Reacting droplets

The movie shows a system that starts to separate into two liquids (yellow and purple), just as oil and water do, but is then kept as a dynamic system of droplets that split, evaporate and form again, by a chemical reaction. This chemical reaction converts yellow molecules to purple, and then back to purple again, and this cycle drives the droplet breakup seen in the last two-thirds of the movie. This simulation is of a very bad model of liquid droplets in living cells, there is a movie here of real droplets in real living cells, from the work of Cliff Brangwynne and co-workers.

It is a bad model because, as you can see in the simulation, the droplets wobble a bit, for example when two droplets coalesce they briefly wobble as they form into a single droplet. This wobble is due to inertia, i.e., the mass of the coalescing droplets, and is suppressed by the viscosity (thickness) of the droplets. The ratio of the effect of inertia to that of viscosity is captured by what is called the Reynolds number. In the simulations above, the Reynolds number is around 0.1, whereas in the experiments it is probably at least a million times smaller — inertia is really irrelevant inside cells. Although this a big difference, I am not sure whether it rules out the above model entirely for understanding cells, or whether the Reynolds number has little effect on these processes.

During the first one-third of the simulation, I keep the reaction switched off, and you see just what happens after you have forced oil and water to mix by stirring them together. Large droplets grow, while smaller ones evaporate, and droplets coalesce — all these result in the average droplet size growing. In oil and water, these droplets just grow and grow until you have droplets large enough to see.

But one third of the way into the simulation run, I turn on a chemical reaction, and droplets that were coalescing now in some cases do the opposite, they break apart. Then in the final third of the run, I increase the reaction rate, and the system goes a bit crazy, with droplets quickly appearing and disappearing. The chemical reaction is messing with growth of the droplets, reversing it in some cases.

The droplets in cells are also controlled by chemical reactions, so some version of the above is occurring in your cells, even as you read this — just at much smaller Reynolds numbers, so with less wobbling when the tiny droplets come together.

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