Structure Factor of a Phase Separating Binary Mixture with Natural and Forceful Interconversion of Species

TL;DR

This paper develops a theoretical framework for understanding the structure factor in a binary mixture undergoing phase separation with interconversion, validated by simulations, revealing how external forces influence domain size.

Contribution

It introduces a modified Cahn-Hilliard-Cook theory incorporating interconversion dynamics and external forcing, providing new insights into nonequilibrium phase separation.

Findings

Qualitative agreement between theory and simulations.

Prediction of steady-state domain size from the structure factor.

Identification of the role of external forces in phase domain evolution.

Abstract

Using a modified Cahn-Hilliard-Cook theory for spinodal decomposition in a binary mixture that exhibits both diffusion and interconversion dynamics, we derive the time-dependent structure factor for concentration fluctuations. We compare the theory and obtain a qualitative agreement with simulations of the temporal evolution of the order parameter and structure factor in a nonequilibrium Ising/lattice-gas hybrid model in the presence of an external source of forceful interconversion. In particular, the characteristic size of the steady-state phase domain is predicted from the lower cut-off wavenumber of the amplification factor in the generalized spinodal-decomposition theory.