Sedimentation of binary mixtures: Phase stacking and Nonequilibrium dynamics

Abstract

Based on equilibrium sedimentation path theory and the local density functional approximation, we investigated the effects of gravity on several relevant types of binary colloidal mixtures. Settled systems are represented by so-called sedimentation paths, which determine the variation of the species-resolved chemical potentials with altitude. Analysing the resulting line segments in the plane of chemical potentials of the bulk phase diagram allows one to rationalize the full equilibrium stacking phenomenology for a given system under gravity. The approach predicts theoretically the stacking sequences of colloidal rod-plate mixtures that were observed in iconic experiments by van der Kooij and Lekkerkerker. Thereby the occurrence of up to five simultaneous phase layers emerges naturally from the mere interplay of gravity and two-phase bulk coexistence, without invoking particle polydispersity. We studied the effects on equilibrium phase stacking upon varying the buoyant mass ratio of both components and our predictions are testable in experiments by systematic variation of the height of sedimentation columns. We have carried out similar sedimentation studies for: plate-spheres mixtures, mass-polydisperse systems, and hard spherocylinders. We suggest that microscopic particle properties, such as the buoyant mass, can be inferred from macroscopic measurements of layer thicknesses in phase stacking sequences. We addressed gravity-induced nonequilibrium flow and structure formation on the basis of power functional theory, adaptive Brownian dynamics computer simulations, and functional machine learning. Power functional theory allows one to rationalize and to model the nonequilibrium behaviour of many-body systems based on the one-body density and velocity field. We have used the approach to categorize systematically the different types of relevant nonequilibrium force contributions and have developed corresponding analytical gradient approximations. Neural functionals, as trained on the basis of both equilibrium and nonequilibrium computer simulation data, were shown to yield accurate predictions for structure formation and design of nonequilibrium flow. We have formulated force-based density functional theory and have demonstrated that neural density functionals outperform the best available hard sphere fundamental measure functionals. We have developed adaptive Brownian dynamics as a performant and highly stable numerical integration scheme for the temporal integration of overdamped many-body Langevin equations of motion, as demonstrated for a particle gel subject to convective sedimentation flow. We have put forward general frameworks for fluctuations of general hyperobservables, for their associated hyperforce correlation functions, and for the gauge invariance of statistical mechanics, where Noether's theorem yields exact sum rules that constrain correlations, as exemplified for ideal and for active sedimentation.