Superadiabatische Kräfte und dynamischer Strukturzerfall in Flüssigkeiten
Zusammenfassung der Projektergebnisse
In the project several studies were carried out that ultimately lead to novel insights into the decay of liquid structure. We give an overview in the following. We have initially presented an explicit and simple approximation for the superadiabatic excess (over ideal gas) free power functional, admitting the study of the nonequilibrium dynamics of overdamped Brownian many-body systems. The functional depends on the local velocity gradient and is systematically obtained from treating the microscopic stress distribution as a conjugate field. The resulting superadiabatic forces are beyond dynamical density functional theory and are of a viscous nature. The high accuracy of the theoretical results was demonstrated by comparison to simulation results. Subsequently we have identified a structural one-body force field that sustains spatial inhomogeneities in nonequilibrium overdamped Brownian many-body systems. This structural force is perpendicular to the local flow direction, it is free of viscous dissipation, it is microscopically resolved in both space and time, and it can stabilize density gradients. From the time evolution in the exact (Smoluchowski) low-density limit, Brownian dynamics simulations, and a novel power functional approximation, we have obtained a quantitative understanding of viscous and structural forces, including memory and shear migration. We have studied the Brownian dynamics of hard spheres under spatially inhomogeneous shear, using event-driven Brownian dynamics simulations and power functional theory. We examined density and current profiles both for steady states and for the transient dynamics after switching on and switching off an external square wave shear force field. We have found that a dense hard sphere fluid undergoes global motion reversal after switching off the shear force field. We used power functional theory with a spatially nonlocal memory kernel to describe the superadiabatic force contributions and obtained good quantitative agreement of the theoretical results with simulation data. The theory provides an explanation for the motion reversal: internal superadiabatic nonequilibrium forces that oppose the externally driven current arise due to memory after switching off. The effect is genuinely viscoelastic: in steady state, viscous forces oppose the current, but they elastically generate an opposing current after switch-off. Using Brownian dynamics simulations, we investigated the response to shear of a two-dimensional system of quasihard disks that are confined in the velocity gradient direction by a smooth external potential. Shearing the confined system leads to a homogenization of the one-body density profile. In order to rationalize this deconfinement effect, we have split the internal one-body force field into adiabatic and superadiabatic contributions. The superadiabatic force field consists of viscous and of structural contributions. An empirical scaling law yields results for the superadiabatic force profiles both in the flow and in the gradient direction, in excellent agreement with the simulation data. Calculating one-body density profiles in equilibrium via particle-based simulation methods involves counting of events of particle occurrences at (histogram-resolved) space points. We provided an alternative method based on a histogram of the local force density. Via an exact sum rule, the density profile is obtained with a simple spatial integration. The method circumvents the inherent ideal gas fluctuations. We have tested the method in Monte Carlo, Brownian dynamics, and molecular dynamics simulations. The results carry a statistical uncertainty smaller than that of the standard counting method, reducing computation time. When an external field drives a colloidal system out of equilibrium, the ensuing colloidal response can be very complex, and obtaining a detailed physical understanding often requires case-by-case considerations. To facilitate systematic analysis, we presented a general iterative (custom flow) scheme for the determination of the unique external force field that yields prescribed inhomogeneous stationary or time-dependent flow. The computer simulation method is based on the exact one-body force balance equation and allows to specifically tailor both gradient and rotational velocity contributions, as well as to freely control the one-body density profile. Hence, compressibility of the flow field can be fully adjusted. The practical convergence to a unique external force field demonstrates the existence of a functional map from both velocity and density to external force field, as predicted by the power functional variational framework. Dispersed colloidal particles that are set into systematic motion by a controlled external field constitute excellent model systems for studying structure formation far from equilibrium. We have identified a unique demixing force that arises from repulsive interparticle interactions in driven binary colloids. The corresponding demixing force density is resolved in space and in time and it counteracts diffusive currents which arise due to gradients of the local mixing entropy. We constructed a power functional approximation that describes superadiabatic demixing as an antagonist to adiabatic mixing as originates from the free energy. When applied to colloidal lane formation the theoretical results are in excellent agreement with our Brownian dynamics computer simulation results for adiabatic, structural, drag and viscous forces. Superadiabatic demixing allows to rationalize the emergence of mixed, laned and jammed states. We demonstrated that the time evolution of the van Hove dynamical pair correlation function is governed by adiabatic forces that arise from the free energy and by superadiabatic forces that are induced by the flow of the van Hove function. The superadiabatic forces consist of drag, viscous, and structural contributions, as occur in active Brownian particles, in liquids under shear and in lane forming mixtures. For hard sphere liquids, we presented a power functional theory that predicts these universal force fields in quantitative agreement with our Brownian dynamics results.
Projektbezogene Publikationen (Auswahl)
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Better than counting: Density profiles from force sampling. Phys. Rev. Lett. 120, 218001 (2018). Selected as PRL Editors’ Suggestion, Volume 120, Issue 21
Daniel de las Heras and Matthias Schmidt
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Structural nonequilibrium forces in driven colloidal systems. Phys. Rev. Lett. 121, 098002 (2018)
Nico C. X. Stuhlmüller, Tobias Eckert, Daniel de las Heras and Matthias Schmidt
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Velocity gradient power functional for Brownian dynamics. Phys. Rev. Lett. 120, 028001 (2018)
Daniel de las Heras and Matthias Schmidt
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Custom flow in overdamped Brownian dynamics. Phys. Rev. E 99, 023306 (2019)
Daniel de las Heras, Johannes Renner, and Matthias Schmidt
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Memory-induced motion reversal in Brownian liquids. Matter 16, 1518 (2020)
Lucas L. Treffenstädt and Matthias Schmidt
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Shear-induced deconfinement of hard disks. Col. Pol. Sci. 298, 895 (2020)
Nikolai Jahreis and Matthias Schmidt
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Superadiabatic demixing in nonequilibrium colloids. Commun. Phys. 3, 23 (2020)
Thomas Geigenfeind, Daniel de las Heras and Matthias Schmidt
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Universality in driven and equilibrium hard sphere liquid dynamics. Phys. Rev. Lett. 126, 058002 (2021)
Lucas L. Treffenstädt and Matthias Schmidt
