Entropy generation for microscale forced convection: effects of different thermal boundary conditions, velocity slip, temperature jump, viscous dissipation, and duct geometry

This work presents closed form solutions for fully developed temperature distribution and entropy generation due to forced convection in microelectromechanical systems (MEMS) in the Slip-flow regime, for which the Knudsen number lies within the range 0.001

Emergent anisotropy and flow alignment in viscous rock

A novel class of nonlinear, visco-elastic rheologies has recently been developed by MUHLHAUS et al. (2002a, b). The theory was originally developed for the simulation of large deformation processes including folding and kinking in multi-layered visco-elastic rock. The orientation of the layer surfaces or slip planes in the context of crystallographic slip is determined by the normal vector the so-called director of these surfaces. Here the model (MUHLHAUS et al., 2002a, b) is generalized to include thermal effects; it is shown that in 2-D steady states the director is given by the gradient of the flow potential. The model is applied to anisotropic simple shear where the directors are initially parallel to the shear direction. The relative effects of textural hardening and thermal softening are demonstrated. We then turn to natural convection and compare the time evolution and approximately steady states of isotropic and anisotropic convection for a Rayleigh number Ra=5.64x10(5) for aspect ratios of the experimental domain of 1 and 2, respectively. The isotropic case has a simple steady-state solution, whereas in the orthotropic convection model patterns evolve continuously in the core of the convection cell, which makes only a near-steady condition possible. This near-steady state condition shows well aligned boundary layers, and the number of convection cells which develop appears to be reduced in the orthotropic case. At the moderate Rayleigh numbers explored here we found only minor influences in the change from aspect ratio one to two in the model domain.

Comparisons of diffusive and viscous contributions to transport coefficients of light gases in single-walled carbon nanotubes

We examine here the relative importance of different contributions to transport of light gases in single walled carbon nanotubes, using methane and hydrogen as examples. Transport coefficients at 298 K are determined using molecular dynamics simulation with atomistic models of the nanotube wall, from which the diffusive and viscous contributions are resolved using a recent approach that provides an explicit expression for the latter. We also exploit an exact theory for the transport of Lennard-Jones fluids at low density considering diffuse reflection at the tube wall, thereby permitting the estimation of Maxwell coefficients for the wall reflection. It is found that reflection from the carbon nanotube wall is nearly specular, as a result of which slip flow dominates, and the viscous contribution is small in comparison, even for a tube as large as 8.1 nm in diameter. The reflection coefficient for hydrogen is 3-6 times as large as that for methane in tubes of 1.36 nm diameter, indicating less specular reflection for hydrogen and greater sensitivity to atomic detail of the surface. This reconciles results showing that transport coefficients for hydrogen and methane, obtained in simulation, are comparable in tubes of this size. With increase in adsorbate density, the reflection coefficient increases, suggesting that adsorbate interactions near the wall serve to roughen the local potential energy landscape perceived by fluid molecules.

Suppression of spurious intermediate frequency modes in under-integrated elements by combined stiffness/viscous stabilization

Solutions employing perturbation stiffness or viscous hourglass control with one-point quadrature finite elements often exhibit spurious modes in the intermediate frequency range. These spurious frequencies are demonstrated in several examples and their origin is explained. Then it is shown that by critically damping the hourglass modes, these spurious mid-range frequency modes can be suppressed. Estimates of the hourglass frequency and damping coefficients are provided for the plane 4-node quadrilateral and a 4-node shell element. Results are presented that show almost complete annihilation of spurious intermediate frequency modes for both linear and non-linear problems. Copyright (c) 2005 John Wiley & Sons, Ltd.

Dissipation of acetochlor and its distribution in surface and sub-surface soil fractions during laboratory incubations

Pesticides in soil are subject to a number of processes that result in transformation and biodegradation, sorption to and desorption from soil components, and diffusion and leaching. Pesticides leaching through a soil profile will be exposed to changing environmental conditions as different horizons with distinct physical, chemical and biological properties are encountered. The many ways in which soil properties influence pesticide retention and degradation need to be addressed to allow accurate predictions of environmental fate and the potential for groundwater pollution. Degradation and sorption processes were investigated in a long-term (100 days) study of the chloroacetanilide herbicide, acetochlor. Soil cores were collected from a clay soil profile and samples taken from 0-30cm (surface), 1.0-1.3m (mid) and 2.7-3.0m (deep) and treated with acetochlor (2.5, 1.25, 0.67 mu g acetochlor g(-1) dry wt soil, respectively). In sterile and non-sterile conditions, acetochlor concentration in the aqueous phase declined rapidly from the surface and subsoil layers, predominantly through nonextractable residue (NER) formation on soil surfaces, but also through biodegradation and biotic transformation. Abiotic transformation was also evident in the sterile soils. Several metabolites were produced, including acetochlor-ethane sulphonic acid and acetochlor-oxanilic acid. Transformation was principally microbial in origin, as shown by the differences between non-sterile and sterile soils. NER formation increased rapidly over the first 21 days in all soils and was mainly associated with the macroaggregate (> 2000 mu m diameter) size fractions. It is likely that acetochlor is incorporated into the macroaggregates through oxidative coupling, as humification of particulate organic matter progresses. The dissipation (ie total loss of acetochlor) half-life values were 9.3 (surface), 12.3 (mid) and 12.6 days (deep) in the non-sterile soils, compared with 20.9 [surface], 23.5 [mid], and 24 days [deep] in the sterile soils, demonstrating the importance of microbially driven processes in the rapid dissipation of acetochlor in soil.

