Active Model B$^-$ from Mass-Conserving Reaction-Diffusion Systems

TL;DR

This paper derives a scalar active field theory, Active Model B$^-$, from a three-component mass-conserving reaction-diffusion system, revealing how negative interfacial coefficients lead to stable microphase separation.

Contribution

It introduces Active Model B$^-$, a novel active field theory capturing microphase separation due to density-dependent interfacial effects.

Findings

Finite-wavelength instability causes microphase separation.

Active Model B$^-$ retains a state-function chemical potential.

Contrasts with unbounded coarsening in two-component systems.

Abstract

We show that the late-time dynamics of a minimal three-component mass-conserving reaction--diffusion system reduce to a scalar active field theory, Active Model B$^-$ (AMB$^-$), in which a density-dependent interfacial coefficient $\kappa(\phi)$ turns negative at high density. This drives a finite-wavelength instability and stabilises microphase-separated patterns, in contrast to the unbounded coarsening of two-component mass-conserving systems. Unlike Active Model B$^+$, AMB$^-$ retains a chemical potential that remains a state function, inherited from the underlying conservation law, but admits no equation of state for the pressure.