Application of the PTT Model to Axisymmetric Free Surface Flows

This work is concerned with numerical simulation of axisymmetric viscoelastic free surface flows using the Phan-Thien-Tanner (PTT) constitutive equation. A finite difference technique for solving the governing equations for unsteady incompressible flows written in Cylindrical coordinates on a staggered grid is described. The fluid is modelled by a Marker-and-Cell type method and an accurate representation of the fluid surface is employed. The full free surface stress conditions are applied. The numerical method is verified by comparing numerical predictions of fully developed flow in a pipe with the corresponding analytic solutions. To demonstrate that the numerical method can simulate axisymmetric free surface flows governed by the PTT model, numerical results of the flow evolution of a drop impacting on a rigid dry plate are presented. In these simulations, the rheological effects of the parameters epsilon and xi are investigated.

Experimental investigation into the effect of stress on dissolution and growth of very soluble brittle salts in aqueous solution

Das Studium der Auflösungs- und Wachstumsprozesse an Feststoff-Flüssigkeits-Grenzflächen unter nicht-hydrostatischen Beanspruchungen ist wesentlich für das Verständnis von Defor-mationsprozessen, die in der Erde ablaufen. Unter diesen genannten Prozessen gehört die Drucklösung zu den wichtigsten duktilen Deformationsprozessen, von der Diagenese bishin zur niedrig- bis mittelgradigen metamorphen Bedingungen. Bisher ist allerdings wenig darüber bekannt, welche mechanischen, physikalischen oder chemischen Potentialenergie-Gradienten die Drucklösung steuern. I.a. wird angenommen, daß die Drucklösung durch Un-terschiede kristallplastischer Verformungsenergien oder aber durch Unterschiede der Normal-beanspruchung an Korngrenzen gesteuert wird. Unterschiede der elastischen Verformungs-energien werden dabei allerdings als zu gering erachtet, um einen signifikanten Beitrag zu leisten. Aus diesem Grund werden sie als mögliche treibende Kräfte für die Drucklösung vernachlässigt. Andererseits haben neue experimentelle und theoretische Untersuchungen gezeigt, daß die elastische Verformung in der Tat einen starken Einfluß auf Lösungs- und Wachstumsmechanismen von Kristallen in einer Lösung haben kann. Da die in der Erdkruste vorherrschenden Deformationsmechanismen überwiegend im elastischen Verformungsbereich der Gesteine ablaufen, ist es sehr wichtig, das Verständnis für die Effekte, die die elastische Verformung verursacht, zu erweitern, und ihre Rolle während der Deformation durch Drucklösung zu definieren. Die vorliegende Arbeit beschäftigt sich mit Experimenten, bei denen der Effekt der mechanisch kompressiven Beanspruchung auf Lösungs- und Wachstumsprozesse von Einzelkristallen unterschiedlicher, sehr gut löslicher, elastisch/spröder Salze untersucht wurde. Diese Salze wurden als Analoga gesteinsbildender Minerale wie Quarz und Calcit ausgewählt. Der Einfluß von Stress auf die Ausbildung der Oberflächenmikrostrukturen in einer untersättigten Lösung wurde an Kaliumalaun untersucht.Lösungsrillen (20 – 40 µm breit, 10 – 40 µm tief und 20 – 80 µm Abstand) entwickelten sich in den Bereichen, in denen die Beanspruchung im Kristall am größten war. Sie verschwanden wieder, sobald der Kristall entlastet wurde. Diese Rillen entwickelten sich parallel zu niedrig indizierten kristallographischen Richtungen und sub-perpendikular zu den Trajektorien, die der maximalen, lokalen kompressiven Beanspruchung entsprachen. Die Größe der Lösungsrillen hing von der lokalen Oberflächenbeanspruchung, der Oberflächenenergie und dem Untersättigungsgrad der wässrigen Lösung ab. Die mikrostrukturelle Entwicklung der Kristalloberflächen stimmte gut mit den theoretischen Vorhersagen überein, die auf den Modellen von Heidug & Leroy (1994) und Leroy & Heidug (1994) basieren. Der Einfluß der Beanspruchung auf die Auflösungsrate wurde an Natriumchlorat-Einzelkristallen untersucht. Dabei wurde herausgefunden, daß sich gestresste Kristalle schneller lösen als Kristalle, auf die keine Beanspruchung einwirkt. Der experimentell beobachtete Anstieg der Auflösungsrate der gestressten Kristalle war ein bis zwei Größenordnungen höher als theoretisch erwartet. Die Auflösungsrate stieg linear mit dem Stress an, und der Anstieg war um so größer, je stärker die Lösung untersättigt war. Außerdem wurde der Effekt der Bean-spruchung auf das Kristallwachstum an Kaliumalaun- und Kaliumdihydrogenphosphat-Ein-zelkristallen untersucht. Die Wachstumsrate der Flächen {100} und {110} von Kalium-alaun war bei Beanspruchung stark reduziert. Für all diese Ergebnisse spielte die Oberflächenrauhigkeit der Kristalle eine Schlüsselrolle, indem sie eine nicht-homogene Stressverteilung auf der Kristalloberfläche verursachte. Die Resultate zeigen, daß die elastische Verformung eine signifikante Rolle während der Drucklösung spielen kann, und eine signifikante Deformation in der oberen Kruste verursachen kann, bei Beanspruchungen, die geringer sind, als gemeinhin angenommen wird. Somit folgt, daß die elastische Bean-spruchung berücksichtigt werden muß, wenn mikrophysikalische Deformationsmodelle entwickelt werden sollen.

