Entwicklung einer Multiskalenmethode für die Simulation von Schmierprozessen

Reibung und Schmierung sind Multiskalenprobleme, d.h. Prozesse auf unterschiedlichen Zeit- und Längenskalen beeinflussen einander und bestimmen die makroskopische Antwort eines Systems. Für Schmierungsprozesse trifft dies insbesondere im Grenzreibungsbereich zu, in dem die Dicke des Schmierspalts in der Größenordnung molekularer Interaktionslängen liegt. Makroskopische Schmierungsmodellierung basiert fast ausschließlich auf der Anwendung der Reynoldsgleichung, während auf atomarer Skala vermehrt Molekulardynamik-Simulationen in den Vordergrund treten. Multiskalenmethoden für Schmierungsphänomene, die über sequentielle Ansätze hinausgehen, sind bisher noch nicht etabliert. Im Rahmen dieser Arbeit wird ein Multiskalenansatz vorgestellt, welcher die Lösung der makroskopischen Bilanzgleichungen in ein Mikro- und Makroproblem aufteilt. Das Makroproblem entsteht durch Mittelung der Bilanzgleichungen über der Spalthöhe, ähnlich zur konventionellen Reynoldsgleichung, und wird mittels expliziter Finite-Volumen-Diskretisierung gelöst, während das Mikroproblem das konstitutive Verhalten des Schmierfilms enthält. Die numerische Implementierung des Makroproblems wird mithilfe gewöhnlicher Konstitutivgesetze validiert und anhand konkreter Beispiele wird gezeigt, dass diese in Zukunft durch Molekulardynamik-Simulationen ersetzt werden können. Außerdem lassen sich analytische Lösungen der linearisierten Grundgleichungen des Makroproblems herleiten, die mit Autokorrelationsfunktionen fluktuierender Zustandsvariablen aus Molekulardynamik-Simulationen verglichen werden. Daraus ergibt sich eine Methode zur simultanen Bestimmung von Viskosität und Schlupflänge aus Gleichgewichts-Simulationen, sowie die Beschreibung des überkritischen Schalltransports in Fluidspalten. Für eine effiziente Umsetzung des vorgestellten Multiskalenansatzes wird eine Ersatzmodellierung benötigt, die zwischen einzelnen Mikrosimulationen interpoliert. Anhand von einfachen Beispielen wird das Anwendungspotential der Gaußprozess-Regression als mögliches Ersatzmodell evaluiert. Die vorliegende Arbeit liefert somit die theoretischen Grundlagen einer simultanen Multiskalensimulation von Schmierungsprozessen, welche in Zukunft zu einem besseren Verständnis der Dissipationsmechanismen im Grenzreibungsbereich beitragen kann

Sound waves, diffusive transport, and wall slip in nanoconfined compressible fluids

Although continuum theories have been proven quite robust to describe confined fluid flow at molecular length scales, molecular dynamics (MD) simulations reveal mechanistic insights into the interfacial dissipation processes. Most MD simulations of confined fluids have used setups in which the lateral box size is not much larger than the gap height, thus breaking thin-film assumptions usually employed in continuum simulations. Here, we explicitly probe the long wavelength hydrodynamic correlations in confined simple fluids with MD and compare to gap-averaged continuum theories as typically applied in e.g. lubrication. Relaxation times obtained from equilibrium fluctuations interpolate between the theoretical limits from bulk hydrodynamics and continuum formulations with increasing wavelength. We show how to exploit this characteristic transition to measure viscosity and slip length in confined systems simultaneously from equilibrium MD simulations. Moreover, the gap-averaged theory describes a geometry-induced dispersion relation that leads to overdamped sound relaxation at large wavelengths, which is confirmed by our MD simulations. Our results add to the understanding of transport processes under strong confinement and might be of technological relevance for the design of nanofluidic devices due to the recent progress in fabrication methods.Comment: 17 pages, 11 figure

