Politely disagreeing with the BBC and a teacher

I am currently teaching biological physics to third-year physics undergraduates. As part of this I teach about how living organisms acquire food molecules, oxygen etc, and how large living organisms, such as ourselves, transport these food molecules, oxygen, etc around our bodies. A fundamental point that I make, is that diffusion is only fast enough to support the demands of life when the movement is over very small distances, around 1 mm or less. Over distances more than very roughly 1 mm, some sort of flow is required to move molecules around. Over distances of centimetres, metres and above, diffusion is very very slow.

For the course, I like to link to webpages with good explanations, pretty pictures etc, and so I Googled diffusion, and one page I looked at was BBC webpage for schools called What is diffusion? At the time writing (24/11/2018), this page includes the text:

“You walk into a coffee shop and immediately smell coffee. Why?

The answer is diffusion. In a coffee shop, the coffee particles move from the coffee machine (an area of high concentration) to the rest of the coffee shop (an area of low concentration).”

This is quite misleading. I contacted the BBC, but the  web form only allowed 500 characters so I couldn’t explain to them what the problem is. They, I think, checked with a teacher they consult. Apparently that teacher thought that the text just above is correct, so the BBC did not want to change it. I don’t want to disagree with a teacher, but they are not right.

As I have more than 500 characters, I can explain.

The time taken to diffuse a distance x is given approximately by: time t = x²/D , where D is the diffusion constant. The diffusion constant for oxygen in air D = 10-5 m2/s. So if the coffee machine is say 10 m from the door, it takes 102/10-5=107 s or about 4 months for oxygen to diffuse from near the coffee machine to your nose, if you stand near the door. The coffee aroma molecules are bigger than oxygen, so diffuse a bit more slowly. So, it would take about 1 year for the molecules that give coffee its distinctive aroma, to diffuse across a typical coffee shop.

Of course, if the barista starts grinding coffee, then you expect to be able to smell it in minutes, not a year. This is because the aroma does not move from the coffee grinder to your nose by diffusion*, but by air flow. The air inside any coffee shop will not be still, it will flow. Customers will open the door, creating draughts, hot air rising from the espresso machine will create convection air currents, and so on. Even if on average air moves at a few centimetres per second, then in a few minutes it will cross a distance of 10 m.

So air flow is the reason you smell delicious coffee aromas within minutes of hearing the coffee grinder start. With only diffusion you would have to wait a year to smell it.

So, I would say the above text is a little misleading. And the distinction between diffusion and flow is important. The fact that diffusion is hopelessly slow over distances of centimetres, metres and more, is why we have a heart. If diffusion could transport oxygen around our bodies (that are a lot smaller than coffee shops, hence many humans can fit inside one coffee shop) then we would not need a heart. Oxygen could diffuse from our lungs to our brain, to our toes, to our fingers, … But diffusion is nowhere near fast enough, flow is required and so our heart needs to beat every minute of our lives to keep this flow of blood going.

* To be fair to the BBC, the last few micrometres inside your nose and onto the smell receptors in your nose will involve diffusion. But crossing the coffee shop is definitely not diffusion.