Diffusion Front Research Articles

Formation and Morphology of Al2O3 Inclusions at the Onset of Liquid Fe Deoxidation by Al Addition

The initial stage of deoxidation and the influence of the oxygen level on the inclusion features were examined. Liquid Fe with various dissolved oxygen content (O) was brought into contact with Al in a quartz tube for a short time, i.e. 1, 5, 30 and 60 s. Microscopic investigations of the quenched samples revealed the formation of Al2O3 inclusions in the Fe-Al reaction zone, resulting from the motion of the diffusion front with time. Specific attention is given to inclusion size, location and morphology as a function of interaction time and O content. The latter was found to influence the inclusion characteristics. The inclusion number increased drastically with O content, which is related to the degree of supersaturation of the melt, one of the most important factors influencing the formation of inclusions. The inclusion morphology evolved from angular to spherical with increasing O content.

Effects of void size, density, and arrangement on deflagration and detonation sensitivity of a reactive empirical bond order high explosive

The shock response of two-dimensional model high explosive crystals with various arrangements of circular voids is explored. We simulate a piston impact using molecular-dynamics simulations with a reactive empirical bond order model potential for a submicron, subnanosecond exothermic reaction in a diatomic molecular solid. Voids of radius 10 nm reduce the minimum initiating velocity by a factor of 4; a single 2.5 nm void (per periodic image) reduces the minimum velocity for detonation by 10% and the exponent of the induction time's pressure dependence by about 4. In square lattices of voids all of one size, reducing that size or increasing the porosity while holding the other parameter fixed causes the hotspots to consume the material more quickly and detonation to occur sooner and at lower piston velocities. The early time behavior is seen to follow a very simple ignition and growth model. The hotspots collectively develop a broad pressure wave (a sonic, diffuse deflagration front) that, upon merging with the lead shock, transforms it into a detonation. The reaction yields produced by triangular lattices are not significantly different. With random void arrangements, the mean time to detonation is 15.5% larger than with the square lattice; the standard deviation of detonation delays is just 5.1%.

Pattern formation and propagation during microwave breakdown

During microwave breakdown at atmospheric pressure, a sharp plasma front forms and propagates toward the microwave source at high velocities. Experiments show that the plasma front may exhibit a complex dynamical structure or pattern composed of plasma filaments aligned with the wave electric field and apparently moving toward the source. In this paper, we present a model of the pattern formation and propagation under conditions close to recent experiments. Maxwell’s equations are solved together with plasma fluid equations in two dimensions to describe the space and time evolution of the wave field and plasma density. The simulation results are in excellent agreement with the experimental observations. The model provides a physical interpretation of the pattern formation and dynamics in terms of ionization-diffusion and absorption-reflection mechanisms. The simulations allow a good qualitative and quantitative understanding of different features such as plasma front velocity, spacing between filaments, maximum plasma density in the filaments, and influence of the discharge parameters on the development of well-defined filamentary plasma arrays or more diffuse plasma fronts.

Large-scale Bright Fronts in the Solar Corona: A Review of “EIT waves”

``EIT waves" are large-scale coronal bright fronts (CBFs) that were first observed in 195 \AA\ images obtained using the Extreme-ultraviolet Imaging Telescope (EIT) onboard the \emph{Solar and Heliospheric Observatory (SOHO)}. Commonly called ``EIT waves", CBFs typically appear as diffuse fronts that propagate pseudo-radially across the solar disk at velocities of 100--700 km s$^{-1}$ with front widths of 50-100 Mm. As their speed is greater than the quiet coronal sound speed ($c_s\leq$200 km s$^{-1}$) and comparable to the local Alfv\'{e}n speed ($v_A\leq$1000 km s$^{-1}$), they were initially interpreted as fast-mode magnetoacoustic waves ($v_{f}=(c_s^2 + v_A^2)^{1/2}$). Their propagation is now known to be modified by regions where the magnetosonic sound speed varies, such as active regions and coronal holes, but there is also evidence for stationary CBFs at coronal hole boundaries. The latter has led to the suggestion that they may be a manifestation of a processes such as Joule heating or magnetic reconnection, rather than a wave-related phenomena. While the general morphological and kinematic properties of CBFs and their association with coronal mass ejections have now been well described, there are many questions regarding their excitation and propagation. In particular, the theoretical interpretation of these enigmatic events as magnetohydrodynamic waves or due to changes in magnetic topology remains the topic of much debate.

