Search Results

NUMERICAL SIMULATION OF TWO-FLUID PROBLEMS

Jean-Frédéric Gerbeau, Claude Le Bris, and Tony Lelièvre

in Mathematical Methods for the Magnetohydrodynamics of Liquid Metals

This chapter deals with the discretization issues raised by multifluid magnetohydrodynamics problems. The additional difficulty compared to those in Chapter 3, is the presence of one (or many) free ... More

This chapter deals with the discretization issues raised by multifluid magnetohydrodynamics problems. The additional difficulty compared to those in Chapter 3, is the presence of one (or many) free interface(s) separating the fluids. Numerically, one has also to resort to up-to-date techniques for the simulation of moving interfaces. In particular, the chapter presents a numerical method based on the Arbitrary Lagrangian Eulerian formulation, and lays emphasis on the stability of the time-advancing schemes. A short review of some other numerical methods to deal with moving interfaces is provided. Some numerical test cases illustrate the capabilities of the ALE method.Less

KINEMATICS AND KINETICS OF CRYSTAL PLASTICITY

A. S. Argon

in Strengthening Mechanisms in Crystal Plasticity

Crystal plasticity is overwhelmingly a consequence of the self similar translations of dislocations, which is viewed as a limiting form of more general shear transformations that also include ... More

Crystal plasticity is overwhelmingly a consequence of the self similar translations of dislocations, which is viewed as a limiting form of more general shear transformations that also include twinning and martensitic transformations. Unlike elastic deformation, which can be homogeneous down to the atomic scale, plastic deformation involving dislocation translations or other shear transformations are locally discrete and inhomogeneous. Plasticity can be viewed as homogeneous only when the discrete processes are homogenized over a representative volume element (RVE), large enough to represent quasi-smooth behavior. Thus, for the purpose of viewing plasticity as a continuum field theory, its applicability is limited to volume elements no smaller than the RVE over which processes have been homogenized. In this chapter, the essential kinematics of inelastic deformation is introduced broadly. This is followed by the development of dislocation line properties that are associated with plastic strain production and the expenditure of plastic work in crystal plasticity, including concepts of dislocation line tension, dislocation mass, forms of interaction of dislocations with applied stresses, with each other, with free surfaces, and inhomogeneities. The principles of thermally activated deformation processes are introduced and then applied to dislocation glide and overcoming of local obstacles by thermal assistance. The detailed developments of dislocation properties emphasize face centered cubic crystals, including a full complement of partial dislocation and their dislocation.Less

SPH method validation

D. Violeau

in Fluid Mechanics and the SPH Method: Theory and Applications

Examples of simple flows are shown here, with emphasis on the validation of SPH from other numerical methods, theoretical solutions of Navier–Stokes equations or experimental data. The examples ... More

Examples of simple flows are shown here, with emphasis on the validation of SPH from other numerical methods, theoretical solutions of Navier–Stokes equations or experimental data. The examples chosen cover a wide range of SPH capabilities, including rigid body motion in a fluid, free-surface water waves, steady confined flows, efforts on an obstacle, multi-phase flows, etc. The chapter gives particular attention to the modelling of open-channel flow, lid-driven cavity, waves induced by water collapse, and moving bodies. These test cases are frequently used by SPH modellers and are easy to reproduce. The chapter tests various numerical schemes, like weakly compressible and truly incompressible schemes, and test the effects of several physical models, like turbulence effects.Less

SPH applied to hydraulic works

D. Violeau

in Fluid Mechanics and the SPH Method: Theory and Applications

Applications of SPH are presented here, up to the three-dimensional viewpoint under real conditions. The examples chosen are selected from real studies in water engineering: the design of coastal ... More

Applications of SPH are presented here, up to the three-dimensional viewpoint under real conditions. The examples chosen are selected from real studies in water engineering: the design of coastal defence, coastal pollution management, and river waterworks. Focus is thus made on environmental flows, according to the author’s experience. The ability of SPH to deal with such flows is investigated in each case. The quality of the results are partially compared to theoretical results derived from the considerations of Chapters 3 and 4, or to experimental results obtained from the similarity considerations of Chapter 3.Less

Adsorption of surfactants at liquid interfaces: thermodynamics

Bob Aveyard

in Surfactants: In Solution, at Interfaces and in Colloidal Dispersions

The thickness and hence material content of a surface is generally unknown, and there are two common definitions of a surface/interface. In one the surface is treated as a phase distinct from the ... More

