Contact angle effects on microdroplet deformation using CFD

In this paper we use computational fluid dynamics (CFD) to study the effect of contact angle on droplet shape as it moves through a contraction. A new non-dimensional number is proposed in order to predict situations where the deformed droplet will form a slug in the contraction and thus have the opportunity to interact with the channel wall. It is proposed that droplet flow into a contraction is a useful method to ensure that a droplet will wet a channel surface without a trapped lubrication film, and thus help ensure that a slug will remain attached to the wall downstream of the contraction. We demonstrate that when a droplet is larger than a contraction, capillary and Reynolds numbers, and fluid properties may not be sufficient to fully describe the droplet dynamics through a contraction. We show that, with everything else constant, droplet shape and breakup can be controlled simply by changing the wetting properties of the channel wall. CFD simulations with contact angles ranging from 30 degrees to 150 degrees show that lower contact angles can induce droplet breakup while higher contact angles can form slugs with contact angle dependent shape. Crown Copyright (c) 2005 Published by Elsevier Inc. All rights reserved.

A parametric study of droplet deformation through a microfluidic contraction: Low viscosity Newtonian droplets

Numerical simulations are conducted to investigate how a droplet of Newtonian liquid. entrained in a higher viscosity Newtonian liquid, behaves when passing through an axisymmetric microfluidic contraction. Simulations are performed using a transient Volume of Fluid finite volume algorithm, and cover ranges of Reynolds and Weber numbers relevant to microfluidic flows. Results are presented for a droplet to surrounding fluid viscosity ratio of 0.001. In contrast to behaviour at higher viscosity ratios obtained previously by the authors, shear and interfacial tension driven instabilities often develop along the droplet Surface. leading to complex shape development, and in some instances, droplet breakup. (c) 2006 Elsevier Ltd. All rights reserved.

Effect of adsorption deformation on thermodynamic characteristics of a fluid in slit pores at sub-critical conditions

Solvation. pressure due to adsorption of fluids in porous materials is the cause of elastic deformation of an adsorbent, which is accessible to direct experimental measurements. Such a deformation contributes to the Helmholtz free energy of the whole adsorbent-adsorbate system due to accumulation of compression or tension energy by the solid. It means that in the general case the solid has to be considered as not solely a source of the external potential field for the fluid confined in the pore volume, but also as thermodynamically nonmert component of the solid-fluid system. We present analysis of nitrogen adsorption isotherms and heat of adsorption in slit graphitic pores accounting for the adsorption deformation by means of nonlocal density functional theory. (c) 2006 Elsevier Ltd. All rights reserved.

Partitioning of deformation within a subduction channel during exhumation of high-pressure rocks: a case study from the Western Alps

The metamorphic belt of the Western Alps was subjected to widespread extensional tectonism at the end of the Eocene (ca. 45-35 Ma). Extension was accommodated by hinterland-directed movements along gently inclined extensional shear zones, which facilitated rapid exhumation of high-pressure and ultra-high-pressure rocks. This deformation resulted in a normal metamorphic sequence. Extension in the inner parts of the Western Alps was coeval with shortening at the front of the belt (foreland-directed thrusts), which took place during decompression, and emplaced higher grade metamorphic units over lower grade metamorphic rocks, thus forming an inverse metamorphic sequence. Two mechanisms for this extensional episode are discussed: (1) collapse of an overthickened lithosphere, and (2) internal readjustments within the orogenic wedge due to subduction channel dynamics. We favour the latter mechanism because it can account for the development of the observed inverse and normal metamorphic sequences along foreland-directed thrusts and hinterland-directed detachments, respectively. This hypothesis is supported by published structural, metamorphic and geochronological data from four geological transects through the Western Alps. This study also emphasizes the importance of post-shearing deformation (e.g. horizontal buckling versus vertical flattening), which can modify the distribution of hinterland- and foreland-directed shear zones in orogenic belts. (c) 2006 Elsevier Ltd. All rights reserved.

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.

Finite deformation model of simple shear of fault with microrotations: apparent strain localisation and en-echelon fracture pattern

Strain localisation is a widespread phenomenon often observed in shear and compressive loading of geomaterials, for example, the fault gouge. It is believed that the main mechanisms of strain localisation are strain softening and mismatch between dilatancy and pressure sensitivity. Observations show that gouge deformation is accompanied by considerable rotations of grains. In our previous work as a model for gouge material, we proposed a continuum description for an assembly of particles of equal radius in which the particle rotation is treated as an independent degree of freedom. We showed that there exist critical values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-surface layers of the fault, even in the absence of inelasticity. Here, we generalise the model to the case of finite deformations characteristic for the gouge deformation. We derive objective constitutive relationships relating the Jaumann rates of stress and moment stress to the relative strain and curvature rates, respectively. The model suggests that the pattern of localisation remains the same as in the linear case. However, the presence of the Jaumann terms leads to the emergence of non-zero normal stresses acting along and perpendicular to the shear layer (with zero hydrostatic pressure), and localised along the mid-line of the gouge; these stress components are absent in the linear model of simple shear. These additional normal stresses, albeit small, cause a change in the direction in which the maximal normal stresses act and in which en-echelon fracturing is formed.