대칭형 다공성 매질의 확산주도 영역에 관한 1차 물질이동 방정식

Comparison of the classical mobile-immobile zone (MIM) model to the derived model led to several conclusions. If the MIM model is to be applied, the initial concentration in the immobile zone has to be down-scaled by a correction factor that is a function of pore geometry. The MIM model was valid only after sufficiently long time has passed, i.e., only after the diffusion front reaches the deepest pore wall in the immobile zone. The MIM mass-transfer coefficient , was inversely proportional to the square of the pore depth. Also it did not depend on the mobile-zone flow velocity, contrary to the number of laboratory and field observations. The classical MIM model displayed a rapid exponential decay of immobile-zone concentration. Meanwhile at large times, the newly derived model displayed similar exponential decay. This was contrary to the mounting evidence of power-law BTC tails observed in laboratory and field settings.

Time‐scale analysis in unsaturated porous media under external wave loads

AbstractExtreme waves caused by tsunamis and storm surges can lead to soil failures in the near‐shore region, which may have severe impact on coastal environments and communities. Multiphase flows in deformable porous media involve several coupled processes and multiple time scales, which are challenging for numerical simulations. The objective of this study is to investigate the roles of the various processes and their interactions in multiphase flows in unsaturated soils under external wave loading, via theoretical time‐scale analysis and numerical simulations. A coupled geomechanics–multiphase flow model based on conservation laws is used. Theoretical analysis based on coupled and decoupled models demonstrates that transient and steady‐state responses are governed by pore pressure diffusion and saturation front propagation, respectively, and that the two processes are essentially decoupled. Numerical simulations suggest that the compressibility of the pore fluids and the deformation of the soil skeleton are important when the transient responses of the media are of concern, while the steady‐state responses are not sensitive to these factors. The responses obtained from the fully coupled numerical simulations are explained by a simplified time‐scale analysis based on coupled and decoupled models. Copyright © 2010 John Wiley & Sons, Ltd.

Lateral uniformity in chemical composition along a buried reaction front in polymers usingoff-specular reflectivity**Official contribution of the National Institute of Standards and Technology; not subject tocopyright in the United States.

Off-specular neutron reflectometry was applied to characterize the form and amplitude oflateral compositional variations at a buried reaction–diffusion front. In this work,off-specular neutron measurements were first calibrated using off-specular x-ray reflectivityand atomic force microscopy via a roughened glass surface, both as a free surface and as aburied interface that was prepared by spin coating thin polymer films upon the glasssurface. All three methods provided consistent roughness values despite the difference intheir detection mechanism. Our neutron results demonstrated, for the first time, that thecompositional heterogeneity at a buried reaction front can be measured; the modelsystem used in this study mimics the deprotection reaction that occurs duringthe photolithographic process necessary for manufacturing integrated circuits.

Role of seepage forces on seismicity triggering

Borehole fluid injection is commonly used for geological sequestration of carbon dioxide, underground storage of natural gas, waste injections, and during stimulations and development of geothermal and hydrocarbon reservoirs. Typically, the injection process induces significant seismicity, with some earthquakes as large as magnitude four. Induced seismicity has also been observed around producing hydrocarbon boreholes. Recently, it has been argued that some induced seismicity data can be explained by a highly nonlinear fluid diffusion mechanism or by the propagation of fluid pressure pulses. The nature of the nonlinearity and the mechanisms by which a pressure pulse can trigger seismicity are still uncertain. In this paper I show that the same spatiotemporal variation of seismicity can be explained and predicted by linear diffusion coupled to deformation of a linear poroelastic medium. By calculating the propagation of Coulomb Yielding Stress (CYS) perturbation with time, it is demonstrated that seismicity can be triggered by this perturbation. The change of CYS along the diffusion front is caused by seepage forces, which are body forces generated by fluid pressure gradients, and can explain induced seismicity during borehole fluid injection and extraction. Using published experimental data, I demonstrate how the spatiotemporal distribution of fluid‐induced seismic events can be used for reservoir modeling and characterization.

