Planar Front Research Articles

Stability of two-phase flow with interfacial flux in porous media: CO2 mineralization

The primary objective of carbon capture, utilization, and storage (CCUS) applications in various natural and engineered porous materials is to achieve a stable and planar CO2 displacement front, thereby suppressing viscous fingering. A stable front can ensure uniform and exhaustive CO2 mineralization throughout a reactive medium (i.e., mineral carbonation). Drawing inspiration from experimental observations of CO2 flooding into cores of portland cement-based materials, we examine the stability of such systems. Under these conditions, the injected CO2 continuously dissolves into the resident water phase, which becomes chemically disequilibrated with the solid minerals and leads to mineral carbonation on the wetted surfaces. Focusing on the early injection time allows us to reduce the complex multiphysical problem to a simple two-phase flow scenario of immiscible displacement with a CO2 interfacial flux sink. The formulated equations are investigated using numerical simulations and linear stability analysis, which results in a closed-form criterion, and provide fundamental insights into system stability. Overall, the results show that several effects combine to stabilize the system, including the sink effect, which acts to eliminate instability; the reduction in flow velocity along the flow path, which limits flow focusing; and the relative increase in stabilizing capillary forces. Therefore, if the system is stable at early stages, it will likely remain stable later on. Finally, this research demonstrates the use of theory to simplify complex problems and shows that even when flow is inherently coupled, the state of systems can often be determined from fluid stability alone.

Spreading, flattening, and logarithmic lag for reaction-diffusion equations in $\mathbb{R}^{N}$: Old and new results

This paper is concerned with the large-time dynamics of bounded solutions of reaction-diffusion equations with bounded or unbounded initial support in \R^{N} . We start with a survey of some old and recent results on the spreading speeds of the solutions and their asymptotic local one-dimensional symmetry. We then derive some flattening properties of the level sets of the solutions if initially supported on subgraphs. We also investigate the special case of asymptotically conical-shaped initial conditions. Lastly, we reclaim some known results about the logarithmic lag between the position of the solutions and that of planar or spherical fronts expanding with minimal speed, for almost-planar or compactly supported initial conditions. We then prove some new logarithmic-in-time estimates of the lag of the position of the solutions with respect to that of a planar front, for initial conditions which are supported on subgraphs with logarithmic growth at infinity. These estimates entail in particular that the same lag as for compactly supported initial data holds true for a class of unbounded initial supports. The paper also contains some related conjectures and open problems.

Design and experimental validation of an aspheric multi-lenticular plano-convex lens for VCSEL beam collimation

In this work, we propose a design method of an aspheric lens that achieves collimation for a VCSEL laser beam. The designed lens features a planar front surface and an aspheric back surface of which the profile is mathematically characterized and precisely determined based on the proposed method. The method is derived from a basic geometric-optics analysis and construction approach. The collimating effect of the lens was first analyzed in simulation and then validated in experimental measurement. The experimental results show that the collimator lens transforms the input VCSEL laser beam divergence angle from 25° (436.33 mrad) to an output angle of 3.6906 mrad.

Nanoparticle uptake by a semi-permeable, spherical cell from an external planar diffusive field. II. Numerical study of temporal and spatial development validated using FEM

In this paper, we present a mathematical study of particle diffusion inside and outside a spherical biological cell that has been exposed on one side to a propagating planar diffusive front. The media inside and outside the spherical cell are differentiated by their respective diffusion constants. A closed form, large-time, asymptotic solution is derived by the combined means of Laplace transform, separation of variables, and asymptotic series development. The solution process is assisted by means of an effective far-field boundary condition, which is instrumental in resolving the conflict of planar and spherical geometries. The focus of the paper is on a numerical comparison to determine the accuracy of the asymptotic solution relative to a fully numerical solution obtained using the finite element method. The asymptotic solution is shown to be highly effective in capturing the dynamic behaviour of the system, both internal and external to the cell, under a range of diffusive conditions.

