Active Cahn--Hilliard theory for non-equilibrium phase separation: quantitative macroscopic predictions and a microscopic derivation

TL;DR

This paper develops a comprehensive active Cahn-Hilliard theory that accurately predicts phase separation phenomena in active systems by deriving it from microscopic particle models, surpassing previous weak-separation assumptions.

Contribution

It introduces an active Cahn-Hilliard model with all terms up to fourth spatial derivatives, derived systematically from microscopic particle dynamics, enabling precise predictions of phase behavior.

Findings

Accurate computation of binodals and interfacial tensions for active systems.

Identification of previously missed contributions in continuum theories.

Enhanced agreement between theory and particle simulations.

Abstract

Phase-separating active systems can display phenomenology that is impossible in equilibrium. The binodal densities are not solely determined by a bulk (effective) free energy, but also affected by gradient terms, while capillary waves and Ostwald processes are determined by three distinct interfacial tensions. These and related phenomena were so far explained at continuum level using a top-down minimal theory (Active Model B+). This theory, by Taylor-expanding in the scalar order parameter (or density), effectively assumes that phase separation is weak, which is not true across most of the phase diagram. Here we develop a quantitative account of active phase separation, by introducing an active counterpart of Cahn-Hilliard theory, constructing the density current from all possible terms with up to four spatial derivatives without Taylor-expanding in the density. From this O(grad^4) theory, we show how to compute binodals and interfacial tensions for arbitrary choices of the five density-dependent 'coefficient functions' that specify the theory (replacing the four constant coefficients of Active Model B+). We further consider a particle model composed of thermal quorum-sensing active particles (tQSAPs) yielding a fully specified example of the O(grad^4) theory upon coarse-graining. We find that to coarse-grain consistently at O(grad^4) requires a novel procedure, based on multiple-scale analysis, to systematically eliminate fast-evolving orientational moments. Using this, we calculate from microscopic physics all five coefficient functions of the active Cahn-Hilliard theory for tQSAPs. We identify contributions that were missed in previous continuum theories, and show how neglecting them becomes justified only in the limit of large quorum-sensing range parameter. Comparison with particle simulations of tQSAPs shows that our O(grad^4) theory improves on previous continuum models [...]