# Compact expansion of a repulsive suspension

## TL;DR

This paper demonstrates that repulsive particles spread in a compact manner with a sharp boundary, exhibiting distinct self-similar expansion regimes driven by interactions and thermal motion.

## Contribution

It introduces a unified theory combining simulations and experiments to describe the compact spreading of repulsive suspensions across different regimes.

## Key findings

- Particles spread with a sharp boundary unlike Brownian diffusion.
- Two self-similar regimes: $t^{1/4}$ and $t^{1/2}$ expansions.
- A logarithmic growth links the two regimes.

## Abstract

Short-range repulsion governs the dynamics of matter from atoms to animals. Using theory, simulations, and experiments, we find that an ensemble of repulsive particles spreads compactly with a sharp boundary, in contrast to the diffusive spreading of Brownian particles. Starting from the pair interactions, at high densities, the many-body dynamics follow non-linear diffusion with a self-similar expansion, growing as $t^{1/4}$; At longer times, thermal motion dominates with the classic $t^{1/2}$ expansion. A logarithmic growth controlled by nearest-neighbor interactions connects the two self-similar regimes.