Strong Phase Separation in a Model of Sedimenting Lattices

TL;DR

This paper demonstrates that sedimenting crystals can exhibit robust, long-range phase separation due to barriers to remixing, with a model showing persistent macroscopic separation even at high noise levels.

Contribution

It introduces a lattice model with coupled species that exhibits strong phase separation driven by long-range interactions, a novel insight into sedimenting crystal behavior.

Findings

Phase separation persists at all temperatures and noise levels.

Long-range interactions cause the phase separation.

Steady state involves slow logarithmic approach due to barriers.

Abstract

We study the steady state resulting from instabilities in crystals driven through a dissipative medium, for instance, a colloidal crystal which is steadily sedimenting through a viscous fluid. The problem involves two coupled fields, the density and the tilt; the latter describes the orientation of the mass tensor with respect to the driving field. We map the problem to a 1-d lattice model with two coupled species of spins evolving through conserved dynamics. In the steady state of this model each of the two species shows macroscopic phase separation. This phase separation is robust and survives at all temperatures or noise levels--- hence the term Strong Phase Separation. This sort of phase separation can be understood in terms of barriers to remixing which grow with system size and result in a logarithmically slow approach to the steady state. In a particular symmetric limit, it is shown that the condition of detailed balance holds with a Hamiltonian which has infinite-ranged interactions, even though the initial model has only local dynamics. The long-ranged character of the interactions is responsible for phase separation, and for the fact that it persists at all temperatures. Possible experimental tests of the phenomenon are discussed.