Suppression of coarsening and emergence of oscillatory behavior in a Cahn-Hilliard model with nonvariational coupling

TL;DR

This paper studies a two-field Cahn-Hilliard model with variational and nonvariational coupling, revealing how activity can suppress coarsening and induce oscillatory and drifting states, with implications for passive and active mixtures.

Contribution

It introduces a detailed analysis of how nonvariational coupling affects coarsening suppression and oscillatory behavior in a generalized Cahn-Hilliard model.

Findings

Nonvariational coupling can suppress coarsening.

Activity induces oscillatory and drifting states.

Bifurcation analysis reveals complex behaviors related to conservation laws.

Abstract

We investigate a generic two-field Cahn-Hilliard model with variational and nonvariational coupling. It describes, for instance, passive and active ternary mixtures, respectively. Already a linear stability analysis of the homogeneous mixed state shows that activity not only allows for the usual large-scale stationary (Cahn-Hilliard) instability of the well known passive case but also for small-scale stationary (Turing) and large-scale oscillatory (Hopf) instabilities. In consequence of the Turing instability, activity may completely suppress the usual coarsening dynamics. In a fully nonlinear analysis we first briefly discuss the passive case before focusing on the active case. Bifurcation diagrams and selected direct time simulations are presented that allow us to establish that nonvariational coupling (i) can partially or completely suppress coarsening and (ii) may lead to the emergence of drifting and oscillatory states. Throughout, we emphasize the relevance of conservation laws and related symmetries for the encountered intricate bifurcation behavior.