surface area would change by $a \Delta a$ as well. If a force $F$ was applied, then we can relate energy as $$F \Delta a = \gamma a \Delta a \implies F = \gamma a$$ Therefore the surface tension exists to stop the surface from deforming. You can imagine surface tension as a rope that ties around a fluid of water to keep it in the same shape. If we cut a line in the surface, the two halves will pull equally by $\gamma a$, so fluids will always be in equilibrium.

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