Stress – structure correlations in grafted polymer films

In der vorliegenden Arbeit wurden experimentelle Untersuchungen zu gepfropften Polymerfilmen durchgeführt. Dabei wurden endgepfropfte poly-methyl-methacrylate (PMMA) Bürsten hergestellt durch „grafting from“ Methoden und polystyrol (PS)/ poly-vinyl-methyl-ether (PVME) Polymerfilme gepfropft auf UV sensitiven Oberflächen untersucht. Zur Strukturuntersuchung wurden die hergestellten Systeme wurden mit Rasterkraftmikroskopie (engl.: Surface Probe Microscopy, SPM), Röntgen - und Neutronenreflektivitätsmessungen, sowie mit Röntgenstreuung unter streifenden Einfall (engl.: Grazing Incidence Small Angle X-Ray Scattering, GISAXS) untersucht. rnEs wurde gezeigt, dass ein aus der Transmissionsstreuung bekanntes Model auch für auch für die GISAXS Analyse polydisperser Polymerdomänen und Kolloidsysteme verwendet werden kann. Der maximale Fehler durch die gemachten Näherungen wurde auf < 20% abgeschätzt.rnErgebnisse aus der Strukturanalyse wurden mit mechanischen Filmeigenschaften verknüpft. Dazu wurden mechanische Spannungsexperimente durchgeführt. Hierzu wurden die zu untersuchenden Filme selektiv auf einzelne Mikro-Federbalken-Sensoren (engl.: Micro Cantilever Sensor, MCS) der MCS Arrays aufgebracht. Dies wurde durch Maskierungstechniken und Mikro-Kontaktdrucken bewerkstelligt. rnPhasenübergansexperimente der gepfropften PS/PVME Filme haben gezeigt, dass die Möglichkeit einer Polymer/Polymer Phasenseparation stark von Propfpunktdichte der gebundenen Polymerketten mit der Oberfläche abhängt. PS/PVME Filmsysteme mit hohen Pfropfpunktdichten zeigten keinen Phasenübergang. Bei niedrig gepfropften Filmsystemen waren hingegen Polymer/Polymer Phasenseparationen zu beobachten. Es wurde geschlussfolgert, dass die gepfropften Polymersysteme einen hinreichenden Grad an entropischen Freiheitsgraden benötigen um eine Phasenseparation zu zeigen. Mechanische Spannungsexperimente haben dabei das Verstehen der Phasenseparationsmechanismen möglich gemacht.rnAus Quellexperimenten dichtgepfropfter PMMA Bürsten, wurden Lösungsmittel-Polymer Wechselwirkungsparameter (-Parameter) bestimmt. Dabei wurde festgestellt, dass sich die erhaltenen Parameter aufgrund von Filmbenetzung und entropischen Effekten maßgeblich von den errechneten Bulkwerten unterscheiden. Weiterhin wurden nicht reversible Kettenverschlaufungseffekt beobachtet.

