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?
Asked by: Roussel
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
'The mathematician's patterns, like the painter's or the poets, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.'