The thickness and hence material content of a surface is generally unknown, and there are two common definitions of a surface/interface. In one the surface is treated as a phase distinct from the surrounding bulk phases, and in the other, due to Gibbs, the Gibbs dividing surface is supposed to be a plane, parallel to the physical interface. The former model gives rise to the surface concentrationΓ‎s of a surfactant, and the Gibbs model introduces the surface excess concentration, Γ‎σ‎. Some thermodynamic quantities for surfaces (e.g. surface chemical potential and Gibbs free energy for surfaces) are defined. Adsorption lowers interfacial tension by an amount termed the surface pressure, and the Gibbs adsorption equation allows the calculation of Γ‎s or Γ‎σ‎ for a surfactant from the variation of interfacial tension of a liquid/fluid interface with surfactant concentration in bulk solution.Less

Mixing, Mass Transfer, and Numerical Models

Thorvald Abel Engh, Geoffrey K. Sigworth, and Anne Kvithyld

in Principles of Metal Refining and Recycling

We want to eliminate dissolved impurities to another phase: slag, gas, solid, or a molten metal that has limited solubility in the main metal. The various phases may be in the form of droplets, ... More

We want to eliminate dissolved impurities to another phase: slag, gas, solid, or a molten metal that has limited solubility in the main metal. The various phases may be in the form of droplets, bubbles, particles, or walls. The contact areas with metal should be large. The aim in reactor design and operation is to achieve relatively high velocities and small dimensions. Relations for mass transfer are also included since the behaviour of systems with molten metals may be different from that usually treated in chemical engineering. In the field of turbulence the Prandtl eddy length is important for describing removal to walls. Hydrogen in aluminium and the pick-up of hydrogen in aluminium from water vapour is studied in some detail, measured, and modelled. It is taken into account that hydrogen gas is two-atomic. The approach concerning aluminium may be applied to a range of metals.Less

Framboid Self-Assembly and Self-Organization

David Rickard

in Framboids

The formation of framboids involves two distinct processes. First, pyrite microcrystals aggregate into spherical groups through surface free energy minimization. The self-assembly of framboid ... More

The formation of framboids involves two distinct processes. First, pyrite microcrystals aggregate into spherical groups through surface free energy minimization. The self-assembly of framboid microcrystals to form framboids is consistent with estimations based on the classical Derjaguin-Landau-Verwey-Overbeek (DVLO) theory, which balances the attraction between particles due to the van der Waals forces against the interparticle electrostatic repulsive force. Second, the microcrystals rearrange themselves into ordered domains through entropy maximization. Icosahedral symmetry tends to minimize short-range attractive interactions and maximize entropy. The physical processes which facilitate this rearrangement are Brownian motion and surface interactions. Curved framboid interface enforce deviation from the cubic close packed structure. In the absence of a curved surface, weakly interacting colloidal particles preferentially self-assemble into a cubic close packed structure, and this is observed in irregular, non-framboidal aggregates of pyrite micro- and nanocrystals.Less

Singularities at interfaces

J. Eggers

in Soft Interfaces: Lecture Notes of the Les Houches Summer School: Volume 98, July 2012

In this set of notes, we will pursue two different themes: pinch-off and making small things.

Tsunamis

John A. Adam

in Rays, Waves, and Scattering: Topics in Classical Mathematical Physics

This chapter describes a mathematical model of tsunami propagation (transient waves). A tsunami is a series of ocean waves triggered by large-scale disturbances of the ocean, including earthquakes, ... More

This chapter describes a mathematical model of tsunami propagation (transient waves). A tsunami is a series of ocean waves triggered by large-scale disturbances of the ocean, including earthquakes, as well as landslides, volcanic eruptions, and meteorites. Tsunamis have very long wavelengths (typically hundreds of kilometers). They have also been called “tidal waves” or “seismic sea waves,” but both terms are misleading. The chapter first considers the boundary-value problem before modeling two special cases of tsunami generation, one due to an initial displacement on the free surface and the other due to tilting of the seafloor. It also discusses surface waves on deep water and how fast the wave energy propagates and concludes with an analysis of leading waves due to a transient disturbance.Less

Quantum Wire

B. K. Ridley

in Hybrid Phonons in Nanostructures

Nanostructures in which the electrons are confined in two directions and unconfined in the third are known as quantum wires. Theories of electron confinement and phonon spectrum in quantum wires have ... More

Nanostructures in which the electrons are confined in two directions and unconfined in the third are known as quantum wires. Theories of electron confinement and phonon spectrum in quantum wires have focused on two simple geometries: wires with rectangular cross section and wires with circular cross section. This chapter covers: scalar and vector potentials in cylindrical coordinates; ionic displacement components for longitudinally polarized modes, and for transversely polarized modes, and for interface modes; hybrid LO modes; energy normalization; acoustic stresses and strains; particle displacements for LA, TA1, and TA2 modes; and free surface.Less