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All content in this area was uploaded by Andreas Nold on Sep 29, 2017

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The moving contact line problem is one of the main unsolved fundamental problems in fluid mechanics, with relevant physical phenomena spanning multiple scales, from the molecular to the macroscopic scale.
In this thesis, at the macroscale, it is shown that classical asymptotic analysis is applicable at the moving contact line. This allows for a direct matching procedure between the inner (nanoscale) region and the outer (macroscale) region, therefore simplifying the analysis presented to date in the literature.
At the mesoscale, a unified derivation for single and binary fluid diffuse interface models is presented, consolidating two models present in the literature. Results from an asymptotic analysis of the sharp interface limit of the binary fluid diffuse interface model are compared with numerical computations of the inner region in the vicinity of a moving contact line.
Finally, the nanoscale structure of the density profile in the vicinity of the con- tact line is studied using density functional theory (DFT). At equilibrium, an effect- ive disjoining pressure is extracted and results are compared with coarse-grained Hamiltonian theory. A derivation of Navier-Stokes like dynamic DFT equations is presented. Results for the moving contact line are compared with predictions from molecular kinetic theory.
Computations for both DFT and diffuse interface approaches are performed us- ing pseudospectral methods mapped to unbounded domains. The numerical scheme is presented, and the inclusion of hard-sphere effects via a fundamental measure the- ory is discussed.

Content uploaded by Andreas Nold

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All content in this area was uploaded by Andreas Nold on Sep 29, 2017

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... Ideas to describe both phases of an inhomogeneous system in one unifying framework originate from van der Waals (1873) (Widom and Rowlinson, 1970;Rowlinson, 1979) and Cahn & Hilliard (1958). Derivations of diffuse interface equations for single and binary fluid systems from a nonequilibrium thermodynamics framework have been presented, amongst others, by Anderson et al. (1998), Jacqmin (1999 and Onuki (2007) (Nold, 2016). ...

Classical Density Functional Theory (DFT) is a statistical-mechanical framework to analyze fluids, which accounts for nanoscale fluid inhomogeneities and non-local intermolecular interactions. DFT can be applied to a wide range of interfacial phenomena, as well as problems in adsorption, colloidal science and phase transitions in fluids. Typical DFT equations are highly non-linear, stiff and contain several convolution terms. We propose a novel, efficient pseudo-spectral collocation scheme for computing the non-local terms in real space with the help of a specialized Gauss quadrature. Due to the exponential accuracy of the quadrature and a convenient choice of collocation points near interfaces, we can use grids with a significantly lower number of nodes than most other reported methods. We demonstrate the capabilities of our numerical methodology by studying equilibrium and dynamic two-dimensional test cases with single- and multispecies hard-sphere and hard-disc particles modelled with fundamental measure theory, with and without van der Waals attractive forces, in bounded and unbounded physical domains. We show that our results satisfy statistical mechanical sum rules.

Surface nanobubbles are nanoscopic gaseous domains on immersed substrates which can survive for days. They were first speculated to exist about 20 years ago, based on stepwise features in force curves between two hydrophobic surfaces, eventually leading to the first atomic force microscopy (AFM) image in 2000. While in the early years it was suspected that they may be an artifact caused by AFM, meanwhile their existence has been confirmed with various other methods, including through direct optical observation. Their existence seems to be paradoxical, as a simple classical estimate suggests that they should dissolve in microseconds, due to the large Laplace pressure inside these nanoscopic spherical-cap-shaped objects. Moreover, their contact angle (on the gas side) is much smaller than one would expect from macroscopic counterparts. This review will not only give an overview on surface nanobubbles, but also on surface nanodroplets, which are nanoscopic droplets (e.g., of oil) on (hydrophobic) substrates immersed in water, as they show similar properties and can easily be confused with surface nanobubbles and as they are produced in a similar way, namely, by a solvent exchange process, leading to local oversaturation of the water with gas or oil, respectively, and thus to nucleation. The review starts with how surface nanobubbles and nanodroplets can be made, how they can be observed (both individually and collectively), and what their properties are. Molecular dynamic simulations and theories to account for the long lifetime of the surface nanobubbles are then reported on. The crucial element contributing to the long lifetime of surface nanobubbles and nanodroplets is pinning of the three-phase contact line at chemical or geometric surface heterogeneities. The dynamical evolution of the surface nanobubbles then follows from the diffusion equation, Laplace's equation, and Henry's law. In particular, one obtains stable surface nanobubbles when the gas influx from the gas-oversaturated water and the outflux due to Laplace pressure balance. This is only possible for small enough surface bubbles. It is therefore the gas or oil oversaturation ζ that determines the contact angle of the surface nanobubble or nanodroplet and not the Young equation. The review also covers the potential technological relevance of surface nanobubbles and nanodroplets, namely, in flotation, in (photo)catalysis and electrolysis, in nanomaterial engineering, for transport in and out of nanofluidic devices, and for plasmonic bubbles, vapor nanobubbles, and energy conversion. Also given is a discussion on surface nanobubbles and nanodroplets in a nutshell, including theoretical predictions resulting from it and future directions. Studying the nucleation, growth, and dissolution dynamics of surface nanobubbles and nanodroplets will shed new light on the problems of contact line pinning and contact angle hysteresis on the submicron scale. © 2015 American Physical Society.

THIS PAPER PRESENTS AN EXPERIMENTAL STUDY OF THE SHAPE OF LIQUID-AIR INTERFACE WHEN THE LIQUID ADVANCES INTO THE AIR IN A CAPILLARY TUBE.THE ANALYSIS SHOWS THAT THIS SHAPE IS INFLUENCED BY INERTIA, VISCOUS, AND INTERFACE FORCES.THE STUDY WAS CONDUCTED IN A GLASS TUBE 1.955 MM IN DIAMETER WITH FIVE DIFFERENT LIQUIDS BEING DRIVEN BY A SOLID PLUNGER AT VELOCITIES FOR WHICH ONLY THE VISCOUS AND THE INTERFACIAL FORCES ARE OF IMPORTANCE.SINCE BOTH THE FORCES AT THE GAS-LIQUID INTERFACE AND AT THE GAS-LIQUID-SOLID JUNCTIONS MUST BE CONSIDERED, A METHOD IS DEVELOPED FOR CORRELATING THE DATA WHERE A SHIFT DETERMINED ONLY BY THE STATIC CONTACT ANGLE IS ADDED TO THE CAPILLARY NUMBER.IT IS FOUND THAT IN THIS MANNER THE DATA OF THE AUTHOR FOR VARIOUS LIQUIDS TESTED, AS WELL AS THE DATA OF OTHER INVESTIGATORS, CAN BE CORRELATED.

From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. These methods are exact for systems of slowly varying or high density. For the ground state, they lead to self-consistent equations analogous to the Hartree and Hartree-Fock equations, respectively. In these equations the exchange and correlation portions of the chemical potential of a uniform electron gas appear as additional effective potentials. (The exchange portion of our effective potential differs from that due to Slater by a factor of 23.) Electronic systems at finite temperatures and in magnetic fields are also treated by similar methods. An appendix deals with a further correction for systems with short-wavelength density oscillations.