Critical phase behavior in multi-component fluid mixtures: Complete scaling analysis

TL;DR

This paper develops a comprehensive scaling analysis of critical phase behavior in multi-component fluid mixtures, incorporating pressure mixing effects, and validates predictions with simulations of polydisperse Lennard-Jones fluids.

Contribution

It introduces a complete scaling formalism for multi-component mixtures, including pressure mixing, and provides new scaling laws for various phase coexistence curves.

Findings

Pressure mixing significantly affects critical behavior near the critical point.

Scaling laws accurately describe cloud and shadow curves in polydisperse mixtures.

Numerical validation confirms the relevance of pressure mixing effects close to criticality.

Abstract

We analyze the critical gas-liquid phase behavior of arbitrary fluid mixtures in their coexistence region. We focus on the setting relevant for polydisperse colloids, where the overall density and composition of the system are being controlled, in addition to temperature. Our analysis uses the complete scaling formalism and thus includes pressure mixing effects in the mapping from thermodynamic fields to the effective fields of 3D Ising criticality. Because of fractionation, where mixture components are distributed unevenly across coexisting phases, the critical behavior is remarkably rich. We give scaling laws for a number of important loci in the phase diagram. These include the cloud and shadow curves, which characterise the onset of phase coexistence, a more general set of curves defined by fixing the fractional volumes of the coexisting phases to arbitrary values, and conventional coexistence curves of the densities of coexisting phases for fixed overall density. We identify suitable observables (distinct from the Yang-Yang anomalies discussed in the literature) for detecting pressure mixing effects. Our analytical predictions are checked against numerics using a set of mapping parameters fitted to simulation data for a polydisperse Lennard-Jones fluid, allowing us to highlight crossovers where pressure mixing becomes relevant close to the critical point.