Statistical and Biological Physics

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Binary Mixtures of Particles with Different Diffusivities Demix

Simon Weber, Christoph Weber, Erwin Frey

According to the Einstein-Stokes relation different Brownian particles of equal size must have the same diffusion constant. However, particle diffusion or motility can also originate from non-thermal, active processes. In this case equal-sized particles can indeed exhibit different diffusivities or motilities. Throughout the last 5 years the influence of size differences, shape, mass and persistent motion on phase separation of active particle systems has been intensively studied.

For binary mixtures, however, former research focused on particles with pronounced persistence in motion, while the exclusive role of differences in diffusion constants remains elusive. We considered a binary mixture of spherical, equal-sized particle species with different diffusion constants interacting only through excluded volume. We find an effective attraction between the less diffusive particles due to caging by the surrounding species of higher diffusivity. This leads to a demixing process between the particle species for systems above a critical size: A single cluster develops solely consisting of the species of lower diffusion constant, which is surrounded by the species of higher motility. We characterize the system’s behavior in terms of diffusivity differences and particle density, finding that demixing is favored for larger relative differences in the diffusion constants and for larger overall packing fractions.

We believe that our findings on phase-separation in binary mixtures of equal-sized particles is of interest to a broad audience of physicists since it constitutes a further example of how activity can give rise to demixing far from thermal equilibrium. We hope to stimulate experimentalists to test our predictions by discussing three potential experimental setups.