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Take a dry piece of napkin & put it against a mirror ==> it falls down.

Dab it in water, oil, or alcohol ==> it now sticks / adheres to the mirror.

How can we explain this in physics terms? Adhesion? Surface tension? Atmospheric pressure?

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The surface tension forces at play at the interface between the wet napkin and the glass are far greater than the force of gravity on the dry napkin. So the wet napkin gets stuck to the glass and resists gravity, where the dry napkin does not, and falls.

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If you hold a up a dry napkin to a mirror, the dominant force acting upon it is gravity pulling it downward. However, if you wet the napkin, the water will change the forces involved because it is a polar molecule and interacts electrostaticly with itself and other molecules by forming hydrogen bonds. The water adheres to the mirror by forming hydrogen bonds with molecules on its surface. Though an individual hydrogen bond is much weaker than the pull of gravity on the napkin, many, many such bonds form between the mirror and the napkin. Therefore, the result is that the napkin sticks to the mirror by adhesion.

Water has unusually high surface tension because it's a highly polar molecule. If you tried this with another fluid such as ethanol, the force holding the napkin to the mirror would be lower.

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