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NASA NTRS2001

Bi-Component Droplet Combustion in Reduced Gravity

This research deals with reduced-gravity combustion of bi-component droplets initially in the mm size range or larger. The primary objectives of the research are to study the effects of droplet internal flows, thermal and solutal Marangoni stresses, and species volatility differences on liquid species transport and overall combustion phenomena (e.g., gas-phase unsteadiness, burning rates, sooting, radiation, and extinction). The research program utilizes a reduced-gravity environment so that buoyancy effects are rendered negligible. Use of large droplets also facilitates visualization of droplet internal flows, which is important for this research. In the experiments, droplets composed of low- and high-volatility species are burned. The low-volatility components are initially present in small amounts. As combustion of a droplet proceeds, the liquid surface mass fraction of the low-volatility component will increase with time, resulting in a sudden and temporary decrease in droplet burning rates as the droplet rapidly heats to temperatures close to the boiling point of the low-volatility component. This decrease in burning rates causes a sudden and temporary contraction of the flame. The decrease in burning rates and the flame contraction can be observed experimentally. Measurements of burning rates as well as the onset time for flame contraction allow effective liquid-phase species diffusivities to be calculated, e.g., using asymptotic theory. It is planned that droplet internal flows will be visualized in future flight and ground-based experiments. In this way, effective liquid species diffusivities can be related to droplet internal flow characteristics. This program is a continuation of extensive ground based experimental and theoretical research on bi-component droplet combustion that has been ongoing for several years. The focal point of this program is a flight experiment (Bi-Component Droplet Combustion Experiment, BCDCE). This flight experiment is under development. However, supporting studies have been performed. Because of space limitations, only some of the research performed over the last two years (since the 5th Microgravity Combustion Workshop) is summarized here.

Shaw, B. D.↗

DOE OSTI2021

Nanoparticle dynamics in the spatial afterglows of nonthermal plasma synthesis reactors

Nonthermal plasma flow tube reactors are industrially scalable systems for the production of nanocrystal (NC) based materials and coatings. One key advantage of nonthermal plasma synthesis is the ability to both synthesize NCs and deposit films in a single reactor, as at the reactor outlet, NCs can be inertially deposited onto a target substrate. The size and morphology of deposited particles can substantially influence the film structure and function. Though NCs are typically near-spherical and monodispersed as-produced in plasma synthesis reactors, NC charge and growth dynamics can be altered substantially when NCs are sampled out of the plasma and through the spatial afterglow region, affecting deposition. Experiments have demonstrated changes of NC size and charge in the spatial afterglow; however, these dynamics remain unexplored and unexplained via theory and simulation. To address this, we developed a constant number Monte Carlo (CNMC) simulation model to examine the mechanisms of NC decharging and growth in the spatial afterglow of plasma flow tube reactors. Collisions between NC and plasma species, diffusive deposition, and electron desorption from NCs are incorporated in the CNMC simulation. The simulation results are specifically compared with previous experiments on Si NCs synthesized from a low pressure Ar-SiH 4 nonthermal plasma reactor. Furthermore, the experiment-model comparison shows that CNMC models can be implemented which accurately model NC size distribution evolution in a spatial afterglow. Simultaneously, results show that improved collision models, energetic species diffusion models, and electron desorption models will be necessary to accurately depict NC dynamics in spatial afterglows.

42 ENGINEERING↗

DOE OSTI2021

Methodologies for Design, Characterization and Testing of Electrolytes that Enable Extreme Fast Charging of Lithium-ion Cells

Selection, testing and validation of electrolyte candidates for Li-ion cells are discussed, based on a 10-minute target for extreme fast charge (XFC). A combination of modeling and laboratory measurements create a timely and synergistic approach to identifying candidate electrolyte formulations. Multi-solvent systems provide a balanced set of properties, wherein lower molecular-weight solvents offer reduced viscosity, increased species diffusivity, and mitigation of concentration polarization at high charge rates. Carefully selected formulations can exhibit peak conductivity and usable conductivity range of two to three times that of the baseline EC-EMC (3:7, wt.) + LiPF 6 . Candidates are also chosen based on stability and longevity within the cell environment. Lab testing coincides with property predictions from the Advanced Electrolyte Model (AEM) and a macro-scale cell model. Furthermore, cell testing utilized coin and pouch cells having NMC532 or NMC811 cathodes with graphite electrodes. Results indicate combinations of low-molecular weight solvents are key for fast-charge electrolytes as they extend the useful conductivity range to both low and higher salt concentrations, and possess higher self-diffusivities compared to conventional solvents. This reduces impacts from concentration polarization. The choice of electrolyte also influences the tendency for lithium metal deposition at the anode, as showcased by experimental and modeling results herein.

