83 research outputs found
Symmetry Analysis in Linear Hydrodynamic Stability Theory: Classical and New Modes in Linear Shear
We present a symmetry classification of the linearised Navier-Stokes
equations for a two-dimensional unbounded linear shear flow of an
incompressible fluid. The full set of symmetries is employed to systematically
derive invariant ansatz functions. The symmetry analysis grasps three
approaches. Two of them are existing ones, representing the classical normal
modes and the Kelvin modes, while the third is a novel approach and leads to a
new closed-form solution of traveling modes, showing qualitatively different
behaviour in energetics, shape and kinematics when compared to the classical
approaches. The last modes are energy conserving in the inviscid case. They are
localized in the cross-stream direction and periodic in the streamwise
direction. As for the kinematics, they travel at constant velocity in the
cross-stream direction, whilst in the streamwise direction they are accelerated
by the base flow. In the viscous case, the modes break down due to damping of
high wavenumber contributions
From the nano- to the macroscale – bridging scales for the moving contact line problem
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 effective 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 using pseudospectral methods mapped to unbounded domains. The numerical scheme is presented, and the inclusion of hard-sphere effects via a fundamental measure theory is discussed.Open Acces
The contact line behaviour of solid-liquid-gas diffuse-interface models
A solid-liquid-gas moving contact line is considered through a
diffuse-interface model with the classical boundary condition of no-slip at the
solid surface. Examination of the asymptotic behaviour as the contact line is
approached shows that the relaxation of the classical model of a sharp
liquid-gas interface, whilst retaining the no-slip condition, resolves the
stress and pressure singularities associated with the moving contact line
problem while the fluid velocity is well defined (not multi-valued). The moving
contact line behaviour is analysed for a general problem relevant for any
density dependent dynamic viscosity and volume viscosity, and for general
microscopic contact angle and double well free-energy forms. Away from the
contact line, analysis of the diffuse-interface model shows that the
Navier--Stokes equations and classical interfacial boundary conditions are
obtained at leading order in the sharp-interface limit, justifying the creeping
flow problem imposed in an intermediate region in the seminal work of Seppecher
[Int. J. Eng. Sci. 34, 977--992 (1996)]. Corrections to Seppecher's work are
given, as an incorrect solution form was originally used.Comment: 33 pages, 3 figure
On the moving contact line singularity: Asymptotics of a diffuse-interface model
The behaviour of a solid-liquid-gas system near the three-phase contact line
is considered using a diffuse-interface model with no-slip at the solid and
where the fluid phase is specified by a continuous density field. Relaxation of
the classical approach of a sharp liquid-gas interface and careful examination
of the asymptotic behaviour as the contact line is approached is shown to
resolve the stress and pressure singularities associated with the moving
contact line problem. Various features of the model are scrutinised, alongside
extensions to incorporate slip, finite-time relaxation of the chemical
potential, or a precursor film at the wall.Comment: 14 pages, 3 figure
A comparison of slip, disjoining pressure, and interface formation models for contact line motion through asymptotic analysis of thin two-dimensional droplet spreading
The motion of a contact line is examined, and comparisons drawn, for a
variety of models proposed in the literature. Pressure and stress behaviours at
the contact line are examined in the prototype system of quasistatic spreading
of a thin two-dimensional droplet on a planar substrate. The models analysed
include three disjoining pressure models based on van der Waals interactions, a
model introduced for polar fluids, and a liquid-gas diffuse-interface model;
Navier-slip and two non-linear slip models are investigated, with three
microscopic contact angle boundary conditions imposed (two of these contact
angle conditions having a contact line velocity dependence); and the interface
formation model is also considered. In certain parameter regimes it is shown
that all of the models predict the same quasistatic droplet spreading
behaviour.Comment: 29 pages, 3 figures, J. Eng. Math. 201
Das Managen von Dienstarbeitsplätzen über eine zentrale Terminalserver-Infrastruktur - am Beispiel der UB
Schulungstermi
Das Managen von Dienstarbeitsplätzen über eine zentrale Terminalserver-Infrastruktur - am Beispiel der UB
Schulungstermi
Das Managen von Dienstarbeitsplätzen über eine zentrale Terminalserver-Infrastruktur - am Beispiel der UB
Schulungstermi
The asymptotics of the moving contact line: cracking an old nut
For contact line motion where the full Stokes flow equations hold, full matched asymptotic solutions using slip models have been obtained for droplet spreading and more general geometries. These solutions to the singular perturbation problem in the slip length, however, all involve matching through an intermediate region that is taken to be separate from the outer-inner regions. Here, we show that the intermediate region is in fact an overlap region representing extensions of both the outer and the inner region, allowing direct matching to proceed. In particular, we investigate in detail how a previously seen result of the matching of the cubes of the free surface slope is justified in the lubrication setting. We also extend this two-region direct matching to the more general Stokes flow case, offering a new perspective on the asymptotics of the moving contact line problem
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