Thickness Optimization of Front and Recombination ITO in Monolithic Perovskite/Silicon Tandem Solar Cells

Optical losses of perovskite/silicon tandem solar cells can be effectively reduced by optimizing the thin‐film layer thicknesses. Herein, the thicknesses of DC sputtered indium tin oxide (ITO) films, which serve as the front electrode and the recombination layer connecting the subcells, are optimized to reach high transparency and good lateral charge transport simultaneously. Optical simulations of the full perovskite/silicon tandem solar cell stacks are performed to find the optimum recombination and front electrode ITO thicknesses for solar cells as well as modules. Implementation of the optimized 25 nm front electrode ITO thickness in semitransparent single‐junction perovskite solar cells increases the short‐circuit density by 1.5 mA cm−2 compared to the former reference thickness of 75 nm. Combined with an optimized 20 nm recombination ITO layer, high short‐circuit density of 20.3 mA cm−2 is reached in perovskite/silicon tandem solar cell devices, which is the highest reported value for planar front perovskite/silicon tandem solar cells to the best of knowledge. Further interface passivation enables 28.8% power conversion efficiency.

A computational study of solidification kinetics in multicomponent alloys

Recent advances in materials processing technologies highlight the need to understand solidification kinetics in multicomponent alloys. Using a finite interface dissipation phase field model, we investigate planar front solidification rates in ternary alloys, used as a model system, as a function of various mass transport processes and nonequilibrium conditions. Simulation results reveal that the off-diagonal diffusion coefficients play an important role in controlling the solid–liquid (S–L) interface velocity and solute partition coefficients. Specifically, under various rapid solidification conditions negative values for the off-diagonal diffusion coefficients increase the solute partition coefficients due to the depletion of liquid phase concentrations ahead of the S–L interface. Given an undercooling, the S–L interface velocity increases with decreasing the off-diagonal diffusion coefficients. In broad terms, our work quantifies the role of coupled mass transport processes and nonequilibrium effects in solidification rates of multicomponent alloys.

Uniform bounds of families of analytic semigroups and Lyapunov Linear Stability of planar fronts

AbstractWe study families of analytic semigroups, acting on a Banach space, and depending on a parameter, and give sufficient conditions for existence of uniform with respect to the parameter norm bounds using spectral properties of the respective semigroup generators. In particular, we use estimates of the resolvent operators of the generators along vertical segments to estimate the growth/decay rate of the norm for the family of analytic semigroups. These results are applied to prove the Lyapunov linear stability of planar traveling waves of systems of reaction–diffusion equations, and the bidomain equation, important in electrophysiology.

Stability of chemical reaction fronts in solids: Analytical and numerical approaches

Localized chemical reactions in deformable solids are considered. A chemical transformation is accompanied by the transformation strain and emerging mechanical stresses, which affect the kinetics of the chemical reaction front to the reaction arrest. A chemo-mechanical coupling via the chemical affinity tensor is used, in which the stresses affect the reaction rate. The emphasis is made on the stability of the propagating reaction front in the vicinity of the blocked state. There are two major novel contributions. First, it is shown that for a planar reaction front, the diffusion of the gaseous-type reactant does not influence the stability of the reaction front – the stability is governed only by the mechanical properties of solid reactants and stresses induced by the transformation strain and the external loading, which corresponds to the mathematically analogous phase transition problem. Second, the comparison of two computational approaches to model the reaction front propagation is performed – the standard finite-element method with a remeshing technique to resolve the moving interface is compared to the cut-finite-element-based approach, which allows the interface to cut through the elements and to move independently of the finite-element mesh. For stability problems considered in the present paper, the previously-developed implementation of the cut-element approach has been extended with the additional post-processing procedure that obtains more accurate stresses and strains, relying on the fact that the structured grid is used in the implementation. The approaches are compared using a range of chemo-mechanical problems with stable and unstable reaction fronts.

Formation of Precipitation Ellipsoidal Disks and Spheres in the Wake of a Planar Diffusion Front.

