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How does the surface of water behave like a stretched membrane? What's the cause for that? I know that the surface molecules experience a net force downward so there is dense layer of water molecules in the surface but how does this leads to minimizing the surface area? Please help me clear my doubts.

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Every one of the water molecules in the bulk liquid exerts a small amount of attractive force upon its nearest neighbors. The total energy of the ensemble of water molecules is minimized when the molecules are pulled close to one another by this force.

When a portion of liquid water is in contact with air, the molecules right at the surface have only half as many nearest neighbors with which to share that force of attraction, and as a result they attract one another more strongly at the surface than they do in the bulk. To minimize their energy, they want to minimize the distance between them, and this makes the surface of the water act like a stretched membrane which strives to minimize its area.

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