## Posts Tagged ‘Brownian Motion’

### Brownian Motion observed in Milk

April 11, 2012

One of the best things about working at NPL is the people one gets to work with. The other day, during a Science Ambassador meeting, James Miall and Robert Ferguson showed a live video projection of the Brownian motion of fat globules in semi-skimmed milk. (There are fat globules in milk? Ughhh!) I was blown away! The one minute video above is typical of what they projected.

I think I was supposed to have seen the demonstration as a child, but the education system failed me – not everything was perfect in the ‘old days’  ;-). When I was a lecturer I bought a ‘smoke cell’ to rectify this shortcoming in my education, but I was unable to convince even myself that I could see the effect. So in my whole life I had never seen ‘Brownian’ motion. I thought the clarity of their demo was fantastic and I loved the fact that it just used normal milk.

So what is Brownian Motion? It is the random motion of large particles caused by the motion of the much smaller molecules that are all around them. In the case above, the circles you see are the fat globules in milk suspended in water as viewed through a web-cam down a microscope. The globules vary in diameter from 0.5 to 5 micrometres. The water in which they are suspended is made of H2O molecules with are typically 0.0003 micrometres across. The picture below tries to capture scale – but I haven’t managed to draw the water molecules small enough. Brownian motion is the jiggling of the gigantic fat globules due to the motion of the tiny water molecules.

Rough indication of the relative size of water molecules (open circles) and an individual globule of fat in the movie at the head of this article (shown a giant incomplete circle). I have failed to draw the water molecules small enough to truly represent their minuscule size.

Is that really plausible? Well, it might not seem so because each fat globule weighs around 60 billion times more than a water molecule. In other words if the water molecules weighed as much as a UK penny coin (3.6 g) then in proportion the globule would weigh around 180,000 tonnes. Think about millions of people continually throwing pennies at an ocean liner: could they really move it? And consider also that there are molecules on all sides of the globule and (since their motions are random) their effect should almost exactly cancel out.

In fact that it is the explanation. And the reason that the motion is so (relatively) easily visible is due to one key fact:

• The speed of the water molecules is stupendous. On average the speed of water molecules at room temperature is around 620 metres per second – well over 1000 m.p.h.

If you are viewing this on a normal computer screen and could somehow have seen an individual water molecule move uninterrupted by collisions with its neighbours, then at this scale of viewing it would have travelled way past the orbit of the moon in one second. So although the molecular mass is tiny, their momentum (the mass multiplied by the velocity) is much larger than one might think.

So although the cancellation of the random jigglings of the water molecules is indeed almost exact, it is not quite perfect. Judging from the video – the globules jiggle at around one tenth of a globule diameter per second – which is around 0.1 micrometers per second, roughly 6 billion times slower than the average speed of the water molecules.

Putting these two factors together we see that the jiggling of the millions of molecules on either side of the fat globules can be almost perfectly balanced – but it only takes an imbalance of around 10 molecules to explain the level of jiggling observed.

Working out detailed numbers for Brownian Motion is hard, and so you won’t be surprised to find that person who sorted it all out was Albert Einstein.