Diffusion Slip Research Articles

Transverse creep and stress relaxation induced by interface diffusion in unidirectional metal matrix composites

Abstract An analytical solution is developed to predict the transverse creep rate induced by interface diffusion in unidirectional fiber-reinforced composites. The driving force for the interface diffusion is the normal stress acting on the interface, which is obtained from rigorous Eshelby inclusion theory. The closed-form solution is an explicit function of the applied stress, volume fraction and radius of the fiber, as well as the modulus ratio between the fiber and the matrix. It is interesting that the solution is formally similar to that of Coble creep in polycrystalline materials. For the application of the present solution in the realistic composites, the scale effect is taken into account by finite element analysis based on a unit cell. Based on the solution, a closed-form solution is also given as a description of stress relaxation induced by interfacial diffusion under constant strain. In addition, the analytical solution for the interface stress presented in this study gives some insight into the relationship between the interface diffusion and interface slip.

A lattice Boltzmann model for diffusion of binary gas mixtures that includes diffusion slip

SUMMARYThis paper describes the development of a lattice Boltzmann (LB) model for a binary gas mixture, and applications to channel flow driven by a density gradient with diffusion slip occurring at the wall. LB methods for single component gases typically use a non‐physical equation of state in which the relationship between pressure and density varies according to the scaling used. This is fundamentally unsuitable for extension to multi‐component systems containing gases of differing molecular masses. Substantial variations in the species densities and pressures may exist even at low Mach numbers; hence, the usual linearized equation of state for small fluctuations is unsuitable. Also, existing methods for implementing boundary conditions do not extend easily to novel boundary conditions, such as diffusion slip. The new model developed for multi‐component gases avoids the pitfalls of some other LB models. A single computational grid is shared by all the species, and the diffusivity is independent of the viscosity. The Navier–Stokes equation for the mixture and the Stefan–Maxwell diffusion equation are both recovered by the model. Diffusion slip, the non‐zero velocity of a gas mixture at a wall parallel to a concentration gradient, is successfully modelled and validated against a simple one‐dimensional model for channel flow. To increase the accuracy of the scheme, a second‐order numerical implementation is needed. This may be achieved using a variable transformation method that does not increase the computational time. Simulations were carried out on hydrogen and water diffusion through a narrow channel for varying total pressure and concentration gradients. Copyright © 2011 John Wiley & Sons, Ltd.

Slow diffusive fault slip propagation following the 6 April 2009 L'Aquila earthquake, Italy

Two laser strainmeters that operate at 1400‐m depth, about 20 km NE of the epicenter of the 6 April 2009 magnitude‐6.3 L'Aquila, Italy, earthquake, have produced a clear record of postseismic strain. Here we show the results from the analysis of the data related to the first few days after the event. Strain after about 1.5 days is fully consistent with afterslip on a stationary region of the earthquake causative fault. The preceding few‐hour‐long transient (whose seismic moment history is quasi‐exponential) is fully consistent with unilateral diffusive slip propagation toward the shallower part of the same fault. The propagation path ends where later afterslip probably occurred. Slip propagation similar to heat diffusion has been suggested to explain the observed scaling law between amplitude and duration of slow earthquakes; here we give the first observational evidence of the role and details of slow rupture propagation.

Lattice Boltzmann modeling of multicomponent diffusion in narrow channels

We investigate lattice Boltzmann (LB) modeling of multicomponent diffusion for finite Knudsen numbers. Analytic solutions for binary diffusion in narrow channels, where both molecular and Knudsen diffusion are of importance, are obtained for the standard and higher-order LB methods and validated against the results from the direct simulation Monte Carlo (DSMC) method. The LB methods are shown to reproduce the diffusion slip phenomena. In the DSMC method, while fluid particles are diffusely reflected on a wall, significant component slip and a kinetic boundary layer are observed. It is shown that a higher-order LB method accurately captures the characteristics observed in the DSMC method.

Yield Mode Transition in Amorphous PET

In the previous paper, we showed in a constant strain rate shear test using an amorphous polyethylene terephthalate (PET) thin plate that 1. there were two kinds of yield mode, diffuse slip line (DSL) and localized shear band (LSB) modes and 2. the DSL mode appeared in a range of relatively high temperature and low strain rate and the LSB mode occurred in a range of relatively low temperature and high strain rate. In this paper, we investigated the condition of the yield mode transition in both tensile and shear tests and showed that 1. the yield mode transition occurred in tensile test as well as in shear test depending on test condition and 2. an example of a critical condition for the transition was given as a function of temperature T and strain rate S by T Sm = C where m and C were the constants.