25 ENERGY STORAGE↗

NASA NTRS2001

Cool Flame Quenching

Cool flame quenching distances are generally presumed to be larger than those associated with hot flames, because the quenching distance scales with the inverse of the flame propagation speed, and cool flame propagation speeds are often times slower than those associated with hot flames. To date, this presumption has never been put to a rigorous test, because unstirred, non-isothermal cool flame studies on Earth are complicated by natural convection. Moreover, the critical Peclet number (Pe) for quenching of cool flames has never been established and may not be the same as that associated with wall quenching due to conduction heat loss in hot flames, Pe approx. = 40-60. The objectives of this ground-based study are to: (1) better understand the role of conduction heat loss and species diffusion on cool flame quenching (i.e., Lewis number effects), (2) determine cool flame quenching distances (i.e, critical Peclet number, Pe) for different experimental parameters and vessel surface pretreatments, and (3) understand the mechanisms that govern the quenching distances in premixtures that support cool flames as well as hot flames induced by spark-ignition. Objective (3) poses a unique fire safety hazard if conditions exist where cool flame quenching distances are smaller than those associated with hot flames. For example, a significant, yet unexplored risk, can occur if a multi-stage ignition (a cool flame that transitions to a hot flame) occurs in a vessel size that is smaller than that associated with the hot quenching distance. To accomplish the above objectives, a variety of hydrocarbon-air mixtures will be tested in a static reactor at elevated temperature in the laboratory (1g). In addition, reactions with chemical induction times that are sufficiently short will be tested aboard NASA's KC-135 microgravity (mu-g) aircraft. The mu-g results will be compared to a numerical model that includes species diffusion, heat conduction, and a skeletal kinetic mechanism, following the work on diffusion-controlled cool flames by Fairlie et,al., 2000.

Pearlman, Howard↗

NASA NTRS1997

Real Time Quantitative 3-D Imaging of Diffusion Flame Species

A low-gravity environment, in space or ground-based facilities such as drop towers, provides a unique setting for study of combustion mechanisms. Understanding the physical phenomena controlling the ignition and spread of flames in microgravity has importance for space safety as well as better characterization of dynamical and chemical combustion processes which are normally masked by buoyancy and other gravity-related effects. Even the use of so-called 'limiting cases' or the construction of 1-D or 2-D models and experiments fail to make the analysis of combustion simultaneously simple and accurate. Ideally, to bridge the gap between chemistry and fluid mechanics in microgravity combustion, species concentrations and temperature profiles are needed throughout the flame. However, restrictions associated with performing measurements in reduced gravity, especially size and weight considerations, have generally limited microgravity combustion studies to the capture of flame emissions on film or video laser Schlieren imaging and (intrusive) temperature measurements using thermocouples. Given the development of detailed theoretical models, more sophisticated studies are needed to provide the kind of quantitative data necessary to characterize the properties of microgravity combustion processes as well as provide accurate feedback to improve the predictive capabilities of the computational models. While there have been a myriad of fluid mechanical visualization studies in microgravity combustion, little experimental work has been completed to obtain reactant and product concentrations within a microgravity flame. This is largely due to the fact that traditional sampling methods (quenching microprobes using GC and/or mass spec analysis) are too heavy, slow, and cumbersome for microgravity experiments. Non-intrusive optical spectroscopic techniques have - up until now - also required excessively bulky, power hungry equipment. However, with the advent of near-IR diode lasers, the possibility now exists to obtain reactant and product concentrations and temperatures non-intrusively in microgravity combustion studies. Over the past ten years, Southwest Sciences has focused its research on the high sensitivity, quantitative detection of gas phase species using diode lasers. Our research approach combines three innovations in an experimental system resulting in a new capability for nonintrusive measurement of major combustion species. FM spectroscopy or high frequency Wavelength Modulation Spectroscopy (WMS) have recently been applied to sensitive absorption measurements at Southwest Sciences and in other laboratories using GaAlAs or InGaAsP diode lasers in the visible or near-infrared as well as lead-salt lasers in the mid-infrared spectral region. Because these lasers exhibit essentially no source noise at the high detection frequencies employed with this technique, the achievement of sensitivity approaching the detector shot noise limit is possible.

