Convection of gloopy stuff

Convection is a fact of life, it is occurring right now in the air around your body. Your body temperature of 37 C is higher than the room temperature, so your body heat is warming air, and this warm air is rising — which is convection. Warm air is lighter than colder air and so due to gravity the lighter warmer air rises, and the heavier colder air falls. So convection occurs in the air in the rooms of your house and place of work. Convection is also key to how both the Earth’s atmosphere and oceans behave. Hot air is constantly rising in the atmosphere, and dense water is constantly falling in the oceans (and seas, lakes, …).

In the Earth’s oceans, water is denser and so falls, not just because it is colder but often because it contains more salt. The saltier water is the denser it is, and so if say a river of fresh water enters an ocean and flows beneath a salty ocean-water layer, then the dense salty water will fall under gravity, so driving convection near the river mouth, and mixing the fresh river water and salty ocean water.

All this is well known, earth scientists have been studying convection for many decades.

But convection occurs even in small volumes, centimetres across and smaller, and pretty much any mixing of two different solutions will result in convection. In pretty much any two solutions, one will almost always be denser than the other. This includes mixing things like polymer or soap solutions, with water. Some collaborators of mine are mixing a water-soluble polymer (called PEG — a very common polymer that is probably in at least some of your shower gels, shampoos, etc) with water. So I am interested in how convection affects this mixing.

Oddly, there seems to have been very little work on this, despite it being a bit more interesting than convection in salty water. With salty water, the larger the difference in the amount of salt between the two mixing solutions, the faster the convection. With polymers it is not so simple. If you have enough polymer then two things happen, the polymer molecules push on each other speeding up the diffusion of the polymer molecules, and the solution becomes thick and gloopy, which slows the flows occurring in convection.

So if you mix water and polymer solution, then there is an optimal amount of polymer in the solution, at which convection is fastest. Any less than that, and the water and polymer solutions have similar densities and so convection is slow, any more and the polymer solution is so gloopy that convection is also slow. This result follows basically trivially from what we know of polymer solutions, but as far as I know it is not in the scientific literature. As the result is so simple to derive, and refers to such a common process, I am a bit surprised that it has not been studied before, but it is hard to predict what has and what has not attracted the attentions of earlier scientists.

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