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On toothpaste and disappearing kangaroos

I don't often talk about technical topics on this site. Indeed, in general I try to talk about things I may not know about at all - facts only get in the way of "interesting" opinions (unless you have your opinion first and try to only read facts you will agree with and ignore or discredit those you don't). Anyway, today I am going to discuss one of the biggest controversies in rheology - the existence or otherwise of a yield stress. By the way, for this post, I will accept and post anonymous requests for clarification of any scientific concepts.

A yield stress is where a material requires a certain amount of stress (which is force over area - so either a bigger force being applied, or it being applied over a smaller area, will result in a bigger stress) before it will flow. The reason why this has come to mind at the moment is that this week, both Welsh tutors, independently, said "dyfal donc adir y garreg" (steady tapping and the rock breaks), which is, of course, saying that a yield stress doesn't exist.

In case you are confused about why there should be a controversy - surely if it exists we can measure it and if not, know why not? - well, the problem, as with all problems in rheology, is one of time. In the bible, the judge Deborah sang a song of praise in which she sang, "and the mountains flowed before God", thereby inventing the Deborah number and a concept of the importance of time of observation. Like mountains, everything will flow given a force being applied (such as gravity, which wasn't invented until much later - people floated upside-down until the 17th century), but you have to actually watch it for long enough. If you observe a mountain over a human life, you won't notice any change. But if you observe a mountain over the timescales available to an immortal being, it will flow. Slowly. You may think watching paint dry is boring. Imagine watching a mountain flow...

There are more physically rigorous arguments proving the nonexistence of a yield stress, but it is so much more entertaining when the bible is relied upon as a scientific source. Besides, as readers of my writing will know, just because it doesn't exist doesn't mean it isn't important. I will explain its importance shortly, but first I will explain the controversy. Basically, even though it doesn't exist, we can measure it.

Let's say I get a really viscous (thick) liquid. Let's say that, at a given stress, it will not respond strongly enough to overcome the friction in the measuring system (in scientific measurements, the measured zero rarely equals the actual zero), so it will seem like there is no motion, so the fluid hasn't yielded, whereas once you get above a critical value, you will suddenly "see" flow, so you will measure a yield stress.

Now, let's say you have a material - silly putty, for example - which will flow in about a minute. Silly putty is a pretty cool material - you can sculpt it or roll it into a ball and bounce it against a wall and it will act like it is solid, but if you leave it, it will begin to flow gradually after a minute, but you will probably only notice it after a few minutes. So if you measure it at a low stress in a few seconds, it will seem solid, while if you take an hour to measure it, it will seem like a liquid - so depending on the time you take to measure it will affect whether you see a yield stress or not.

Anyway, why is a yield stress important? Well, commercially, when you squeeze your toothpaste (a common "yield stress" material), you want it to flow. But when it reaches your toothbrush, you want it to stay there until you brush your teeth.

Environmentally, tailings dams for mining waste show a yield stress at the top. This is very important if you are a small wallaby with big feet. Remembering that stress is force divided by area, the relatively small mass and big feet enable the wallaby to hop across tailings dams safely. There are wallabies who owe their existences to the yield stress (even if it doesn't exist). Unfortunately for kangaroos, with much larger bodies but only slightly larger feet, a larger weight over only slightly larger feet makes the stress they impose larger - they overcome the yield stress, and goodbye kangaroo.

So to summarise, given a liberal slant, old sayings and folk proverbs can be applied to "prove" scientific concepts by taking them out of context...


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