Measurement of residual stress by load and depth sensing indentation with spherical indenters

A new experimental technique is presented for making measurements of biaxial residual stress using load and depth sensing indentation (nanoindentation). The technique is based on spherical indentation, which, in certain deformation regimes, can be much more sensitive to residual stress than indentation with sharp pyramidal indenters like the Berkovich. Two different methods of analysis were developed: one requiring an independent measure of the material's yield strength and the other a reference specimen in the unstressed state or other known reference condition. Experiments conducted on aluminum alloys to which controlled biaxial bending stresses were applied showed that the methods are capable of measuring the residual stress to within 10-20% of the specimen yield stress. Because the methods do not require imaging of the hardness impressions, they are potentially useful for making localized measurements of residual stress, as in thin films or small volumes, or for characterization of point-to-point spatial variations of the surface stress.

Size effect on the lattice parameter of KCl during mechanical milling

The size effect on the lattice parameter of ionic KCl nanocrystals was studied systematically during mechanical milling of Pure KCl powder under vacuum. The results suggest anomalous lattice expansion, with the lattice parameter increasing from 6.278 angstrom at d = 6 mu m to 6.30307 angstrom at d = 85 mn. The defects generated during ball milling of KCl and surface stress are deemed to be responsible for this lattice parameter expansion. (C) 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Towards the Use of Radar Winds in Numerical Weather Prediction

Numerical weather prediction (NWP) models provide the basis for weather forecasting by simulating the evolution of the atmospheric state. A good forecast requires that the initial state of the atmosphere is known accurately, and that the NWP model is a realistic representation of the atmosphere. Data assimilation methods are used to produce initial conditions for NWP models. The NWP model background field, typically a short-range forecast, is updated with observations in a statistically optimal way. The objective in this thesis has been to develope methods in order to allow data assimilation of Doppler radar radial wind observations. The work has been carried out in the High Resolution Limited Area Model (HIRLAM) 3-dimensional variational data assimilation framework. Observation modelling is a key element in exploiting indirect observations of the model variables. In the radar radial wind observation modelling, the vertical model wind profile is interpolated to the observation location, and the projection of the model wind vector on the radar pulse path is calculated. The vertical broadening of the radar pulse volume, and the bending of the radar pulse path due to atmospheric conditions are taken into account. Radar radial wind observations are modelled within observation errors which consist of instrumental, modelling, and representativeness errors. Systematic and random modelling errors can be minimized by accurate observation modelling. The impact of the random part of the instrumental and representativeness errors can be decreased by calculating spatial averages from the raw observations. Model experiments indicate that the spatial averaging clearly improves the fit of the radial wind observations to the model in terms of observation minus model background (OmB) standard deviation. Monitoring the quality of the observations is an important aspect, especially when a new observation type is introduced into a data assimilation system. Calculating the bias for radial wind observations in a conventional way can result in zero even in case there are systematic differences in the wind speed and/or direction. A bias estimation method designed for this observation type is introduced in the thesis. Doppler radar radial wind observation modelling, together with the bias estimation method, enables the exploitation of the radial wind observations also for NWP model validation. The one-month model experiments performed with the HIRLAM model versions differing only in a surface stress parameterization detail indicate that the use of radar wind observations in NWP model validation is very beneficial.

Kinetic approach to dislocation bending in low-mobility films

A kinetic model has been developed for dislocation bending at the growth surface in compressively stressed low-mobility films such as III-V nitrides. It is based on a reduction in the number of atoms at the growth surface. Stress and nonstress sources of driving force for such a reduction are discussed. A comparison between the derived equations and experimentally measured stress evolution data yields good agreement between the predicted and observed angles through which dislocations bend.

