Lattice Gas Analysis of Liquid Front in Non-Crimp Fabrics

The liquid flow front during impregnation of non-crimp fabrics is considered. Irregularities in fibre bundle architecture lead to generation of bubbles at this front. The velocity of this interface is highly influenced by capillary forces mainly caused by the small fibres inside the bundles. In order to better understand which shapes the liquid front takes up at different conditions, a lattice gas model has been applied. First, the macroscopic properties of the solved gas in the liquid are discussed. Next, bubble inclusions are analyzed as to liquid–gas interface position and concentrations of minor component in each phase. The capillary effects at the fluid front are studied for systems both with and without gaps between the bundles. The flow in the interior of the fibre bundles is scrutinized, as well, by also considering the viscous stresses. The flow through unidirectional fabrics is considered by a one-dimensional model, which suggests that the liquid front inside bundles and gaps moves with the same speed when the liquid front inside the bundle has to catch up with the liquid front in the gap.     

Experimental investigation on macroscopic domain formation and evolution in polycrystalline NiTi microtubing under mechanical force

This paper reports the experimental results on macroscopic deformation instability and domain morphology evolution during stress-induced austenite → martensite (A→M) phase transformation in superelastic NiTi polycrystalline shape memory alloy microtubes. High-speed data and image acquisition techniques were used to investigate the dynamic and quasi-static events which took place in a displacement-controlled quasi-static tensile loading/unloading process of the tube. These events include dynamic formation, self-merging, topology transition, convoluted front motion and front instability of a macroscopic deformation domain. The reported phenomena brought up several fundamental issues regarding the roles of macroscopic domain wall energy and kinetics as well as their interplay with the bulk strain energy of the tube in the observed morphology instability and pattern evolution under a mechanical force. These issues are believed to be essential elements in the theoretical modeling of macroscopic deformation patterns in polycrystals and need systematic examination in the future.     

Injection of a salt solution into a geothermal reservoir saturated with superheated vapor

The injection of water containing a dissolved admixture into a high-temperature geothermal reservoir saturated with superheated vapor is considered. Behind the evaporation front on which the admixture precipitates a dissolution front separating regions with the initial concentration and with the concentration of the saturated solution coexisting with the solid salt phase is formed. It is found that the self-similar solution of the problem with two moving boundaries is two-valued. With variation of the parameters and the initial and boundary conditions the solutions may approach each other and at certain critical values merge. In the supercritical region the self-similar solution does not exist. The non-existence of a solution can be interpreted as the filling of the pores with precipitated salt and the cessation of the phase motion.     

Simulation of gas–solid particle flows over a wide range of concentration

A two-fluid model of gas–solid particle flows that is valid for a wide range of the solid-phase volume concentration (dilute to dense) is presented. The governing equations of the fluid phase are obtained by volume averaging the Navier–Stokes equations for an incompressible fluid. The solid-phase macroscopic equations are derived using an approach that is based on the kinetic theory of dense gases. This approach accounts for particle–particle collisions. The model is implemented in a control-volume finite element method for simulations of the flows of interest in two-dimensional, planar or axisymmetric, domains. The chosen mathematical model and the proposed numerical method are applied to three test problems and one demonstration problem. © 1998 John Wiley & Sons, Ltd.     

Formation fronts of a nonlinear elastic medium from a medium without shear stresses

The fronts of phase transition of a medium without shear stresses to a nonlinear incompressible anisotropic elastic medium are considered. The mass flux through unit area of a front is assumed to be known. The variation of the tangential components of the medium’s velocity and the variation of the arising shear stresses are studied. An explicit form of boundary conditions is found using the existence condition of a discontinuity front structure. The Kelvin–Voight viscoelastic model is adopted for this structure.     

The effect of geometry on ice shelf ocean cavity ventilation: a laboratory experiment

A laboratory experiment is constructed to simulate the density-driven circulation under an idealized Antarctic ice shelf and to investigate the flux of dense and freshwater in and out of the ice shelf cavity. Our results confirm that the ice front can act as a dynamic barrier that partially inhibits fluid from entering or exiting the ice shelf cavity, away from two wall-trapped boundary currents. This barrier results in a density jump across the ice front and in the creation of a zonal current which runs parallel to the ice front. However despite the barrier imposed by the ice front, there is still a significant amount of exchange of water in and out of the cavity. This exchange takes place through two dense and fresh gravity plumes which are constrained to flow along the sides of the domain by the Coriolis force. The flux through the gravity plumes and strength of the dynamic barrier are shown to be sensitive to changes in the ice shelf geometry and changes in the buoyancy fluxes which drive the flow.     