Pattern formation is one of the examples of self-organization. In the generation of patterns, the coupling between the mass transport of the chemical species and their chemical reactions plays an important role. Periodic precipitation (Liesegang phenomenon) is a type of pattern formation in which layered precipitation structures form in the wake of the diffusion front. Here, we show a new type of precipitation pattern formation in zeolitic imidazolate framework-67 in a solid hydrogel column in a test tube manifested in the generation of precipitation ellipsoidal disks and spheres in the wake of the planar diffusion front of the outer electrolyte (2-methylimidazole). To increase the probability of the emergence of ellipsoidal disks and spheres, the surfaces of the borosilicate test tubes were chemically treated and functionalized. To support the experimental findings, we developed a reaction-diffusion model that qualitatively describes the formation of precipitate ellipsoidal disks and spheres in a test tube.

The effect of confinement on thermal convection and longitudinal macrosegregation in directionally solidified dilute succinonitrile–camphor alloy

Directional solidification experiments were conducted in a succinonitrile–0.24 wt% camphor alloy with an emphasis on the planar front interface temperature dynamics using different sample thicknesses. The interface temperature was found to depend significantly on the thickness due to non-negligible convection effects in the thicker samples. The results were interpreted with the help of an order of magnitude analysis and a boundary layer model, which permitted estimation of the solute macrosegregation profile. The experiments and corresponding analyses performed in this work constitute an experimental characterization of convection effects as a function of sample thickness.

Transmission electron microscopy of the rapid solidification microstructure evolution and solidification interface velocity determination in hypereutectic Al-20at.%Cu after laser melting

The evolution of rapid solidification (RS) microstructure and solidification interface velocity has been studied experimentally by in-situ transmission electron microscopy and postmortem characterization for hypereutectic Al-20at.%Cu (37 wt.%Cu) after laser melting. Four morphologically distinct regions formed via growth modes changing from θ-Al2Cu phase dendrites to eutectic cell growth, possibly α-Al dendrite growth (α-cell), banded growth, and α-Al plane front growth. Tendency for faceting and low capacity for solute trapping limited the θ-phase dendrite growth to solidification interface velocity v < 0.07 m/s. Consequently, formation of pro-eutectic micro-constituent was suppressed, and RS microstructure formation was dominated by eutectic, α-cell, and banded morphology grains for the Al-20at.%Cu alloy. Eutectic growth operated for interface velocity of 0.1 m/s ≤ v < 0.3 m/s, with a transition from regular lamellar, 2-λ and 1-λ mode to a dense irregular morphology dominated by α-phase at v = 0.3 m/s. Interface temperature calculations indicated feasibility of α-cell growth mode for 0.3 m/s ≤ v < 0.7 m/s. Banded growth occurred for 0.7 m/s ≤ v < 1.3 m/s. Plane front α-phase growth was evident for interface velocities v ≥ 1.3 m/s. Previous work on rapid solidification microstructure development in hypereutectic Al-Cu alloys reported a regime of α-cell growth subsequently to eutectic and prior to transition to banded growth for Al-19at.%Cu (36 wt.%Cu), while for Al-22at.%Cu (40 wt.%Cu) eutectic growth transitioned directly to α-plane front growth without emergence of a banded regime. Based on the current study the disappearance of the banded growth regime occurs for a composition larger than 20at.%Cu.

Spectral induced polarization responses of carbonate precipitation in gel-saturated media with and without electron conductors

SUMMARY Interest in the use of carbonate precipitation for the purposes of soil stabilization, carbon capture and environmental remediation has created a need for geophysical techniques capable of characterizing the 3-D extent of precipitation in the subsurface. The use of spectral induced polarization, a geophysical technique sensitive to mineral precipitation and dissolution processes, has been investigated in previous studies; nevertheless, debate still exists regarding measured induced polarization (IP) signals relating to the formation of calcite. In this study, calcite was precipitated within gel-saturated media through highly controlled double-diffusion methods. Three experiments were conducted to study both the inherent IP response of calcite in isolation, as well as the IP response when precipitated within a low-polarizability background medium (quartz sand) and a high-polarizability medium (a sand–magnetite mixture). The results support that in isolation, the polarization of the electrical double layer surrounding individual calcite grains is not a significant contributor to IP signatures from calcite precipitation. However, under certain circumstances the precipitation of calcite, in the quartz-sand and sand–magnetite mixtures, can produce a strong IP response when the precipitation blocks a current conduction pathway. If metallic mineral grains are present then they may act as conduits for current if they become embedded in an insulating calcite wall, creating a significant electrode polarization which dominates the IP signal. Equivalent circuit models indicate that the precipitation of calcite as a thin planar front normal to the current path is analogous to a simple lossy capacitor blocking most DC current but being thin enough to measurably polarize. Circuit models also suggest that the total impedance seen from the sand–magnetite sample is simply the sum of the impedance of the disseminated grains and the grains encased in the calcite front. The encased grains also have a higher relaxation time which may indicate a different polarization mechanism than from disseminated magnetite.

