Water in general forms strong intermolecular forces called hydrogen bonds. Water droplets like on the underside of a door handle have a side exposed to air and so the molecules form stronger bonds within the droplet as there are less molecules to bond with surrounding it. This results in a cohesive property. Since droplets are very light, on this scale these bonds are sometimes stronger than the force of gravity, allowing it to grip the bottom of the handle.
edit: cohesive property causes the droplet’s spherical shape, adhesive property causes it to stick to surfaces. Both are a result of the intermolecular forces
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