Effects of strong magnetic fields on photoionised clouds

Simulations are presented of the photoionisation of three dense gas clouds threaded by magnetic fields, showing the dynamical effects of different initial magnetic field orientations and strengths. For moderate magnetic field strengths the initial radiation-driven implosion phase is not strongly affected by the field geometry, and the photoevaporation flows are also similar. Over longer timescales, the simulation with an initial field parallel to the radiation propagation direction (parallel field) remains basically axisymmetric, whereas in the simulation with a perpendicular initial field the pillar of neutral gas fragments in a direction aligned with the magnetic field. For stronger initial magnetic fields, the dynamics in all gas phases are affected at all evolutionary times. In a simulation with a strong initially perpendicular field, photoevaporated gas forms filaments of dense ionised gas as it flows away from the ionisation front along field lines. These filaments are potentially a useful diagnostic of magnetic field strengths in H ii regions because they are very bright in recombination line emission. In the strong parallel field simulation the ionised gas is constrained to flow back towards the radiation source, shielding the dense clouds and weakening the ionisation front, eventually transforming it to a recombination front.     

Interface Conditions for a Phase Field Model with Anisotropic and Non-Local Interactions

An alternative formulation of the phase field method is utilized from an integral equation perspective. The technique allows one to derive macroscopic conditions at the interface from the microscopic potentials. Differential geometry and asymptotic analysis yield interface conditions, in arbitrary spatial dimension, for interactions that may include anisotropy as well as non-local potentials. The interface conditions can be expressed in various formulations, for example, in terms of the principal curvature directions of the interface, or the second order directional derivatives of the (signed) distance function and the Hessian of the surface tension.     

On consistent micromechanical estimation of macroscopic elastic energy,coherence energy and phase transformation strains for SMA materials

An apparatus of micromechanics is used to isolate the key ingredients entering macroscopic Gibbs free energy function of a shape memory alloy (SMA) material. A new self-equilibrated eigenstrains influence moduli (SEIM) method is developed for consistent estimation of effective (macroscopic) thermostatic properties of solid materials, which in microscale can be regarded as amalgams of n-phase linear thermoelastic component materials with eigenstrains. The SEIM satisfy the self-consistency conditions, following from elastic reciprocity (Betti) theorem. The method allowed expressing macroscopic coherency energy and elastic complementary energy terms present in the general form of macroscopic Gibbs free energy of SMA materials in the form of semilinear and semiquadratic functions of the phase composition. Consistent SEIM estimates of elastic complementary energy, coherency energy and phase transformation strains corresponding to classical Reuss and Voigt conjectures are explicitly specified. The Voigt explicit relations served as inspiration for working out an original engineering practice-oriented semiexperimental SEIM estimates. They are especially conveniently applicable for an isotropic aggregate (composite) composed of a mixture of n isotropic phases. Using experimental data for NiTi alloy and adopting conjecture that it can be treated as an isotropic aggregate of two isotropic phases, it is shown that the NiTi coherency energy and macroscopic phase strain are practically not influenced by the difference in values of austenite and martensite elastic constants. It is shown that existence of nonzero fluctuating part of phase microeigenstrains field is responsible for building up of so-called stored energy of coherency, which is accumulated in pure martensitic phase after full completion of phase transition. Experimental data for NiTi alloy show that the stored coherency energy cannot be neglected as it considerably influences the characteristic phase transition temperatures of SMA material.     