Stability of fluid flow past a membrane

The stability of fluid flow past a membrane of infinitesimal thickness is analysed in the limit of zero Reynolds number using linear and weakly nonlinear analyses. The system consists of two Newtonian fluids of thickness R* and H R*, separated by an infinitesimally thick membrane, which is flat in the unperturbed state. The dynamics of the membrane is described by its normal displacement from the flat state, as well as a surface displacement field which provides the displacement of material points from their steady-state positions due to the tangential stress exerted by the fluid flow. The surface stress in the membrane (force per unit length) contains an elastic component proportional to the strain along the surface of the membrane, and a viscous component proportional to the strain rate. The linear analysis reveals that the fluctuations become unstable in the long-wave (alpha --> 0) limit when the non-dimensional strain rate in the fluid exceeds a critical value Lambda(t), and this critical value increases proportional to alpha(2) in this limit. Here, alpha is the dimensionless wavenumber of the perturbations scaled by the inverse of the fluid thickness R*(-1), and the dimensionless strain rate is given by Lambda(t) = ((gamma) over dot* R*eta*/Gamma*), where eta* is the fluid viscosity, Gamma* is the tension of the membrane and (gamma) over dot* is the strain rate in the fluid. The weakly nonlinear stability analysis shows that perturbations are supercritically stable in the alpha --> 0 limit.

Size and temperature dependent stability and phase transformation in single-crystal zirconium nanowire

A novel size dependent FCC (face-centered-cubic) -> HCP (hexagonally-closed-pack) phase transformation and stability of an initial FCC zirconium nanowire are studied. FCC zirconium nanowires with cross-sectional dimensions < 20 are found unstable in nature, and they undergo a FCC -> HCP phase transformation, which is driven by tensile surface stress induced high internal compressive stresses. FCC nanowire with cross-sectional dimensions > 20 , in which surface stresses are not enough to drive the phase transformation, show meta-stability. In such a case, an external kinetic energy in the form of thermal heating is required to overcome the energy barrier and achieve FCC -> HCP phase transformation. The FCC-HCP transition pathway is also studied using Nudged Elastic Band (NEB) method, to further confirm the size dependent stability/metastability of Zr nanowires. We also show size dependent critical temperature, which is required for complete phase transformation of a metastable-FCC nanowire.

Wrinkling of Atomic Planes in Ultrathin Au Nanowires

A detailed understanding of structure and stability of nanowires is critical for applications. Atomic resolution imaging of ultrathin single crystalline Au nanowires using aberration-corrected microscopy reveals an intriguing relaxation whereby the atoms in the close-packed atomic planes normal to the growth direction are displaced in the axial direction leading to wrinkling of the (111) atomic plane normal to the wire axis. First-principles calculations of the structure of such nanowires confirm this wrinkling phenomenon, whereby the close-packed planes relax to form saddle-like surfaces. Molecular dynamics studies of wires with varying diameters and different bounding surfaces point to the key role of surface stress on the relaxation process. Using continuum mechanics arguments, we show that the wrinkling arises due to anisotropy in the surface stresses and in the elastic response, along with the divergence of surface-induced bulk stress near the edges of a faceted structure. The observations provide new understanding on the equilibrium structure of nanoscale systems and could have important implications for applications in sensing and actuation.

Simulations of impinging droplets with surfactant-dependent dynamic contact angle

An arbitrary Lagrangian-Eulerian (ALE) finite element scheme for computations of soluble surfactant droplet impingement on a horizontal surface is presented. The numerical scheme solves the time-dependent Navier-Stokes equations for the fluid flow, scalar convection-diffusion equation for the surfactant transport in the bulk phase, and simultaneously, surface evolution equations for the surfactants on the free surface and on the liquid-solid interface. The effects of surfactants on the flow dynamics are included into the model through the surface tension and surfactant-dependent dynamic contact angle. In particular, the dynamic contact angle (theta(d)) of the droplet is defined as a function of the surfactant concentration at the contact line and the equilibrium contact angle (theta(0)(e)) of the clean surface using the nonlinear equation of state for surface tension. Further, the surface forces are included into the model as surface divergence of the surface stress tensor that allows to incorporate the Marangoni effects without calculating the surface gradient of the surfactant concentration on the free surface. In addition to a mesh convergence study and validation of the numerical results with experiments, the effects of adsorption and desorption surfactant coefficients on the flow dynamics in wetting, partially wetting and non-wetting droplets are studied in detail. It is observed that the effects of surfactants are more in wetting droplets than in the non-wetting droplets. Further, the presence of surfactants at the contact line reduces the equilibrium contact angle further when theta(0)(e) is less than 90 degrees, and increases it further when theta(0)(e) is greater than 90 degrees. Nevertheless, the presence of surfactants has no effect on the contact angle when theta(0)(e) = 90 degrees. The numerical study clearly demonstrates that the surfactant-dependent contact angle has to be considered, in addition to the Marangoni effect, in order to study the flow dynamics and the equilibrium states of surfactant droplet impingement accurately. The proposed numerical scheme guarantees the conservation of fluid mass and of the surfactant mass accurately. (C) 2015 Elsevier Inc. All rights reserved.