Optoelectronic optimization of graded-bandgap thin-film AlGaAs solar cells. Part II: optimal antireflection front-surface texturing.

In Part I [Appl. Opt.59, 1018 (2020)APOPAI0003-693510.1364/AO.381246], we used a coupled optoelectronic model to optimize a thin-film AlGaAs solar cell with a graded-bandgap photon-absorbing layer and a periodically corrugated Ag backreflector combined with localized ohmic Pd-Ge-Au backcontacts, because both strategies help to improve the performance of AlGaAs solar cells. However, the results in Part I were affected by a normalization error, which came to light when we replaced the hybridizable discontinuous Galerkin scheme for electrical computation by the faster finite-difference scheme. Therefore, we re-optimized the solar cells containing an n-AlGaAs photon-absorbing layer with either a (i) homogeneous, (ii) linearly graded, or (iii) nonlinearly graded bandgap. Another way to improve the power conversion efficiency is by using a surface antireflection texturing on the wavelength scale, so we also optimized four different types of 1D periodic surface texturing: (i) rectangular, (ii) convex hemi-elliptical, (iii) triangular, and (iv) concave hemi-elliptical. Our new results show that the optimal nonlinear bandgap grading enhances the efficiency by as much as 3.31% when the n-AlGaAs layer is 400nm thick and 1.14% when that layer is 2000nm thick. A hundredfold concentration of sunlight can enhance the efficiency by a factor of 11.6%. Periodic texturing of the front surface on the scale of 0.5-2 free-space wavelengths provides a small relative enhancement in efficiency over the AlGaAs solar cells with a planar front surface; however, the enhancement is lower when the n-AlGaAs layer is thicker.

The impact of convection on morphological instability of a planar crystallization front

A linear morphological stability analysis of a planar solid-liquid phase interface describing the solidification processes of a binary melt with convection is carried out. The developed theory includes conductive and convective heat and mass transfer mechanisms near the phase interface and generalizes previously known theories of morphological stability. The amplification rate as a function of wavenumber of perturbations and neutral stability curve that divides the stability/instability parametric domains are obtained. It is shown that these domains are highly dependent of convection intensity, which represents a stabilizing factor for solidification processes. A criterion of concentration supercooling in the steady-state solidification conditions with convection is found. The obtained dispersion relation and neutral stability curve define various crystallization scenarios such as (i) morphological instability and concentration supercooling appearing to the formation of a two-phase mushy layer, (ii) morphological stability and concentration supercooling leading to the existence of a slurry layer, (iii) morphological stability without concentration supercooling when the planar solidification front is stable, and (iv) morphological instability without concentration supercooling forming the mesoscopically rough phase interface.

Direct ageing of LPBF Al-1Fe-1Zr for high conductivity and mechanical performance