Yield Mode Transition at Constant Strain Rate Shear in Amorphous PET

In order to investigate yielding in amorphous polymers, shear and tensile tests have been performed in the conventional ranges of strain rate and temperature using amorphous samples. In the serial study, when the experiments on the effect of strain rate on yield stress have been executed at room temperature using amorphous polyethylene terephthalate (PET) samples, the yield mode was discovered to change drastically at a critical strain rate. In this paper, this yield mode transition was investigated at shearing. It was shown that 1.there were two different yield modes, (a) yielding governed mainly by localized shear bands (; LSB mode) and (b) yielding by diffuse slip lines (; DSL mode) and 2.while the LSB mode appeared in the case where the strain rate was high and the temperature was low, the DSL one occurred where the strain rate was low and the temperature was high.

Onsager-Casimir Reciprocal Relations Based on the Boltzmann Equation and Gas-Surface Interaction. Gaseous Mixtures

The approach to the Onsager-Casimir reciprocity relations based on the linearized Boltzmann equation and gas-surface interaction law regarding kinetic coefficients which are neither odd nor even with respect to time reversal is applied to gaseous mixtures. As an example, the slip velocity problem is considered. It is shown that using the reciprocal relations the viscous, thermal and diffuse slip coefficients can be calculated simultaneously solving a unique kinetic coefficient.

Computer simulation of diffusion-limited cluster-cluster aggregation with an Epstein drag force

The motion of particles, dispersed in a medium, between collisions with each other can, in limiting situations, be either ballistic (straight line) or diffusive (random walker). The diffusive regime can be divided into two distinct subregimes. The "continuum regime" exhibits Stokes-Einstein-type diffusion (no-slip surface boundary condition) with a frictional coefficient proportional to the particle size (linear dimension). The "Epstein regime," as we shall refer to it, is characterized by a frictional coefficient proportional to the particle cross-sectional area, hence an Epstein-type diffusion (slip surface). The purpose of the current study is to illuminate the dynamics of dilute-limit aggregation in the Epstein regime. We present results from low volume fraction Monte Carlo simulations of cluster-cluster aggregation in the Epstein regime with the particle motion based on each particle's cross-sectional area. Our findings indicate that aggregates grown under Epstein conditions have a fractal dimension of approximately 1.8, similar to that of diffusion-limited cluster-cluster aggregates (DLCA) in the continuum regime. The kinetic exponent z in the Epstein regime is found to be z approximately 0.8, lower than its value for both the continuum regime DLCA (z = 1) and for the ballistic cluster aggregation regime (z approximately 2). Cluster size distribution data for Epstein systems are found to scale at large cluster sizes with exponents consistent with the kinetic data. A scaling argument for predicting the kinetic exponent and kernel homogeneity based on the mass or size dependence of the particle velocity and collision cross section is presented and is seen to give accurate results for dilute and intermediate values of particle volume fractions not only for the current study, but also for work done by other researchers with various choices for the aggregation kernel.

Modelling of multi-component gas flows in capillaries and porous solids

The paper presents a derivation of the governing equations for multi-component convective-diffusive flow in capillaries and porous solids starting from a well-defined model and clear assumptions. The solution for the continuum regime is discussed in detail including a derivation of the diffusion slip boundary condition based on an improved momentum transfer theory. The Stefan–Maxwell species momentum equations are also re-examined and important distinctions made between the local and tube-averaged equations. An equation for the pressure gradient is derived and some examples of binary flows in capillaries are discussed. The theory for free-molecule flow is standard but the equations are recast into a form identical to the continuum equations which suggests an obvious method of interpolation for flow at arbitrary Knudsen number. There are no problems concerning viscous terms which have marred other derivations. The extension to flow in porous bodies is achieved by introducing a porosity–tortuosity factor but, unlike other treatments, this parameter is not absorbed into the gas diffusivities and flow permeability. It can then be eliminated from all but one of the equations and, with appropriate boundary conditions, the flux ratios can be obtained in terms of a mean pore radius only. The porosity–tortuosity parameter simply controls the absolute flux level and is best interpreted as a length scale-factor. The theory is applied with success to the prediction of some experimental data for helium–argon counter-diffusion and it is shown that, contrary to common belief, the mean pore radius is well-defined by flux ratio measurements if these are made with non-zero pressure differences.

CFD of turbulent transport of particles behind a backward-facing step using a new model— k- ε- Sp

The k- ε- S p model, describing two-dimensional gas–solid two-phase turbulent flow, has been developed. In this model, the diffusion flux and slip velocity of solid particles are introduced to represent the particle motion in two-phase flow. Based on this model, the gas–solid two-phase turbulent flow behind a vertical backward-facing step is simulated numerically and the turbulent transport velocities of solid particles with high density behind the step are predicted. The numerical simulation is validated by comparing the results of the numerical calculation with two other two-phase turbulent flow models ( k- ε- A p, k- ε- k p) by Laslandes and the experimental measurements. This model, not only has the same virtues of predicting the longitudinal transport of the solid particles as the present practical two-phase flow models, but also can predict the lateral transport of the solid particles correctly.

