Dissolving together

I am continuing to play around with systems that start to separate into two phases (the green and the red phase in the movie above) but don’t get very far before one phase (the green one) dissolves. I have tweaked some parameters above, so that green droplets form, and the system is a bit bigger (I also changed the orientation, sorry if that is confusing). if you follow the movie carefully, it seems clear that the dissolution of the green droplets is via fronts that are pretty straight (horizontal), one front that moves upwards, dissolving droplets as it goes, while another moves downwards. When they meet in the middle, the green droplets are all gone.

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Liquids that briefly come apart

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?

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A story of a Frenchman, a Baron and a paint guy

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.

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Salt fingers

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.

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What do an American Ivy League university and a Wetherspoons in Wrexham (Wales) have in common?

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.

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Rising hot air and a Baron

StruttAs 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.

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Politely disagreeing with the BBC and a teacher

Artists at All City Coffee 25I 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.

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Teaching data fitting better

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.

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