Question

How come a drop of water can stay hanging from the ceiling without falling immediately on the floor? How does it stick to the ceiling surface?

Water molecules attract other water molecules. In fact, every molecule of all 'normal' liquids attract each other. In general, every neutral atom or molecule attracts one another -- more or less, when they are a little distance apart, and tend to repel each other when you push them too close together. The forces in action for this to happen are certainly electrical in nature -- they are generally known as Van der Waals' forces, and they are mainly due to forces between two dipoles (i.e. uneven charge distributions whose total charge is zero). However, a side note is that the molecules need not be polar on their own, they will induce a dipole moment when they are brought together, and thus attract each other.

Water, if left alone in a zero-gravity space (or equivalently, when in free fall), will tend to form itself into a sphere. Since every molecule pulls on one another, and the molecules on the surface have no molecule to pull on them from the outside, this causes what is known as 'surface tension'. This is the reason why one can overfill a glass with water, past the top, by a couple millimeters. Now, since there is tension in the surface, water tries to minimize the surface (it is like a balloon with extremely flexible surface), and since a sphere has the least surface area for a given volume, it forms a sphere.

Now, still assuming there is no gravity, assume we bring this sphere of water into contact with another piece of solid material, which has a planar surface. (This obviously is our ceiling.) What will happen next depends on the strength of the attraction between a water molecule and and a 'ceiling molecule'. If the attraction between water and ceiling is stronger than the attraction between water and water, the water will tend to stick to the surface. Then it is said that the water has 'wet' the surface. If water-water attraction is greater, the water will just not stick to the surface -- then we say the water did not wet the surface. This phenomenon is easily observed, water will readily wet most materials (i.e. spread out on them), but with some good quality car polish, it will just 'bead up'. When it beads up, it is NOT wetting the surface, in fact, in absence of gravity, it would form into a sphere.

Now, if the water can wet the surface, it sticks to it. It has found a way to reduce the tension by reducing the surface area further, since now the water next to the surface has very little tension, so it does not really 'count', and the rest of the area is less than the original sphere. Thus it sticks to the surface.

If gravity was absent, the story would end here. We would see all sizes of water droplets stuck on surfaces. However, the presence of gravity changes the problem. Now, the force which holds the water droplet against the surface is proportional to the area. In the case of a sphere of radius r, this is proportional to r*r. But then, the weight is proportional to the volume of the sphere, which is proportional to r*r*r for a sphere of radius r. So, for a large enough radius, no matter how strong the attraction is, the force of gravity will overcome the attraction between water and ceiling (since r^3 grows faster than r^2) and the droplet will have to drop.

As another piece of information, take mercury, which is a liquid metal. It is a metal, and atomic, so it is not polar. If you spill it on most surfaces (i.e. stone, wood, aluminum) it will bead up into almost perfect spheres. It will not wet it. The attraction between mercury-mercury is much stronger than attraction with wood, stone or aluminum. However, less is known what happens when you bring it into contact with gold -- it wets it! In fact, it will form a thin layer of mercury wherever it touches it -- the attraction between mercury and gold is so strong, one will have a hard time removing the mercury from the gold (Believe me, I know, gold is one of the few materials dense enough to sink in mercury, and I was trying to test that. The piece of jewelry had to go the jeweler's to get cleaned.) SO DON'T TRY THIS AT HOME, MERCURY IS POISONOUS. I think this example shows that the sticking has nothing to do with either having polar molecules or static charges, although the forces involved are electromagnetic in nature.
Answered by: Yasar Safkan, Ph.D. M.I.T., Software Engineer, Istanbul, Turkey

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'The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.'

Bertrand Russell
(1872-1970)