Oils and water often spontaneously separate to form two coexisting liquids, one mainly oil, and one mainly water. For example, if you add olive oil to vinegar the two liquids separate out into droplets of oil in the vinegar. But at least for some oils, they mix in at least some proportions with water at higher temperatures, so you can have a single hot mixed liquid, that on cooling separates out into oil droplets in water. This is a well studied and common phenomenon. But what if you simultaneously cool, and mix in more water? For example, what if you start with with hot oil in water, with for example, 20% oil, that is sufficiently hot that water will dissolved all the oil? Then you cool to a lower temperature, where water can only dissolve say 15% oil, but at the same time you mix in an equal volume of pure water?
Just before Christmas I wrote a blog post about Baron Rayleigh’s work on convection, he showed how a layer of colder fluid (eg air or water) on top of warmer fluid, would lead to convection — flow of the colder fluid downwards to be replaced by warmer fluid from the bottom. Rayleigh’s work is a classic, and has been built on to help us understand, amongst many other things, Earth’s weather/climate. Rayleigh assumed that the flow was driven by gravity. The colder fluid on top falls because it is denser. Convection is everywhere in Earth’s atmosphere and oceans. It is sometimes called Rayleigh-Bénard convection, to honour Baron Rayleigh who developed the theory, and Henri Bénard, who did the experiments that inspired the theory.
Above is a computer simulation of a phenomenon often called salt fingers. They occur in world’s seas and oceans, for example they are common in the Caribbean. Salt fingers form when there is a layer of warm salty water above a layer of colder but less salty water. The point is that salty water is denser than less salty water, so typically a layer of salt water on top of a layer of fresher water is unstable, the denser layer on top falls down through the less dense layer below due to gravity — this is convection. However, here the water on top is not just saltier it is also warmer. This temperature difference works in the opposite direction to the difference in the amount of salt. Warmer water is less dense that cold water and so a layer of warm water floats on a layer of colder water.
I currently have 50 reports, and two dissertations to mark, and on Thursday next week I’ll have not one but two exam papers to mark. So I am taking a break from the endless marking to share with you something surprising that I have learnt, not about science but about history. My sister bought me The Silk Roads by Peter Frankopan, for Christmas, and I am enjoying reading it. The book mentions the Ivy League (i.e., posh, presitigious and expensive) Yale university in the north east of the United State, although it omits the Elihu Yale Wetherspoons pub (i.e., pub that is not posh, lacks prestige but has cheap beer) in Wrexham in north east Wales.
As I write the UK politics is in a bit of a mess. The referendum that kicked off this mess started in the actions of an Eton educated posh boy: David Cameron. But not all Eton educated posh boys have been a disaster for Britain. The picture above is of the partially-Eton-educated 3rd Baron Rayleigh, a brilliant late-Victorian scientist and genuine member of the aristocracy. Continue reading
Above is an image taken from a BBC webpage What is diffusion? – part of their Bitesize website, and aimed at 11 to 14 year olds*. So if you are from the BBC and you don’t like me using it, then just let me know and I will take it down, but the image on that page is fundamentally misleading, as I will explain. So arguably it should not appear on the BBC’s website either.
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.
One of the most useful skills we teach on the physics degree is data analysis. This is important in almost all scientific research, and it is also key to good decision making in other fields such as economics, as well as being a core part of data science — increasing numbers of our graduates are going into the growing number of careers as data scientists. One basic task in data analysis is fitting a model to noisy data, eg fitting a straight line y = mx + c to data of the form a set of points (x , y). As far as I know there is essentially complete consensus about how to determine the best values of the two fit parameters, the intercept c and the slope m. This is to minimise the sum of the squared differences between the fit function, and the data points.
I have just gotten back from the 3rd Sir Sam Edwards – New Horizons in Soft matter meeting. The meeting has an emphasis on bringing together soft matter scientists from universities and companies. As a university-based scientist it is fascinating to hear of the soft matter challenges companies face.
These vary from turning tons of potatoes into crisps, to making cosmetics that are sold for silly money.
I have just finished reading Outnumbered by David Sumpter. It is very readable, and says some interesting things about modern machine learning. Machine learning, in particular deep learning, is a hot topic at the moment, so I was curious to read about it, and about related stuff like how Facebook, Google, etc, use it.