Biological & Soft Matter Seminar: Compact expansion of a repulsive suspension

Abstarct:

We find that a suspension of particles that mutually repel by short-ranged interactions spreads compactly. In a compact expansion, the density is strictly zero beyond a cutoff distance, in contrast to diffusive expansion, where the density field gradually decays to zero. We identify that in the dense limit, where particle separation is, on average, smaller than the interaction length, the drop expands in a self-similar fashion. Starting from the pair potential, we show that in the continuum limit, the suspension's expansion follows a nonlinear diffusion equation that captures the self-similar profile of the expansion. The density profile is parabolic, and the area of the ensemble grows as the square root of time. At long times or for sparse initial conditions, the area grows logarithmically with time, and the drop stays compact. We verify the theoretical results by simulations of thousands of particles and by numerical integration of the partial differential equations. We tested the theory experimentally using colloidal particles interacting through screened Coulomb repulsion. We observe the compact expansion of the suspension, consistent with the theoretically and numerically predicted dynamics in the dilute limit.