Solution of Fractional Diffusion Equation with a Moving Boundary Condition by Variational Iteration Method and Adomian Decomposition Method

In this paper, the approximate analytic solutions of the mathematical model of time fractional diffusion equation (FDE) with a moving boundary condition are obtained with the help of variational iteration method (VIM) and Adomian decomposition method (ADM). By using boundary conditions, the explicit solutions of the diffusion front and fractional releases in the dimensionless form have been derived. Both mathematical techniques used to solve the problem perform extremely well in terms of efficiency and simplicity. Numerical solutions of the problem show that only a few iterations are needed to obtain accurate approximate analytical solutions. The results obtained are presented graphically.

The Transition between Sharp and Diffusive Wetting Fronts as a Function of Imbibing Fluid Properties

The efficiency of one fluid displacing another in a permeable medium depends on the pore‐scale dynamics at the main wetting front. Experiments have shown that the frontal dynamics can result in two different flow regimes: a sharp and a diffuse front. In the sharp front regime, the displacing fluid occupies nearly all the pores and throats behind the main wetting front and the saturation changes abruptly. In contrast, in the diffuse front regime, pores are filled gradually at the main wetting front, and the saturation change is gradual in space. The different fronts can greatly alter the relative permeability curves, the trapping mechanisms, and the displacement efficiency. Directly measuring the sharpness of the front is difficult. Instead, we correlated the front sharpness to saturation overshoot, which occurs for moderate‐ to high‐flux vertical displacements of low‐density fluid by a higher density fluid in one‐dimensional, homogenous, permeable media. We hypothesized that the sharpness of wetting front can be explained by competition between two different pore‐filling mechanisms (called snap off and piston like), with the competition controlled by the velocity of the front and thus the injected flux. We conducted a series of infiltration experiments to determine the saturation profile as a function of flux for seven different fluids. We found that for each fluid there is a flux (called overshoot flux) below which saturation overshoot ceases and the front is diffuse. We found that the overshoot flux depends inversely on the invading fluid's viscosity and shows little or no dependence on the invading fluid's surface tension, vapor pressure, or miscibility with water.

Diffusion of Au atoms and (5×2) phase formation on the Si(111) (7×7) surface

In this article we investigate the complex 1D mesoscopic model of adatom diffusion and the evolution of an ordered phase on the substrate surface. The analysis of the theoretical model is compared with the experimental results of the spreading of Au adatoms on Si(111)-(7×7) surface. The steady state solutions and their stability conditions are determined within the concept of the traveling-wave solution. It is shown that the formation of the ordered phase (5×2) and the difference in the diffusion of Au on (7×7) and on (5×2) structure results in a sharp edge of diffusion front which corresponds to the coverage of a saturated (5×2) phase. This edge moves linearly in time and α can be determined by experiment. The system of model equations enables the damped waves solution or temporary evolution of two steps.

Quark-nova remnants

(Abridged) XTE J1810-197 and 1E 1547.0-5408 are two transient AXPs exhibiting radio emission with unusual properties. In addition, their spin down rates during outburst show opposite trends, which so far has no explanation. Here, we extend our quark-nova model for AXPs to include transient AXPs, in which the outbursts are caused by transient accretion events from a Keplerian (iron-rich) degenerate ring. For a ring with inner and outer radii of 23.5 km and 26.5 km, respectively, our model gives a good fit to the observed X-ray outburst from XTE J1810-197 and the behavior of temperature, luminosity, and area of the two X-ray blackbodies with time. The two blackbodies in our model are related to a heat front (i.e. Bohm diffusion front) propagating along the ring's surface and an accretion hot spot on the quark star surface. Radio pulsations in our model are caused by dissipation at the light cylinder of magnetic bubbles, produced near the ring during the X-ray outburst. The delay between X-ray peak emission and radio emission in our model is related to the propagation time of these bubbles to the light cylinder. We predict a ~1 year and ~1 month delay for XTE J1810-197 and 1E 1547.0-5408, respectively. The observed flat spectrum, erratic pulse profile, and the pulse duration are all explained in our model as a result of X-point reconnection events induced by the dissipation of the bubbles at the light cylinder. The spin down rate of the central quark star can either increase or decrease depending on how the radial drift velocity of the magnetic islands changes with distance from the central star. We suggest an evolutionary connection between transient AXPs and typical AXPs in our model.

