Tag Archives: viscosity

Reynolds’ World

What’s it like for little things like bacteria to move around? How do they swim from place to place?

We know that swimming feels different from walking. Part of it is the feeling of being suspended, where instead of the firm solidity of the earth and the  insubstantial give of air, we have the water on all sides, supporting not just our feet but our legs, arms, and body. But also, it’s a lot harder to move through water! The same quality that makes us feel supported also impedes movement, so that even a very efficient swimmer will be easily outpaced by someone strolling along on dry land.

Scientists have a way to quantify that  difference, using a measure called the Reynolds number. The Reynolds number compares how strong inertial forces are in a fluid, which come from the particle size and the weight of the particles, with the viscosity of the fluid. If a fluid has low inertial forces compared to its viscosity, it has a low Reynolds number, and if it has high viscosity compared to its inertial forces, then its Reynolds number is low. So fluids with a high Reynolds number are easier to move through, and fluids with a low Reynolds number are harder to move through. The pitch of the Trinity pitch drop would have a very low Reynolds number! And fluid flow in high Reynolds number environments tends to have more chaos, vortices and eddies that can arise because of how easy it is to move light things that don’t stick together, like molecules of air.

So it turns out that what strategy you use to move in a low Reynolds number environment is different from what you’d use in a high Reynolds number environment. Of course, we already know that, because if we try to walk or run in water, it doesn’t work very well! Running is a great way to get around when you are moving through thin air with the solid ground beneath you, but humans have developed various modes of swimming for water, that take advantage of our anatomy and account for the different nature of water.

But remember, we are largely made up of water! So what about our moving cells and bacteria, which have to get around in a low Reynolds number environment all the time? And keep in mind that our cells are very small, subject to molecular forces and a lot closer to the size of water molecules than we are. Not surprisingly, there are different forms of swimming that take place in our cells. One of the most common is using a rotating propeller, a little like the blade on a helicopter, to move forward. These structures are called flagella and are common on the surface of various types of cells, to use rotary motion as a way of easily moving through the high Reynolds number environment.

So the next time you are walking around with ease, take a moment to imagine how different it is for everything moving from place to place in and around your cells. It is a whole different world, right inside our own!

Pitch and Viscosity

For the last 69 years, there has been an experiment running at Trinity College Dublin where I work, consisting of a glass funnel with pitch tar inside that is very slowly dripping out. Pitch is an extremely slow-moving fluid, so each drop takes about ten years to form and fall, and this is the first time it’s been captured on video:

Even knowing that pitch is extremely slow-moving and viscous, I still felt an expectation watching the video that once the drop fell, it would merge with the bottom pitch. But of course it doesn’t: it falls over, and that merging will take a long time. Pitch is twenty billion times more viscous than water; for comparison, honey is only about a thousand times more viscous. So pitch flows more slowly and is harder to stir, but why?

Picture a drop of liquid up close. The liquid is comprised of molecules, which are moving somewhat freely but also interacting with each other (if they were moving completely independently, the substance would be a gas). But the molecules at the edge of the drop are experiencing additional forces, interacting with either the air or the container around the drop in addition to the other molecules in the drop. So if we tilt the drop, or try to push it through a tube, those edge molecules are going to flow more slowly, if they are next to a containing wall, or more quickly, if they are next to air. Different layers in the liquid are more or less easy to move, and this means that under the same impetus to flow, the layers end up moving at different speeds. So there is actually friction within the drop, between different layers of molecules! The friction due to intermolecular interactions is stronger in some liquids than others, which is where we get high-viscosity liquids like pitch and low-viscosity liquids like water. Both are subject to the same physical laws, but the strength of intermolecular forces slows the pitch down by an incredible amount. And that’s the microscopic explanation for the macroscopic phenomenon we call viscosity.

For more about an older and better known pitch drop experiment in Australia, which has yet to drop, and differing senses of time in general, I heartily recommend this Radiolab episode.