Analysis of chaotic instabilities in a rotating body with internal energy dissipation

Melnikov's method is used to analytically predict the onset of chaotic instability in a rotating body with internal energy dissipation. The model has been found to exhibit chaotic instability when a harmonic disturbance torque is applied to the system for a range of forcing amplitude and frequency. Such a model may be considered to be representative of the dynamical behavior of a number of physical systems such as a spinning spacecraft. In spacecraft, disturbance torques may arise under malfunction of the control system, from an unbalanced rotor, from vibrations in appendages or from orbital variations. Chaotic instabilities arising from such disturbances could introduce uncertainties and irregularities into the motion of the multibody system and consequently could have disastrous effects on its intended operation. A comprehensive stability analysis is performed and regions of nonlinear behavior are identified. Subsequently, the closed form analytical solution for the unperturbed system is obtained in order to identify homoclinic orbits. Melnikov's method is then applied on the system once transformed into Hamiltonian form. The resulting analytical criterion for the onset of chaotic instability is obtained in terms of critical system parameters. The sufficient criterion is shown to be a useful predictor of the phenomenon via comparisons with numerical results. Finally, for the purposes of providing a complete, self-contained investigation of this fundamental system, the control of chaotic instability is demonstated using Lyapunov's method.

Effect of rolling on dissipation in fault gouges

Sliding and rolling are two outstanding deformation modes in granular media. The first one induces frictional dissipation whereas the latter one involves deformation with negligible resistance. Using numerical simulations on two-dimensional shear cells, we investigate the effect of the grain rotation on the energy dissipation and the strength of granular materials under quasistatic shear deformation. Rolling and sliding are quantified in terms of the so-called Cosserat rotations. The observed spontaneous formation of vorticity cells and clusters of rotating bearings may provide an explanation for the long standing heat flow paradox of earthquake dynamics.

Anisotropic viscous models of large-deformation Mohr-Coulomb failure

We have developed a way to represent Mohr-Coulomb failure within a mantle-convection fluid dynamics code. We use a viscous model of deformation with an orthotropic viscoplasticity (a different viscosity is used for pure shear to that used for simple shear) to define a prefered plane for slip to occur given the local stress field. The simple-shear viscosity and the deformation can then be iterated to ensure that the yield criterion is always satisfied. We again assume the Boussinesq approximation, neglecting any effect of dilatancy on the stress field. An additional criterion is required to ensure that deformation occurs along the plane aligned with maximum shear strain-rate rather than the perpendicular plane, which is formally equivalent in any symmetric formulation. We also allow for strain-weakening of the material. The material can remember both the accumulated failure history and the direction of failure. We have included this capacity in a Lagrangian-integration-point finite element code and show a number of examples of extension and compression of a crustal block with a Mohr-Coulomb failure criterion. The formulation itself is general and applies to 2- and 3-dimensional problems.

An anisotropic viscous representation of Mohr-Coulomb failure for use is modelling coupled mantle-continent dynamics

In mantle convection models it has become common to make use of a modified (pressure sensitive, Boussinesq) von Mises yield criterion to limit the maximum stress the lithosphere can support. This approach allows the viscous, cool thermal boundary layer to deform in a relatively plate-like mode even in a fully Eulerian representation. In large-scale models with embedded continental crust where the mobile boundary layer represents the oceanic lithosphere, the von Mises yield criterion for the oceans ensures that the continents experience a realistic broad-scale stress regime. In detailed models of crustal deformation it is, however, more appropriate to choose a Mohr-Coulomb yield criterion based upon the idea that frictional slip occurs on whichever one of many randomly oriented planes happens to be favorably oriented with respect to the stress field. As coupled crust/mantle models become more sophisticated it is important to be able to use whichever failure model is appropriate to a given part of the system. We have therefore developed a way to represent Mohr-Coulomb failure within a code which is suited to mantle convection problems coupled to large-scale crustal deformation. Our approach uses an orthotropic viscous rheology (a different viscosity for pure shear to that for simple shear) to define a prefered plane for slip to occur given the local stress field. The simple-shear viscosity and the deformation can then be iterated to ensure that the yield criterion is always satisfied. We again assume the Boussinesq approximation - neglecting any effect of dilatancy on the stress field. An additional criterion is required to ensure that deformation occurs along the plane aligned with maximum shear strain-rate rather than the perpendicular plane which is formally equivalent in any symmetric formulation. It is also important to allow strain-weakening of the material. The material should remember both the accumulated failure history and the direction of failure. We have included this capacity in a Lagrangian-Integration-point finite element code and will show a number of examples of extension and compression of a crustal block with a Mohr-Coulomb failure criterion, and comparisons between mantle convection models using the von Mises versus the Mohr-Coulomb yield criteria. The formulation itself is general and applies to 2D and 3D problems, although it is somewhat more complicated to identify the slip plane in 3D.