Miscible Thermo-Viscous Fingering Instability in Porous Media. Part 2: Numerical Simulations

In this second part of a two-part study, full nonlinear simulations of miscible thermo-viscous fingering are carried out using Hartley transform-based Pseudo-spectral method. Vorticity-streamfunction formulation is applied to the model equations developed in Part 1. Time evolutions of nonlinear fingers are examined qualitatively by plotting concentration and temperature iso-surfaces. The effect of increase in the thermal mobility ratio as well as decrease in the thermal lag coefficient is examined first for a hypothetical value of the Lewis number, Le = 1. For fixed solutal mobility ratio, an enhancement in instability is observed with the increase in the thermal mobility ratio for all values of the thermal lag coefficient. However, at large values of the Lewis number, the instability is seen to be strictly dominated by the solutal mobility ratio. At unity thermal lag coefficient, for the tested values of the other parameters, less complex finger structures are observed than in a reference isothermal case with the same solutal mobility ratio but zero thermal mobility ratio. As the thermal lag coefficient is decreased, a highly diffuse thermal front lags farther behind the fluid front, and the stabilizing effect of strong thermal diffusion gets alleviated. Consequently, the fluid front becomes as unstable as the reference isothermal case. The qualitative observations are further substantiated quantitatively using relative contact area (R.C.A.) and Sweep Efficiency as well as through identifying the relative contributions of solutal and thermal vorticity components in the development of the instability. The conclusions drawn from this study are in complete qualitative agreement with the ones obtained from Part 1, particularly using the initial value calculations (IVC) approach. Such agreement infers the superiority of (IVC) approach over the quasi-steady-state approximation (QSSA) approach in linear stability analysis of the problem under investigation.

Interphase development in a three-component polymer system with asymmetric mobility

We report a study on the interphase evolution in a system composed by three polymeric components with markedly different mobility distributed between two layers. One of the layers is a low-Tg blend containing a low molecular weight polystyrene (PS) as a plasticizer (low-M PS) and PS chains with much higher molecular weight (high-M PS). The counterpart is a high-Tg layer composed by polyphenylene oxide. The system was annealed at several temperatures between Tg of the polymer layers and the subsequent interphase development probed by optical sectioning with confocal Raman microspectroscopy. The profiles obtained revealed the existence of two diffusion fronts that advance in opposite directions, both showing a similar response with time and temperature. These fronts act as well-defined boundaries that structure the interphase into three well-defined regions with almost constant PS volume fraction. We discuss this particular phenomenology proposing a simple diffusion model that describes the main interphase features. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 627–633, 2010

Sensitivity effects of void density and arrangement in a REBO high explosive

The shock response of two-dimensional model high explosive crystals with various arrangements of circular voids is explored. We simulate a piston impact using molecular dynamics simulations with a Reactive Empirical Bond Order (REBO) model potential for a sub-micron, sub-ns exothermic reaction in a diatomic molecular solid. In square lattices of voids all of one size, reducing that size or increasing the porosity while holding the other parameter fixed causes the hotspots to consume the material more quickly and detonation to occur sooner and at lower piston velocities. The early time behavior is seen to follow a very simple ignition and growth model. The hotspots are seen to collectively develop a broad pressure wave (a sonic, diffuse deflagration front) that, upon merging with the lead shock, transforms it into a detonation. The reaction yields produced by triangular lattices are not significantly different. With random void arrangements, the mean time to detonation is 15.5% larger than with the square lattice; the standard deviation of detonation delays is just 5.1%.

Hierarchical wrinkling patterns

This paper reports a simple and flexible method for generating hierarchical patterns from wrinkling instability. Complex features with gradually changing topographies are generated by using the spontaneous wrinkling of a rigid membrane (titanium) on a soft foundation (polystyrene) compressed via the diffusion of a solvent. We show that the morphology of these unreported wrinkled patterns is directly related to the rheological properties of the polymer layer and the geometry of the diffusion front. Based on these ingredients, we rationalize the mechanism for the formation of hierarchical wrinkling patterns and quantify our experimental findings with a simple scaling theory. Finally, we illustrate the relevance of our structuration method by studying the mechanosensitivity of fibroblasts.

