Tuesday, June 29, 2010

My glass of water

A glass of water sits on my desk. The glass is clear and the water is clear, therefore the boundaries between them vanish. Instead of pondering if my glass is half-full or half-empty, I'm thinking about the water. In my glass, sitting still on my desk, the water looks like such a simple thing, but it is composed of zillions of tiny molecules of two atoms of hydrogen and one of oxygen pinned together like Micky-Mouse ears.

A single molecule of water is quite dull to the non-chemist like myself. But, put together a bucketfull of these molecules and an exciting thing happens: liquidity. The molecules slosh as one, they fill the nooks and cranies of their container completely and can disolve almost anything given enough time. Along with gases, liquids are considered a fluid. Their physical properties (like density and pressure) are continuous, there are no gaps or instantaneous changes occuring thoughout their volume. Like projectiles and pendulums, fluids follow Newton's laws. Mass, energy and momentum are all still conserved but, the equations describing their motion are exceptionally complex for even the simplest case.

If I drop a stone in the center of my glass a circular ripple will move outwards, taking the information about the pebble's disturbance to the edge of the glass, where it will be reflected back. This ripple is a type of wave, and though it looks like the water is moving outwards, it isn't. Instead, each water particle moves up and down, then its neighbor moves up and down next – exactly like what happens in a stadium when the audience does the wave. If I blew on the surface of the water, I would create similar waves, except this time they would be moving in one direction instead of radially away from a point. In the ocean, you get waves created this way by the wind. The waves formed can move across entire ocean basins and crash against distant shores long after the wind that formed them has stopped blowing.

If, instead of a stone, I released a drop of dye into my completely still glass of water, a different effect would occur. The momentum of the dye dropping would take the dye down into the middle of the glass. From there it would spread out in random tendrils, the edges between the dye and the water would become blurred and ultimately I would have a homogeneous (evenly mixed) solution of dye and water. But I haven't stirred or disturbed the water in the glass, so how does the dye get evenly mixed in? It is because I keep my office well above absolute zero, so the water and dye particles in the glass all have thermal energy, and this energy causes the particles to move. At the dye-water boundary, some of the dye will move out into the water and some of the water will move into the dye, blurring this boundary. With enough time this effect, diffusion, will completely mix the dye and water.

To mix in the dye faster I could stir the water in a constant circle with a chopstick. When I pull out the chopstick, the water would continue moving in a circle, which is also called an eddy, whirlpool, or vortex. The edges would be higher than the center because of centrifugal forces, that is, each water particle, once set into motion, wants to move in a straight line until it encounters the glass edge. At the edge, there is no choice except to move in a circle. A similar effect would occur if you spun the glass, or in the case of the oceans, spun the globe beneath. The effect of the spinning earth is called the coriolis force (which isn't really a force) and creates eddies in the ocean basins that spin in different directions in the north and south hemisphere. When you flush your toilet, a whirlpool often forms, but its direction doesn't depend on the hemisphere, instead it is dependent on the conditions within the toilet itself.

Perhaps I want to mix my dye and water even faster, so I put a lid on the glass and shake it. The moving water would stretch the boundary with the dye in random directions, creating more boundary surface area allowing for faster diffusion. The sloshing water can be described as turbulent, that is, the flow interacts with itself creating an element of randomness and becomes chaotic.

What I find most interesting about water, especially in the ocean, is that all of these phenomenon can happen at the same time and at all scales. On a tiny scale there can be turbulence, on a slightly larger scale there can be eddies, larger scales still may contain waves. Ultimately we reach the scale of tides, but that is a topic for another day.

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