Nonequilibrium mixture dynamics: A model for mobilities and its consequences

TL;DR

This paper extends Model B to derive a mobility matrix for liquid mixtures, revealing two distinct regimes and providing analytical and simulation results for multi-component dynamics after a thermal quench.

Contribution

It introduces a new approximate mobility matrix depending on a single parameter, unifies existing models, and analyzes mixture dynamics with analytical and simulation validation.

Findings

Identification of two mobility regimes: collective motion and interdiffusion.

Analytical solutions for two- and three-component systems match Monte Carlo simulations.

Observation of transient fractionation phenomena during mixture evolution.

Abstract

Extending the famous Model B for the time evolution of a liquid mixture, we derive an approximate expression for the mobility matrix that couples the different mixture components. This approach is based on a single component fluid with particles that are artificially grouped into separate species labelled by ``colors''. The resulting mobility matrix depends on a single dimensionless parameter, which can be determined efficiently from experimental data or numerical simulations, and includes existing standard forms as special cases. We identify two distinct mobility regimes, corresponding to collective motion and interdiffusion, respectively, and show how they emerge from the microscopic properties of the fluid. As a test scenario, we study the dynamics after a thermal quench, providing a number of general relations and analytical insights from a Gaussian theory. Specifically, for systems with two or three components, analytical results for the time evolution of the equal time correlation function compare well to results of Monte Carlo simulations of a lattice gas. A rich behavior is observed, including the possibility of transient fractionation.