The novel Al-1Fe-1Zr alloy leverages the non-equilibrium solidification conditions characteristic of the laser powder bed fusion (LPBF) process, namely a high thermal gradient (G) and solidification front velocity (R). The multiscale characterization of its microstructure in as-built and peak-aged conditions by SEM, TEM with EDS and automated crystal orientation mapping (ACOM), brings new insights on alloy design for LPBF. The solidification conditions permit the solute supersaturation of Fe and Zr, with the latter precipitating as L12-Al3Zr nanoparticles following ageing, bringing a high strengthening contribution. In conventional Al alloy ingots, Fe tends to create coarse particles which are detrimental to ductility. Here the Fe particles show a fine globular morphology in the as-built condition, and fine faceted Fe-rich intermetallics are obtained upon ageing. Nanoindentation and in situ tensile tests in the SEM coupled with microscale strain measurements shed light on the relation between microstructural and strain heterogeneities in the as-built condition. Our characterization results for this new Al-1Fe-1Zr grade are synthesized into a simple model for its solidification upon LPBF. In particular, the origin of melt pool boundaries is revealed. These are associated with Fe depletion caused by an early planar growth front, and the evolution of these zones upon ageing is presented. With a high potential for industrial applications, the novel alloy with the two elements Zr and Fe exhibiting low solubility at equilibrium and diffusivity in the Al matrix permit to achieve high conductivity (27 MS/m) and yield strength (330MPa) after a simple direct ageing step at 400°C/4h.

Intrinsic instabilities of hydrogen and hydrogen/ammonia premixed flames: Influence of equivalence ratio, fuel composition and pressure

Premixed lean hydrogen-air flames exhibit instabilities due to hydrodynamic instabilities but also thermo-diffusive instabilities. However, in the case of ammonia/hydrogen blends, the effect of ammonia addition on instabilities is still unclear. To investigate intrinsic instabilities in premixed ammonia/hydrogen-air flames, a parametric study of laminar premixed flames is performed for different fuel contents, from pure hydrogen (H2) to a blend of 40% of H2 and 60% of ammonia (NH3) in volume, equivalence ratios (0.4 to 1.0) and pressures (1 and 10 bar) to investigate thermo-diffusive instabilities. Numerical simulations using detailed chemistry are performed where an initial perturbation is set to disturb the planar flame front and to compute its growth rate. During the initial linear phase, the perturbation’s amplitude grows or decreases depending on the flame’s mixture propensity to be unstable or stable, respectively. At small times, the linear growth rate of the perturbation can be estimated and compared to theory. As expected, the maximum growth rate obtained in the linear phase depends on the mixture’s equivalence ratio, fuel ratio, and pressure. Ammonia addition leads to a reduced peak growth rate, likely due to lower reactivity leading to a higher Zel’dovich number. Very lean mixtures (equivalence ratios of 0.4 and 0.5) are thermo-diffusively unstable, regardless of the ammonia content, due to hydrogen’s preferential diffusion.

On the critical initiation of planar detonation in Noble-Abel and van der Waals gas

The critical decay rate theory (C.A. Eckett, J.J. Quirk, J.E. Shepherd, Journal of Fluid Mechanics 421 (2000) 147–183) on detonation initiation in unsteady flow was extended from ideal to Noble-Abel and van der Waals gas, in which the finite molecular volume effect (or repulsion force) and the inter-molecular attraction effect (or attraction force) were included. Considering the reactive Euler equations, the reaction zone temperature-gradient equation was established independently of the equation of state and wave geometry, and then solved asymptotically by assuming large activation energy, planar wave front and a one-step irreversible reaction model. A critical decay time was derived as the critical condition for detonation initiation. It was found that the inter-molecular attraction effect makes initiation more difficult by increasing the critical decay time, whereas the finite molecular volume effect promotes initiation. The real gas effects are enhanced when increasing the reduced activation energy and/or decreasing the heat capacity ratio of perfect gas. The applicability and generality of the asymptotic solutions were evaluated by comparison with quasi-unsteady simulation employing detailed reaction models for hydrogen-air and ethylene-air mixtures, and with the further simplified, fully analytical solutions based on strong-shock assumption. The critical conditions of the asymptotic solutions are qualitatively consistent with those obtained with the detailed mechanisms. The asymptotic solutions can also be well reproduced by the simple analytical solutions in most conditions. This study thus establishes a simple, yet reliable, method to evaluate the real gas effect on detonation initiation in high-pressure conditions.

