Hierarchical microphase separation in non-conserved active mixtures

TL;DR

This paper introduces a new model combining two mechanisms of time-reversal symmetry breaking in active mixtures, revealing a hierarchical microphase separation with nested droplet structures.

Contribution

The paper develops Model AB+ that integrates two TRS-breaking mechanisms, demonstrating a novel hierarchical microphase separation in active mixtures.

Findings

Hierarchical microphase separation with nested droplets.

Large droplets of fluid 2 contain smaller fluid 1 droplets.

The phenomenon occurs at slow reaction rates.

Abstract

Non-equilibrium phase separating systems with reactions can break time-reversal symmetry (TRS) in two distinct ways. Firstly, the conservative and non-conservative sectors of the dynamics can be governed by incompatible free energies; when both sectors are present, this is the leading-order TRS violation, captured in its simplest form by 'Model AB'. Second, the diffusive dynamics can break TRS in its own right. This happens only at higher order in the gradient expansion (but is the leading behaviour without reactions present) and is captured by 'Active Model B+' (AMB+). Each of the two mechanisms can lead to microphase separation, by quite different routes. Here we introduce Model AB+, for which both mechanisms are simultaneously present, and show that for slow reaction rates the system can undergo a new type of hierarchical microphase separation, whereby a continuous phase of fluid 1 contains large droplets of fluid 2 within which small droplets of fluid 1 are continuously created and then absorbed into the surrounding fluid-1 phase. In this state of 'bubbly microphase separation' the small-scale 1-in-2 droplets arise by the conservative diffusive dynamics with the larger scale 2-in-1 structure governed by the nonconservative reactions.