Storm in a Teacup: The Physics of Everyday Life(23)

The bottle that the hungry blue tit was hopping about on contained a mixture of all sorts of goodies. Most of milk (nearly 90 percent) is water, but floating around in that are sugars (that’s the lactose that some people can’t tolerate), protein molecules assembled into minuscule round cages, and bigger globules of fat. All of this is jumbled up together, but if you leave it to sit for a while, a pattern emerges. The fat globules in milk are tiny—between one and ten microns in size, which means you could fit somewhere between 100 and 1,000 of them in a line between the millimeter markers on a ruler. And those tiny blobs are less dense than the water around them. There’s less “stuff” in the same volume of space. So as they’re being jostled about with everything else, there’s a tiny difference in where they go. Gravity is pulling the water around them downward a tiny bit harder than it’s pulling the fat globules, and the fat is very gently squeezed upward. That means that the fat is ever so slightly buoyant, and will very slowly rise up through the milk.

The question is: How fast will it rise? And here’s where the viscosity of the water starts to matter. Viscosity is just a measure of how hard it is for one layer of a fluid to slide over another layer. Imagine stirring a cup of tea. As the spoon goes around, the liquid around the spoon has to move, flowing past other liquid next to it. Water isn’t very viscous, so it’s very easy for those layers to move past each other. But then think about stirring a cup of syrup. Each sugar molecule is holding on to the ones around it very firmly. To move these molecules past each other, you’ve got to break those bonds before the molecules can move on. So it’s hard work to shunt the fluid about, and we say that the syrup is viscous.

In the milk, the fat globules are pushed upward because they’re buoyant. But if they want actually to move upward, they have to shove the liquid around them out of the way. As part of that pushing process, the nearby liquid has to slide over itself, so its viscosity matters. The more viscous it is, the more resistance there is to the fat globules rising.

Right under the blue tit’s feet, this battle is going on. Each fat globule is being pushed upward by its buoyancy, but it experiences a drag force because of the liquid around it having to move to let it pass. And the same forces acting on the same sort of fat globule come to a different compromise for different globule sizes. The drag has a much greater effect when you’re small, because you have a large surface area relative to your mass. You’ve only got a small buoyancy to use to shove quite a lot of the surrounding stuff out of the way. So even though the smaller fat globule is in exactly the same liquid, it rises more slowly than a bigger one. In the world of the small, viscosity generally trumps gravity. Things move slowly. And your exact size matters a lot.

In the milk, the larger fat globules rise faster, bump into some smaller, slower ones, and stick to them, forming clusters. These clusters experience less drag for their buoyancy because they’re even bigger than individual globules, so they rise even faster. The blue tit just has to sit and wait at the top, and breakfast will arrive at its feet.

And then came homogenization.? Milk manufacturers worked out that if they squeezed the milk at very high pressure through very tiny tubes, they could break up the fat globules and reduce their diameter by about a factor of five. That reduces the mass of each one by a factor of 125. Now the weedy upward buoyant push on each globule provided by gravity is completely overwhelmed by viscous forces. The homogenized fat globules rise so slowly that they might as well not bother.§ Just making them smaller shifts the battle into different terrain where viscosity can score a clear victory. Cream won’t rise to the top anymore. The blue tits had to find another source of breakfast.

So the forces are the same, but the hierarchy is different.? Both gases and liquids have viscosity—even though gas molecules don’t stick to each other like the ones in liquids, they jostle each other a lot, and the giant game of bumper cars has the same effect. This is why an insect and a cannon ball don’t fall at the same speed unless you take all the air away and drop them in a vacuum. Air viscosity matters a lot for the insect, and hardly at all for the cannon ball. If you take the air away, gravity is the only force that matters in both cases. And a tiny insect trying to fly in air uses the same techniques that we use to swim in water. Viscosity dominates their surroundings, just as it does ours in the pool. The smallest insects are swimming through air much more than they’re flying through it.

Homogenized milk demonstrates the principle, but its application goes far beyond the doorstep. Next time you sneeze, you might want to think about the size of the droplets you’re spraying around the room. What stops cream going up also stops disease coming down.

Tuberculosis has been with humans for millennia. The earliest record of it is in ancient Egyptian mummies from 2400 BCE; Hippocrates knew it as “phthisis” in 240 BCE, and European royalty were called upon to cure the “king’s evil” in medieval times. As the Industrial Revolution drove people to live in towns, “consumption,” the disease of the urban poor, was responsible for a quarter of all deaths in England and Wales in the 1840s. But it wasn’t until 1882 that the culprit was found, a tiny bacterium called mycobacterium tuberculosis. Charles Dickens described the common sight of consumptives coughing, but he couldn’t write about one of the most important aspects of the malady, because he couldn’t see it. Tuberculosis is an airborne disease. Carried out of the lungs with each cough are thousands of fluid droplets, plumes of minuscule crusaders. Some of them will contain the tiny rod-shaped TB bacteria, each only one ten-thousandth of an inch long. The fluid droplets themselves start off fairly big, perhaps one hundredth of an inch. These droplets are being pulled downward by gravity and once they hit the floor, at least they’re not going anywhere else. But it doesn’t happen quickly, because it’s not just liquids that are viscous. Air is too—it has to be pushed out of the way as things move through it. As the droplets drift downward, they are bumped and jostled by air molecules that slow their descent. Just as the cream rises slowly through viscous milk to the top of the bottle, these droplets are on course to slide through the viscous air to reach the floor.