Velocity slip and temperature jump coefficients for gaseous mixtures. III. Diffusion slip coefficient

The diffusion slip coefficient is calculated for binary gaseous mixtures on the basis of the McCormack kinetic model of the Boltzmann equation, which is solved by the discrete velocity method. The calculations are carried out for the three mixtures of noble gases: neon–argon, helium–argon, and helium–xenon. Two models of the intermolecular interaction potential were considered. It was shown that this coefficient strongly depends on the potential. It was concluded that the use of the rigid spheres model does not provide physical results. An example of application of the diffusion slip coefficient is given.

Boundary slip phenomena in a binary gas mixture

The slip phenomena in gas mixtures are of fundamental significance in the specification of boundary conditions for flows in the slip regime. In a recent paper, new explicit results for the slip coefficients appropriate to binary gas mixtures were reported. The present work being reported extends the previous work to a higher level of accuracy by involving a higher order Chapman-Enskog expansion. In particular, new expressions for the slip coefficients are presented which are applicable for arbitrary models of the intermolecular interaction. Limiting expressions for the slip coefficients are given (for a simple gas) and the accuracy of the theory is discussed. Numerical calculations of the slip coefficients for different binary gas mixtures using the first and second order Chapman-Enskog approximations and the rigid sphere and Lennard-Jones (12-6) potential models have been carried out. The thermal creep and diffusion slip coefficients are found to be sensitive to the order of the approximation and to the potential model used. A comparison of the new higher order results with some of our previously obtained experimental data for the thermal transpiration effect has also been carried out and shows excellent agreement between the theory and the experiments which confirms the accuracy of the theory.

Diffusive mass transfer with superimposed frictional flow

For the superimposing of the diffusive flows – ordinary diffusion and molecular motion – with a frictional, i.e. viscous flow, several models have been proposed. In the continuum region and in the Knudsen region the models are identical. They are different however in the transition region 1< Kn<0.01. A description of the effects in this region has to take into account: pressure diffusion, slip flow and diffusion slip. It will be shown that only the model of parallel connection of ordinary and pressure diffusion on the one side and the concentration and the pressure term of molecular motion on the other side is physically plausible in the transition region. For this approach it is necessary to consider the convective compensation flow caused by the diffusion for a viscous frictional flow. On this basis an equation for the diffusive flow in the whole range of Knudsen-numbers will be derived, which includes the above-mentioned effects.

The theory of droplet diffusiophoresis for concentrated solutions

The theoretical diffusiophoresis velocity is obtained for a droplet of a concentrated solution suspended in a binary gaseous mixture. The droplet is characterized by a high thermal conductivity. The droplet radius is assumed to be much greater than the mean free path for gaseous-mixture molecules. One of the gaseous-mixture molecular components is the vapor of the droplet solvent. According to the formula obtained in this study, the droplet is driven toward lower concentration of the volatile gaseous-mixture component by diffusive slip and in the opposite direction by phase transition. An increase in the relative mass concentration of the volatile solvent in the droplet enhances effects associated with the dependence of surface tension on the volatile-component concentration and the reactive transport due to the surface nonuniformity of phase transition. As the relative mass concentration of the volatile solvent in the droplet approaches unity, the effect of diffusive slip tends to vanish.

Mass transfer within the gas-phase of porous media

The laws of various transport modes—viscous flow, diffusion and Knudsen flow—can be caused by the gradients of concentration, total and partial pressure. Their combined transports are derived and proved by selected experiments in the continuum as well as in the Knudsen region. The combination of these transport modes leads to phenomena like pressure diffusion, slip flow and diffusive slip. The three transport coefficients—the permeability, the binary diffusion coefficient and the Knudsen coefficient—can be determined by steady-state permeability and diffusion measurements. Nonsteady-state measurements deliver additional information about the pore structure of the porous medium. The presented measurements were carried out at cylindrical samples of rock salt with low porosity. Hydrogen and nitrogen were used as nonadsorbing gases. The binary diffusion experiments confirm Graham’s law with good accuracy.

