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Short answer:

Water beads form on a surface when the cohesion of the water molecules with each other is much greater than the adhesion of the water to the surface. Water cohesion results in water having high surface tension and hence a strong tendency to form spherical droplets. Water adhesion to waxy or oily materials is small. The result is a tendency to form water beads.

This phenomena, or the lack there of, is called wetting and has been studied for centuries. The cohesion of a liquid is directly related to the surface tension of a liquid. Water, which has a high surface tension, readily forms beads on materials which are hydrophobic, i.e. materials with a small adhesion to water. The waxed surface of a car has small adhesion and so water beads form regularly. The raw painted surface of the car would have more adhesion with water and so greater wettability. The opposite extreme, the tendency of a liquid to wet a surface due to strong adhesion, is critical to a situation such as lubrication where the liquid should coat the solid surface. It is the two properties combined, adhesion and cohesion, which determine wettabilty and beading.

Long Answer:

When one speaks of water beading on a surface, one means the formation of small droplets of water on a surface. This phenomena depends not only on the properties of water and the surface, but most importantly on the property of the interaction of the water with the surface. In science, this is the topic of "wetting" and one describes the tendency in terms of the "wettability" of a particular combination of liquid and surface. Beading is a manifestation of low wettability or little wetting.

A liquid droplet on a surface tends to form a more nearly spherical shape if the forces of attraction (or cohesion) between the liquid molecules is strong and the forces between the liquid and and the solid (adhesion) are weak. We associate strong cohesive forces of a liquid with a high surface tension and a high surface tension opposes wetting. Water is an example of a liquid with high surface tension.

The interaction of water with a surface like wax or plastic or Teflon is an example weak adhesion or weak forces between the liquid molecules and solid surface. Thus, wetting is highly unfavorable and formation of nearly spherical droplets is favored and we say water beads. Surfaces like metal or glass have somewhat stronger adhesive forces so wetting is greater and droplets are less spherical.

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