Systematic extension of the Cahn-Hilliard model for motility-induced phase separation

Abstract

We consider a continuum model for motility-induced phase separation (MIPS) of active Brownian particles [J. Chem. Phys. 142, 224149 (2015)]. Using a recently introduced perturbative analysis [Phys. Rev. E 98, 020604(R) (2018)], we show that this continuum model reduces to the classic Cahn-Hilliard (CH) model near the onset of MIPS. This makes MIPS another example of the so-called active phase separation. We further introduce a generalization of the perturbative analysis to the next higher order. This results in a generic higher order extension of the CH model for active phase separation. Our analysis establishes the mathematical link between the basic mean-field MIPS model on the one hand, and the leading order and extended CH models on the other hand. Comparing numerical simulations of the three models, we find that the leading order CH model agrees nearly perfectly with the full continuum model near the onset of MIPS. We also give estimates of the control parameter beyond which the higher order corrections become relevant and compare the extended CH model to recent phenomenological models.

arXiv comment10 pages, 5 figures

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• Coexistence of active Brownian discs: Van der Waals theory and analytical results
• Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production
• Critical behavior of active Brownian particles: Connection to field theories
• Field-Theory of Active Chiral Hard Disks: A First-Principles Approach to Steric Interactions
• Nonreciprocity induces resonances in two-field Cahn-Hilliard model
• Stationary broken parity states in active matter models
• Coexistence of uniform and oscillatory states resulting from nonreciprocity and conservation laws
• Bifurcations of front motion in passive and active Allen-Cahn-type equations
• Periodic patterns displace active phase separation
• Motility-induced crystallization and rotating crystallites
• Active Cahn-Hilliard theory for nonequilibrium phase separation: quantitative macroscopic predictions and a microscopic derivation
• Derivation and Analysis of Amplitude Equation for Generalized AMB+ in Presence of Chemical Reaction