Quantitative analysis of microstructures produced by creep of Ti–48Al–2Cr–2Nb–1B: Thermal and athermal mechanisms

A γ-based TiAl alloy with equiaxed microstructure and fine grain size has been studied to analyze the deformation mechanisms responsible for the creep behavior. The microstructures produced by creep and high temperature deformation have been examined by TEM to obtain information about the different aspects characterizing the primary and secondary stages of creep. Mechanical twinning has been confirmed to occur in a fraction of the grains that never exceeds 50% while 1/2 ‹110› dislocations are active within all the γ grains. The twins are only responsible for a small amount of strain, but they lead to a subdivision of the microstructure and determine (directly or indirectly) the hardening process observed during the primary stage of creep. We have proposed that during the secondary stage the creep rate is determined by the unblocking of pinned dislocations by processes such as a pipe diffusion or cross slip that allow thermally activated glide of 1/2‹110› dislocations on (001) planes.

New Light on Some Old Problems: Revisiting the Stefan Tube, Graham's Law, and the Bosanquet Equation

The Stefan diffusion tube is modeled with the recently developed binary friction model (BFM), and it is shown that this model can describe all kinds of vapor flow regimes from Stefan diffusion to pure pressure-driven flow but also Knudsen and (diffusive) slip flow. From the BFM simple criteria are derived for the transition between various regions, the criteria of which are also relevant to the fields of gas adsorption, heterogeneous catalysis, and drying of porous materials. For isobaric counterdiffusion the BFM shows where the limits of Graham's law are. For equimolar counterdiffusion analogously the area of applicability of the Bosanquet equation is derived from the BFM and an extended equation is given.

A modified Maxwell-Stefan model for transport through inert membranes: the binary friction model

This paper focuses mainly on the development of a model for permeation through inert membranes, as encountered in many cases in ultrafiltration and in gas permeation through inert porous plugs. The ultrafiltration model is made up of a boundary layer transport model and a porous membrane model in series, which are connected by an equilibrium relation. The boundary layer model is developed with the Vieth approximation for turbulent diffusivity. For the internal membrane transport, a modification of the Maxwell-Stefan-Lightfoot equation is derived (the binary friction model), which in a natural way includes both interspecies (diffusive) and species-wall forces. Application for the partial separation of PEG-3400 from aqueous solution shows that membrane friction coefficients can simply be estimated from membrane resistance measurements and mixture viscosity data. The only adjustable parameter to be determined is the distribution coefficient between the free solution and the membrane pores. The differences between the Lightfoot approach and the dusty gas model (DGM) are shown to stem from errors in the drivations of the latter, thus invalidating the dusty gas approach in the normal region in which viscous friction effects become important. For gases, the binary friction model is developed to include Knudsen and viscous wall friction terms as well as intermolecular diffusion. It is shown to give excellent coverage of the He-Ar diffusion data of Evans et al. ( J. Appl. Phys., 33 (1962) 2682; 34 (1963) 2020), with wall friction coefficients derived directly from Knudsen coefficients and gas viscosity data. The apparent success of the DGM in describing the same phenomena is shown to be caused by the relatively small importance of the wall friction forces at elevated pressures, and by the correct transition to Knudsen flow at low pressures. In addition, it is shown that diffusive slip phenomena in capillaries can be described well by the binary friction model.

Flow and diffusion of gases in capillaries and porous media

The methods and results of the treatment of flow and diffusion phenomena in the rarefied gas mixture flowing in a capillary or a porous medium are discussed. The interior flow of a gas mixture at all Knudsen numbers is analyzed by means of the “dusty gas model” and the exact kinetic theory. The problems of the free-molecular diffusion, the diffusion in a viscous flow and the viscous slip, diffusion slip and thermal creep at small Knudsen numbers are considered. The comparison of the results for the “dusty gas model”, moment-transfer arguments and exact kinetic theory allows us to establish the range of validity of different methods and practical application of the theoretical expressions. Some kinetic effects (diffusion-pressure effect, separation effect, thermomolecular pressure difference) are analysed.

Molecular Dynamics Simulation of Temperature-Dependent Tensile Fracture of Nanoscale Polycrystal. An Analysis of Temperature Dependence.

The tensile fracturing process of a nanoscale polycrystalline pure iron, which was newly developed in a previous paper for MD simulation analysis, was examined. The simulation analysis was performed in the temperature range from 100 K to 700 K. Temperature dependences of tensile strength σB and Young's modulus are first studied, and σB is found to decrease with increasing temperature. Regarding the fracture mechanism, defects are generated on the grain boundaries as the strain increases at room or low temperature, until the defects reach a cross point of three grain boundaries. Moreover, trangranular defects are generated as the strain increases. At high temperature, the fracture is caused by grain boundary diffusion and large-scale slip formation near the grain boundaries, which finally leads to the defect formation. In other words, increasing temperature results in the fracture mode transition from a cleavage fracture to a ductile one.