Sound waves, diffusive transport, and wall slip in nanoconfined compressible fluids

Although continuum theories have been proven quite robust to describe confined fluid flow at molecular length scales, molecular dynamics (MD) simulations reveal mechanistic insights into the interfacial dissipation processes. Most MD simulations of confined fluids have used setups in which the lateral box size is not much larger than the gap height, thus breaking thin-film assumptions usually employed in continuum simulations. Here we explicitly probe the long-wavelength hydrodynamic correlations in confined simple fluids with MD and compare to gap-averaged continuum theories as typically applied in, e.g., lubrication. Relaxation times obtained from equilibrium fluctuations interpolate between the theoretical limits from bulk hydrodynamics and continuum formulations with increasing wavelength. We show how to exploit this characteristic transition to measure viscosity and slip length in confined systems simultaneously from equilibrium MD simulations. Moreover, the gap-averaged theory describes a geometry-induced dispersion relation that leads to overdamped sound relaxation at large wavelengths, which is confirmed by our MD simulations. Our results add to the understanding of transport processes under strong confinement and might be of technological relevance for the design of nanofluidic devices

Height-Averaged Navier–Stokes Solver for Hydrodynamic Lubrication

Modelling hydrodynamic lubrication is crucial in the design of engineering components as well as for a fundamental understanding of friction mechanisms. The cornerstone of thin-film flow modelling is the Reynolds equation -- a lower-dimensional representation of the Stokes equation. However, the derivation of the Reynolds equation is based on assumptions and fixed form constitutive relations, that may not generally be valid, especially when studying systems under extreme conditions. Furthermore, these explicit assumptions about the constitutive behaviour of the fluid prohibit applications in a multiscale scenario based on measured or atomistically simulated data. Here, we present a method that considers the full compressible Navier-Stokes equation in a height-averaged sense for arbitrary constitutive relations. We perform numerical tests by using a reformulation of the viscous stress tensor for laminar flow to validate the presented method comparing to results from conventional Reynolds solutions. The versatility of the method is shown by incorporating models for mass-conserving cavitation, wall slip and non-Newtonian fluids. This allows testing of new constitutive relations that not necessarily need to take a fixed form, and may be obtained from experimental or simulation data.Comment: 12 pages, 9 figure

dtool and dserver: A flexible ecosystem for findable data

Making data FAIR—findable, accessible, interoperable, reproducible—has become the recurring theme behind many research data management efforts. dtool is a lightweight data management tool that packages metadata with immutable data to promote accessibility, interoperability, and reproducibility. Each dataset is self-contained and does not require metadata to be stored in a centralised system. This decentralised approach means that finding datasets can be difficult. dtool’s lookup server, short dserver, as defined by a REST API, makes dtool datasets findable, hence rendering the dtool ecosystem fit for a FAIR data management world. Its simplicity, modularity, accessibility and standardisation via API distinguish dtool and dserver from other solutions and enable it to serve as a common denominator for cross-disciplinary research data management. The dtool ecosystem bridges the gap between standardisation-free data management by individuals and FAIR platform solutions with rigid metadata requirements

dtool and dserver: A flexible ecosystem for findable data.

Making data FAIR-findable, accessible, interoperable, reproducible-has become the recurring theme behind many research data management efforts. dtool is a lightweight data management tool that packages metadata with immutable data to promote accessibility, interoperability, and reproducibility. Each dataset is self-contained and does not require metadata to be stored in a centralised system. This decentralised approach means that finding datasets can be difficult. dtool's lookup server, short dserver, as defined by a REST API, makes dtool datasets findable, hence rendering the dtool ecosystem fit for a FAIR data management world. Its simplicity, modularity, accessibility and standardisation via API distinguish dtool and dserver from other solutions and enable it to serve as a common denominator for cross-disciplinary research data management. The dtool ecosystem bridges the gap between standardisation-free data management by individuals and FAIR platform solutions with rigid metadata requirements