剪胀性砂土边界面模型的研究

剪胀性对于砂土,尤其是中密以及密实砂土,是一个非常显著的特性。相变线是剪胀性砂土的特征曲线,能够反映砂土的围压以及初时孔隙比对变形特性的影响。本文在边界面塑性理论的框架内,把相变状态参量引入到剪胀方程以及塑性硬化模量中,建立了一个能够描述砂土剪胀性以及循环特性的本构模型。本模型采用一套参量可以模拟不同初时孔隙比、不同围压、排水(或不排水)条件下单调(或循环)加载的应力-应变特性。验证表明本模型数值计算与试验结果相吻合。     

About macroscopic models of instability pattern formation

Various macroscopic models to describe instability pattern formation are discussed in this paper. They are similar to the Ginzburg–Landau envelope equation, but they can remain valid away from the bifurcation and are based on the technique of Fourier series with slowly varying coefficients. We focus on two questions: the need to take phase changes into account and the boundary conditions to be associated with macroscopic models. The analysis is carried out on the basis of numerical simulations for the problem of a compressed beam on a nonlinear foundation that is quite similar to the well known Swift–Hohenberg equation. The first macroscopic model involves a real envelope so that the phase is assumed to be constant. The second model is also macroscopic and it is a sort of Ginzburg–Landau equation with a complex envelope. The third one follows from a multi-scaled approach with a numerical bridging between the full model near the boundary and a macroscopic model in the bulk.     

A tensorial description of the transformation kinetics of the martensitic phase transformation

Based on a local examination of the phase transition front, a macroscopic second order tensor describing the thermodynamic force for the phase transformation is proposed. Consequently, an associated thermodynamic flux is introduced. These tensorial variables are embedded into a material law which describes the behavior of steels during the austenite–martensite phase transformation. The material law is implemented into a finite element formulation. Homogeneous tests in pure tension/compression and torsion are performed to verify the behavior of the material law. Due to the independent modeling of the behavior of the phases, the influence of the yield stress of the austenite on the transformation kinetics can be verified. A classical example is presented to show the ability of the model to calculate large structural problems.     

Droplet Imbibition into Paper Coating Layer: Pore-Network Modeling Simulation

Liquid penetration into thin porous media such as paper is often simulated using continuum-scale single-phase Darcy’s law. The underlying assumption was that a sharp invasion front percolates through the layer. To explore this ambiguous assumption and to understand the controlling pore-scale mechanisms, we have developed a dynamic pore-network model to simulate imbibition of a wetting phase from a droplet into a paper coating layer. The realistic pore structures are obtained using the FIB-SEM imaging of the coating material with a minimum resolution of 3.5 nm. Pore network was extracted from FIB-SEM images using Avizo software. Data of extracted pore network are used for statistically generating pore network. Droplet sizes are chosen in the range of those applicable in inkjet printing. Our simulations show no sharp invasion front exists and there is the presence of residual non-wetting phase. In addition, penetration of different sizes of droplets of different material properties into the pore network with different pore body and pore throat sizes are performed. We have found an approximately linear decrease in droplet volume with time. This contradicts the expected \(\sqrt{t}\)-behavior in vertical imbibition that is obtained using macroscopic single-phase Darcy’s law. With increase in flow rate, transition of imbibition invasion front from percolation-like pattern to a more sharper one with less trapping of non-wetting phase is also reported. Our simulations suggest that the single-phase Darcy’s law does not adequately describe liquid penetration into materials such as paper coating layer. Instead Richards equation would be a better choice.     

An Analysis of Phase‐Field Alloys and Transition Layers

A phase‐field approach to binary alloys is studied. Formal asymptotics of the system of parabolic differential equations leads to new interface relations as part of a macroscopic model which arises in the limit of vanishing interface thickness. Under suitable conditions we prove that the phase‐field system has a unique solution which converges to the limiting macroscopic solution. The concentration and phase are monotonic across the interface for a simplified system. Transition layers in concentration are induced due to the change in phase and the change in material diffusion across the interface. Excess impurities may be trapped as a consequence of these layers. (Accepted October 28, 1996)     

Crack front pinning by design in planar heterogeneous interfaces

The propagation of an interfacial crack front along the weak plane of a thin film stack is considered. A simple patterning technique is used to create a toughness contrast within this perfectly two-dimensional weak interface. The transparency of the specimens allows us to directly observe the propagation of the purely planar crack obtained during a DCB (double cantilever beam) test. The effect on the crack front morphology of macroscopic unidimensional patterns in the direction of propagation is studied. In these weak pinning conditions, the geometry of the front quantitatively agrees with the first-order expansion proposed by Gao and Rice [1989. First-order perturbation analysis of crack trapping by arrays of obstacles. J. Appl. Mech. 56, 828-836] which accounts for the effect of the interfacial crack front geometry on the stress intensity factor.     