The importance of wet-powder dynamic mechanical properties in understanding granulation

Granule impact deformation has long been recognised as important in determining whether or not two colliding granules will coalesce. Work in the last 10 years has highlighted the fact that viscous effects are significant in granulation. The relative strengths of different formulations can vary with strain rate. Therefore, traditional strength measurements made at pseudo-static conditions give no indication, even qualitatively, of how materials will behave at high strain rates, and hence are actually misleading when used to model granule coalescence. This means that new standard methods need to be developed for determining the strain rates encountered by granules inside industrial equipment and also for measuring the mechanical properties of granules at these strain rates. The constitutive equations used in theoretical models of granule coalescence also need to be extended to include strain-rate dependent components.

Quantum mechanics as an approximation to classical mechanics in Hilbert space

Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket and a quasidensity operator that is not positive definite. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Quantum mechanics is then viewed as a limiting form of classical mechanics, as Planck's constant approaches zero, rather than the other way around. The forms of semiquantum approximations to classical mechanics, analogous to semiclassical approximations to quantum mechanics, are indicated.

Quantum symmetries and the Weyl–Wigner product of group representations

In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's theorem. In the phase-space formulation, they have real, true unitary representations in the space of square-integrable functions on phase space. Each such phase-space representation is a Weyl–Wigner product of the corresponding Hilbert space representation with its contragredient, and these can be recovered by 'factorizing' the Weyl–Wigner product. However, not every real, unitary representation on phase space corresponds to a group of automorphisms, so not every such representation is in the form of a Weyl–Wigner product and can be factorized. The conditions under which this is possible are examined. Examples are presented.

Magma Flow Instabilities in a Volcanic Conduit: Implications for Long-Period Seismicity

Silicic volcanic eruptions are typically accompanied by repetitive Long-Period (LP) seismicity that originates from a small region of the upper conduit. These signals have the capability to advance eruption prediction, since they commonly precede a change in the eruption vigour. Shear bands forming along the conduit wall, where the shear stresses are highest, have been linked to providing the seismic trigger. However, existing computational models are unable to generate shear bands at the depths where the LP signals originate using simple magma strength models. Presented here is a model in which the magma strength is determined from a constitutive relationship dependent upon crystallinity and pressure. This results in a depth-dependent magma strength, analogous to planetary lithospheres. Hence, in shallow highly-crystalline regions a macroscopically discontinuous brittle type of deformation will prevail, whilst in deeper crystal-poor regions there will be a macroscopically continuous plastic deformation mechanism. This will result in a depth where the brittle-ductile transition occurs, and here shear bands disconnected from the free-surface may develop. We utilize the Finite Element Method and use axi-symmetric coordinates to model magma flow as a viscoplastic material, simulating quasi-static shear bands along the walls of a volcanic conduit. Model results constrained to the Soufrière Hills Volcano, Montserrat, show the generation of two types of shear bands: upper-conduit shear bands that form between the free-surface to a few 100 metres below it and discrete shear bands that form at the depths where LP seismicity is measured to occur corresponding to the brittle-ductile transition and the plastic shear region. It is beyond the limitation of the model to simulate a seismic event, although the modelled viscosity within the discrete shear bands suggests a failure and healing cycle time that supports the observed LP seismicity repeat times. However, due to the paucity of data and large parameter space available these results can only be considered to be qualitative rather than quantitative at this stage.

An investigation of the effect of powder on the impact characteristics between a ball and a plate using free falling experiments

The study of the mechanisms of mechanical alloying requires knowledge of the impact characteristics between the ball and vial in the presence of milling powders. In this paper, foe falling experiments have br cn used to investigate the characteristics of impact events involved in mechanical milling. The effects of milling conditions, including impact velocity, ball size and powder thickness. on the coefficient of restitution and impact force are studied. It is found that the powder has a significant influence on the impact process due to its porous structure. This effect can be demonstrated using a modified Kelvin model. This study also confirms that the impact force is a relevant parameter for characterising the impact event due to its sensitivity to the milling conditions. (C) 1998 Elsevier Science S.A.