Coexistence of patterned phases in chemically active multicomponent mixtures

TL;DR

This paper develops a theoretical framework to understand complex stationary patterns in chemically active multicomponent mixtures by combining phase separation and reaction-diffusion processes.

Contribution

It introduces a Lyapunov functional and a generalized Gibbs phase rule to predict coexisting patterns in chemically active mixtures, advancing understanding of pattern formation.

Findings

Identified a Lyapunov functional for certain chemical reactions.

Derived a generalized Gibbs phase rule for pattern coexistence.

Demonstrated modular creation of complex patterns from independent phases.

Abstract

Chemically active mixtures exhibit complex patterns that emerge from the interplay of physical interactions and reactions among components. Individually, these two processes are well-understood: Physical interactions can give rise to phase separation, whereas reactions can form reaction-diffusion patterns. To understand the combination of both processes, we identify a Lyapunov functional for a class of chemical reactions. By minimizing this functional, we identify a generalized Gibbs phase rule that governs the number of coexisting patterns, and we demonstrate that complex patterns can be created by the modular combination of independent phases. Our theory unveils complex stationary patterns in chemically active mixtures and provides a framework for analyzing more complex systems.