An analytical study on the instability phenomena during the phase transitions in a thin strip under uniaxial tension

In the experiments on stress-induced phase transitions in SMA strips, several interesting instability phenomena have been observed, including a necking-type instability (associated with the stress drop), a shear-type instability (associated with the inclination of the transformation front) and an orientation instability (associated with the switch of the inclination angle). In order to shed more lights on these phenomena, in this paper we conduct an analytical study. We consider the problem in a three-dimensional setting, which implies that one needs to study the difficult problem of solution bifurcations of high-dimensional nonlinear partial differential equations. By using the smallness of the maximum strain, the thickness and width of the strip, we use a methodology, which combines series expansions and asymptotic expansions, to derive the asymptotic normal form equations, which can yield the leading-order behavior of the original three-dimensional field equations. An important feature of the second normal form equation is that it contains a turning point for the localization (necking) solution of the first equation. It is the presence of such a turning point which causes the inclination of the phase transformation front. The WKB method is used to construct the asymptotic solutions, which can capture the shear instability and the orientation instability successfully. Our analytical results reveal that the inclination of the transformation front is a phenomenon of localization-induced buckling (or phase-transition-induced buckling as the localization is caused by the phase transition). Due to the similarities between the development of the Luders band in a mild steel and the stress-induced transformations in a SMA, the present results give a strong analytical evidence that the former is also caused by macroscopic effects instead of microscopic effects. Our analytical results also reveal more explicitly the important roles played by the geometrical parameters.     

Propagation and Evolution of Wave Fronts in Two-Phase Porous Media

An investigation is made into the propagation and evolution of wave fronts in a porous medium which is intended to contain two phases: the porous solid, referred to as the skeleton, and the fluid within the interconnected pores formed by the skeleton. In particular, the microscopic density of each real material is assumed to be unchangeable, while the macroscopic density of each phase may change, associated with the volume fractions. A two-phase porous medium model is concisely introduced based on the work by de Boer. Propagation conditions and amplitude evolution of the discontinuity waves are presented by use of the idea of surfaces of discontinuity, where the wave front is treated as a surface of discontinuity. It is demonstrated that the saturation condition entails certain restrictions between the amplitudes of the longitudinal waves in the solid and fluid phases. Two propagation velocities are attained upon examining the existence of the discontinuity waves. It is found that a completely coupled longitudinal wave and a pure transverse wave are realizable in the two-phase porous medium. The discontinuity strength of the pore-pressure may be determined by the amplitude of the coupled longitudinal wave. In the case of homogeneous weak discontinuities, explicit evolution equations of the amplitudes for two types of discontinuity waves are derived.     

Physicochemical Processes in the Interaction Of Aerosol with the Combustion Front of Forest Fuel Materials

An experimental study has been performed to investigate the integral characteristics of the processes of heat and mass transfer and phase transformations during interaction of a droplet flow with the combustion front of a highly porous condensed material. The macroscopic regularities of the suppression of flaming combustion and thermal decomposition of typical forest fuel material due to the removal of heat as a result of its absorption during vaporization and convective cooling were studied. Three modes of interaction of a droplet aerosol with the burning forest fuel materials were considered. The time of combustion termination and the time of thermal decomposition of forest fuel materials were determined. The mechanisms of the main physicochemical processes occurring during interaction of droplet flow with the combustion front of typical forest fuel materials were established.     

Macroscopic and microscopic characteristics of a fuel spray impinged on the wall

An experimental study was performed to investigate the macroscopic behavior and atomization characteristics of a high-speed diesel spray impinged on the wall at various injection and impinging conditions. The development processes of sprays impinged on the wall were visualized using the spray visualization system composed of a Nd:YAG laser and an intensified charge-coupled device (ICCD) camera. The atomization characteristics of the impinged spray on the wall were also explored in terms of mean droplet diameter and velocity distributions by using a phase Doppler particle analyzer (PDPA) system. The results provide the effects of injection parameters, wall conditions, and the other various experimental conditions on the macroscopic behavior and atomization characteristics of the impinged sprays on the wall.