Size-Dependent Elastic Properties Of Ni Nanofilms By Molecular Dynamics Simulation

Size-dependent elastic properties of Ni nanofilms are investigated by molecular dynamics ( MD) simulations with embedded atom method (EAM). The surface effects are considered by calculating the surface relaxation, surface energy, and surface stress. The Young's modulus and yield stress are obtained as functions of thickness and crystallographic orientation. It is shown that the surface relaxation has important effects on the the elastic properties at nanoscale. When the surface relaxation is outward, the Young's modulus decreases with the film thickness decreasing, and vice versa. The results also show that the yield stresses of the films increase with the films becoming thinner. With the thickness of the nanofilms decreasing, the surface effects on the elastic properties become dominant.

Novel Mechanical Behavior Of Zno Nanorods

A novel stress-strain relation with two stages of linear elastic deformation is observed in [0 0 0 1]-oriented ZnO nanorods under uniaxial tensile loading. This phenomenon results from a phase transformation from wurtzite (WZ, P6(3)mc space group) to a body-centered tetragonal structure with four-atom rings (denoted as BCT-4) belonging to the P4(2)/mnm space group. The analysis here focuses on the effects of nanorod size and temperature on the phase transformation and the associated mechanical behavior. It is found that as size is increased from 19.5 to 45.5 angstrom, the critical stress for nucleation of the transformation decreases by 25% from 21.90 to 16.50 GPa and the elastic moduli of the WZ- and BCT-4-structured nanorods decrease by 24% (from 299.49 to 227.51 GPa) and 38% (from 269.29 to 166.86 GPa), respectively. A significant temperature effect is also observed, with the critical stress for transformation initiation decreasing 87.8% from 17.89 to 2.19 GPa as temperature increases from 300 to 1500 K. (c) 2007 Elsevier B.V. All rights reserved.

Grain Boundary Effects On Plastic Deformation And Fracture Mechanisms In Cu Nanowires: Molecular Dynamics Simulations

Metallic nanowires have many attractive properties such as ultra-high yield strength and large tensile elongation. However, recent experiments show that metallic nanowires often contain grain boundaries, which are expected to significantly affect mechanical properties. By using molecular dynamics simulations, here, we demonstrate that polycrystalline Cu nanowires exhibit tensile deformation behavior distinctly different from their single-crystal counterparts. A significantly lowered yield strength was observed as a result of dislocation emission from grain boundaries rather than from free surfaces, despite of the very high surface to volume ratio. Necking starts from the grain boundary followed by fracture, resulting in reduced tensile ductility. The high stresses found in the grain boundary region clearly play a dominant role in controlling both inelastic deformation and fracture processes in nanoscale objects. These findings have implications for designing stronger and more ductile structures and devices on nanoscale.

Size-dependent elastic properties of Ni nanofilms by molecular dynamics simulation

Size-dependent elastic properties of Ni nanofilms are investigated by molecular dynamics ( MD) simulations with embedded atom method (EAM). The surface effects are considered by calculating the surface relaxation, surface energy, and surface stress. The Young's modulus and yield stress are obtained as functions of thickness and crystallographic orientation. It is shown that the surface relaxation has important effects on the the elastic properties at nanoscale. When the surface relaxation is outward, the Young's modulus decreases with the film thickness decreasing, and vice versa. The results also show that the yield stresses of the films increase with the films becoming thinner. With the thickness of the nanofilms decreasing, the surface effects on the elastic properties become dominant.