Modelling and Optimization of A Light Trapping Scheme in A Silicon Solar Cell Using Silicon Nitride (SiNx) Anti-Reflective Coating

Solar cells system has been gaining remarkable attention in the photovoltaic (PV) industry in recent years. Therefore, many people used solar cells in their life. Hence, from time to time, many industries keep improve it to get the best of efficiency of the solar cell. In this work, it presents ray tracing of light trapping (LT) schemes in thin c-Si to enhance broadband light absorption within 300 - 1,200 nm wavelength region. For the ray tracing simulation, mono c-Si wafer with 100 μm thickness is investigated and solar spectrum (AM1.5G) at normal incidence is used. Random planar and upright pyramid front surface with silicon nitride (SiNx) anti-reflective coatings (ARC) with the difference thicknesses are the LT schemes being studies in this work. The broadband anti-reflective coating can effectively reduce the optical loss and improve the energy efficiency in the solar cells. The optical properties of the thin c-Si are analyzed with incremental LT schemes. Not only that, the current density also calculated from the absorption curve. Optical properties and current density were evaluated to find out the best thickness and refractive index of the silicon nitride (SiNx). The initial simulation results show that the solar cell current density is about 24.81 mA/cm2. A great Jmax enhancement in solar cell was achieved with utilizing the ARC thickness and type of front surface. Among the 6 proposed scheme, the scheme with upright pyramid front surface of 75 nm SiNx ARC thickness realized a good improvement in current density of 41.19 mA/cm2. This leads to Jmax enhancement of 66.02 % when compared to the reference c-Si. HIGHLIGHTS Solar cell energy conversion efficiencies for commercially available multicrystalline silicon solar cells are around 14 - 20 % which still insufficient Energy conversion efficiency of solar cell can be enhanced by adding the anti-reflective coating on the front layer of light trapping scheme SiNx as a single layer anti-reflective coating with a certain thickness shown a good behavior in reducing the light reflection hence, effectively absorbing more light into the scheme and leads to enhancing the energy conversion efficiency GRAPHICAL ABSTRACT

Stability of Front Solutions of the Bidomain Allen–Cahn Equation on an Infinite Strip

The bidomain model is the standard model for cardiac electrophysiology. In this paper, we study the bidomain Allen–Cahn equation, in which the Laplacian of the classical Allen–Cahn equation is replaced by the bidomain operator, a Fourier multiplier operator whose symbol is given by a homogeneous rational function of degree two. The bidomain Allen–Cahn equation supports planar front solutions much like the classical case. In contrast to the classical case, however, these fronts are not necessarily stable due to a lack of maximum principle; they can indeed become unstable depending on the parameters of the system. In this paper, we prove nonlinear stability and instability results for bidomain Allen–Cahn fronts on an infinite two-dimensional strip. We show that previously established spectral stability/instability results in imply stability/instability in the space of bounded uniformly continuous functions by establishing suitable decay estimates of the resolvent kernel of the linearized operator.

Stochastic Cellular Automata Modeling of CO2 Hydrate Growth and Morphology.

Carbon dioxide (CO2) hydrates are important in a diverse range of applications and technologies in the environmental and energy fields. The development of such technologies relies on fundamental understanding, which necessitates not only experimental but also computational studies of the growth behavior of CO2 hydrates and the factors affecting their crystal morphology. As experimental observations show that the morphology of CO2 hydrate particles differs depending on growth conditions, a detailed understanding of the relation between the hydrate structure and growth conditions would be helpful. To this end, this work adopts a modeling approach based on hybrid probabilistic cellular automata to investigate variations in CO2 hydrate crystal morphology during hydrate growth from stagnant liquid water presaturated with CO2. The model, which uses free energy density profiles as inputs, correlates the variations in growth morphology to the system subcooling ΔT, i.e., the temperature deficiency from the triple CO2-hydrate-water equilibrium temperature under a given pressure, and properties of the growing hydrate-water interface, such as surface tension and curvature. The model predicts that when ΔT is large, parabolic needle-like or dendrite crystals emerge from planar fronts that deform and lose stability. In agreement with chemical diffusion-limited growth, the position of such planar fronts versus time follows a power law. In contrast, the tips of the emerging parabolic crystals steadily grow in proportion to time. The modeling framework is computationally fast and produces complex growth morphology phenomena under diffusion-controlled growth from simple, easy-to-implement rules, opening the way for employing it in multiscale modeling of gas hydrates.