Castles of sand
Question: Why does damp sand hold the shape of my castle-shaped bucket on the
beach whereas dry sand just crumbles away to nothing?
Answer: To understand this problem you need to consider two ideas: friction
and surface tension.
If you put a small block of wood on a table you can slide it around easily,
but if you put a heavy weight on top of the block you will need to apply a much
bigger force to move the block. This is a simple example of friction. The bigger
the force holding the block against the table, the bigger the force needed to
make it slide.
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Sand consists of lots of small, hard grains of rock that can slide over each
other. If the forces pushing the sand grains together are small, then the grains
slide easily over each other. This is the case for the dry sand in the bucket.
The sand grains are only pushed together by the weight of any grains above them,
so when you tip the bucket upside-down they slide easily until they form a
conical pile. The angle of the sides of the pile is sometimes known as the angle
of repose.
When the sand is damp, each grain is coated with a thin film of water, which
tends to collect at the points where the grains touch. Surface tension acts at
the surface of the water, producing the same result as if the water were covered
by a stretched skin that is always in tension. You can see another example of
surface tension if you fill a glass of water a bit too full鈥攁 little water
can be held in place a millimetre or two above the rim of the glass by surface
tension.
Where the droplets of water adhere to the sand grains, the tension is applied
to each grain, and this effectively pulls each grain against its neighbour,
providing quite a strong force between them even if there is no weight of sand
above. This force is enough to provide plenty of friction so that your
sandcastle stays together.
Interestingly, if you try to make your sandcastle entirely underwater with
completely wet sand, again there are no surfaces between water and air in the
sand mix, so there are no surface tension forces and again your castle will flop
into a conical pile. This proves that it is not simply the water gluing the sand
together that allows you to make castles with damp sand.
Guy Houlsby
Department of Engineering Science
Oxford University
Answer: When water is added to the sand, it forms 鈥減endular鈥� bridges between
the sand grains, which hold them together. This force is stronger than gravity
and hence prevents the walls of the sandcastle from falling down.
These pendular bridges work through the water鈥檚 surface tension. The surface
of the liquid bridges are concave, and this generates a 鈥渃apillary action鈥� which
helps to hold the grains of sand firmly together.
If you keep adding water to the sand mix the pendular bridges start to merge
and you pass through the so-called 鈥渇unicular鈥� state and reach the 鈥渃apillary鈥�
state (see Diagram).
The concave liquid surfaces continue to generate a
capillary action which holds the sand grains together.
However, if you add even more water the surface curvature becomes convex and
the capillary suction pressure disappears. This is known as the 鈥渄roplet鈥� state.
The water no longer creates any attractive force between the particles and the
walls of the castle will begin to slump and flow as a liquid slurry. The next
time you visit the beach with your bucket and spade, try it!
Incidentally, these liquid forces are used commercially to agglomerate or
鈥済ranulate鈥� many fine powders, such as dishwashing detergents, fertilisers and
the drug powders that you find inside capsules.
In these cases, when the water dries, salts crystallise out of solution to
form permanent solid bridges between the grains which continue to hold the
agglomerate together even when dry. You could try the same when building your
castles, using a concentrated salt solution instead of water to see if the
castle will hold together once it has dried.
Simon Iveson
Mayfield, New South Wales
This week鈥檚 questions
Shrinking world: I once heard that if the Earth were shrunk to the size of a
squash ball or racketball, the planet would be smoother than a real squash
ball.
Is this true? And if the converse happened and the ball were expanded to the
size of the Earth, how high would the mountains be?
By e-mail
No name or address supplied
Hard work: It is well known that water expands when it freezes, which is why
frozen pipes burst. This means that water can do work as it freezes. Where does
the energy come from for this to happen? This is especially puzzling considering
that energy is being removed from the water in order to freeze it.
Perry Bebbington
Nuthall, Nottinghamshire