Distribution of cytochrome c in polyacrylate microgels

The uptake of cytochrome c from aqueous solution (pH = 7, ionic strength 40 mM) into weakly cross-linked sodium polyacrylate microgels is investigated by means of micromanipulator-assisted light microscopy and laser scanning confocal microscopy. It is shown that the protein is distributed uniformly in the gels at equilibrium. The kinetics of the interaction is investigated by means of time-resolved deswelling curves, and by observations of the diffusion fronts of fluorescently labeled cytochrome c in single gel particles. The time to reach the deswollen equilibrium state of the gels is short, in general, and decreases rapidly with increasing protein concentration in the solution, indicative of a rapid diffusive transport inside the microgels. The results are compared with results for lysozyme binding with the same type of network, and with results for macrogels in the literature. The importance of net attractive protein–protein forces for the mechanism of binding is highlighted.

Diffusion front capturing schemes for a class of Fokker–Planck equations: Application to the relativistic heat equation

In this research work we introduce and analyze an explicit conservative finite difference scheme to approximate the solution of initial-boundary value problems for a class of limited diffusion Fokker–Planck equations under homogeneous Neumann boundary conditions. We show stability and positivity preserving property under a Courant–Friedrichs–Lewy parabolic time step restriction. We focus on the relativistic heat equation as a model problem of the mentioned limited diffusion Fokker–Planck equations. We analyze its dynamics and observe the presence of a singular flux and an implicit combination of nonlinear effects that include anisotropic diffusion and hyperbolic transport. We present numerical approximations of the solution of the relativistic heat equation for a set of examples in one and two dimensions including continuous initial data that develops jump discontinuities in finite time. We perform the numerical experiments through a class of explicit high order accurate conservative and stable numerical schemes and a semi-implicit nonlinear Crank–Nicolson type scheme.

Compaction properties, drug release kinetics and fronts movement studies from matrices combining mixtures of swellable and inert polymers. II. Effect of HPMC with different degrees of methoxy/hydroxypropyl substitution

The aim of this paper is the modification of the release behaviour of hydrophilic HPMC-based matrices of different substitution degree (E4M, F4M, K4M) by the introduction of a new inert polymeric excipient hydroxypropylcellulose-methyl methacrylate (HCMMA) at different proportions (75:25, 50:50 and 25:75). The product (HCMMA) was dried either in a vacuum oven – OD copolymers – or freeze-dried—FD copolymers. HPMC E4M formulations showed the worst compaction properties. All mixtures presented a percentage of theophylline release between 47% and 32% at 1440 min. The drying methods employed had only influence over the drug release in E4M and K4M formulations, at higher proportions of HCMMA, showing the highest release the mixtures containing OD-HCMMA. Combinations of diffusion and erosion release mechanisms were found to matrix tablets. All mixtures with F4M did not modify relaxation rate constant values of Peppas and Shalin equation ( k r ) respect to F4M 100%. However, all mixtures with K4M showed the highest k r values, which decreased when HCMMA proportion decreased. Only K4M mixtures showed a different diffusion front movement than the other mixtures. The modulation of theophylline monoaxial release was obtained using a high percentage of HCMMA, and HPMCs with a substantial difference of hydroxypropyl groups (F4M and K4M or E4M).

Effect of dispersion on the onset of convection during CO2 sequestration

Dissolution of carbon dioxide (CO2) injected into saline aquifers causes an unstable high-density diffusive front. Understanding how instability fingers develop has received much attention because they accelerate dissolution trapping, which favours long-term sequestration. The time for the onset of convection as the dominant transport mechanism has been traditionally studied by neglecting dispersion and treating the CO2–brine interface as a prescribed concentration boundary by analogy to a thermal convection problem. This work explores the effect of these simplifications. Results show that accounting for the CO2 mass flux across the prescribed concentration boundary has little effect on the onset of convection. However, accounting for dispersion causes a reduction of up to two orders of magnitude on the onset time. This implies that CO2 dissolution can be accelerated by activating dispersion as a transport mechanism, which can be achieved adopting a fluctuating injection regime.