Diffuvisity Induced Segregation

It takes only a small difference in size or shape for particles to spontaneously demix. The famous "Brazil Nut Effect" is one common example.

There are perhaps sociological analogs, where racial, income-based, or religious clustering arises from small differences. A Google or Google-Scholar search for "auto-segregation" or  "self-segregation" brings out many of these examples.

It was with much interest that I read "Binary Mixtures of Particles with Different Diffusivities Demix" (paywalled). The abstract reads:

The influence of size differences, shape, mass, and persistent motion on phase separation in binary mixtures has been intensively studied. Here we focus on the exclusive role of diffusivity differences in binary mixtures of equal-sized particles. We find an effective attraction between the less diffusive particles, which are essentially caged in the surrounding species with the higher diffusion constant. This effect leads to phase separation for systems above a critical size: A single close-packed cluster made up of the less diffusive species emerges. Experiments for testing our predictions are outlined.

There is a non-paywalled video that shows the demixing process in the supplemental materials section.

Here is a decent commentary:

Soluble substances normally become evenly distributed throughout the solvent medium, thanks to passive molecular diffusion. The rate at which this occurs depends on the diffusion constant of the molecule concerned, whose magnitude increases with the temperature. In mixtures that have attained thermal equilibrium, particles of equal size normally exhibit the same diffusion constant. "We were interested in what happens when particles of equal size differ in their diffusion constants," says Simon Weber, first author on the new paper.