Kane, Daniel J.↗

NASA NTRS2014

A Radiation Chemistry Code Based on the Greens Functions of the Diffusion Equation

Ionizing radiation produces several radiolytic species such as.OH, e-aq, and H. when interacting with biological matter. Following their creation, radiolytic species diffuse and chemically react with biological molecules such as DNA. Despite years of research, many questions on the DNA damage by ionizing radiation remains, notably on the indirect effect, i.e. the damage resulting from the reactions of the radiolytic species with DNA. To simulate DNA damage by ionizing radiation, we are developing a step-by-step radiation chemistry code that is based on the Green's functions of the diffusion equation (GFDE), which is able to follow the trajectories of all particles and their reactions with time. In the recent years, simulations based on the GFDE have been used extensively in biochemistry, notably to simulate biochemical networks in time and space and are often used as the "gold standard" to validate diffusion-reaction theories. The exact GFDE for partially diffusion-controlled reactions is difficult to use because of its complex form. Therefore, the radial Green's function, which is much simpler, is often used. Hence, much effort has been devoted to the sampling of the radial Green's functions, for which we have developed a sampling algorithm This algorithm only yields the inter-particle distance vector length after a time step; the sampling of the deviation angle of the inter-particle vector is not taken into consideration. In this work, we show that the radial distribution is predicted by the exact radial Green's function. We also use a technique developed by Clifford et al. to generate the inter-particle vector deviation angles, knowing the inter-particle vector length before and after a time step. The results are compared with those predicted by the exact GFDE and by the analytical angular functions for free diffusion. This first step in the creation of the radiation chemistry code should help the understanding of the contribution of the indirect effect in the formation of DNA damage and double-strand breaks.

Plante, Ianik↗

DOE OSTI2022

A reaction–diffusion model for grayscale digital light processing 3D printing

We report that digital light processing (DLP) 3D printing is an additive manufacturing process that utilizes light patterns to photopolymerize a liquid resin into a solid. Due to the accuracy of modern digital micromirror devices (DMD) and recent advances in resin chemistry, it is now possible to create functionally graded structures using different light intensity values, also known as grayscale DLP (g-DLP). Different intensities of light lead to differences in the polymer crosslinking density after curing, which ultimately produces a part with gradients of material properties. However, g-DLP is a complicated process. First, the DLP printing is a highly coupled chemical and physical process that involves light propagation, chemical reactions, species diffusion, heat transfer, volume shrinkage, and changes in mechanical behaviors of the curing resin. Second, in g-DLP, light gradients create strong in plane gradients of chemical species concentrations in the curing liquid resin due to the strong dependence of light intensity on the rate of monomer crosslinking. Furthermore, light gradients through the depth create concentration gradients due to the degree of cure dependent light absorption and the use of photoabsorbers. These complex physical features of the printing process must be understood in order to properly control printing parameters such as light exposure time, printing speed, and grayscale variations to achieve accurate mechanical properties. In this paper, a photopolymerization reaction–diffusion model is developed and used in conjunction with experiments to investigate the coupled effects of light propagation, chemical reaction rates, and species diffusion during g-DLP 3D printing. The model is implemented numerically utilizing the finite difference method and simulation results are compared to experimental findings of simple printed structures. The agreement between experimental and model predictions of simple quantities of interest, such as geometric feature sizes, shows that the model can capture the overcure due to free-radical and other species diffusion during printing when grayscale patterns are employed. This model lays the groundwork for future extensions that can incorporate more complex coupled physics such as heat transfer, volume shrinkage, and material property evolution, which are critically important in utilizing g-DLP 3D printing for the fabrication of high-performance parts which excellent geometric and material property tolerances.

36 MATERIALS SCIENCE↗

NASA NTRS1992

Experimental dehydration of natural obsidian and estimation of DH2O at low water contents

Water diffusion experiments were carried out by dehydrating rhyolitic obsidian from Valles Caldera (New Mexico, USA) at 510-980 degrees C. The starting glass wafers contained approximately 0.114 wt% total water, lower than any glasses previously investigated for water diffusion. Weight loss due to dehydration was measured as a function of experiment duration, which permits determination of mean bulk water diffusivity, mean Dw. These diffusivities are in the range of 2.6 to 18 X 10(-14) m2/s and can be fit with the following Arrhenius equation: ln mean Dw (m2/s) = -(25.10 +/- 1.29) - (46,480 +/- 11,400) (J/mol) / RT, except for two replicate runs at 510 degrees C which give mean Dw values much lower than that defined by the above equation. When interpreted according to a model of water speciation in which molecular H2O is the diffusing species with concentration-independent diffusivity while OH units do not contribute to the transport but react to provide H2O, the data (except for the 510 degrees C data) are in agreement with extrapolation from previous results and hence extend the previous data base and provide a test of the applicability of the model to very low water contents. Mean bulk water diffusivities are about two orders of magnitude less than molecular H2O diffusivities because the fraction of molecular H2O out of total water is very small at 0.114 wt% total water and less. The 510 degrees C experimental results can be interpreted as due to slow kinetics of OH to H2O interconversion at low temperatures.

NASA Program Exobiology↗

DOE OSTI2024

First-principles investigation of lanthanides diffusion in HCP zirconium via vacancy-mediated transport

The diffusion of lanthanide fission products plays an important role in the growth of the fuel-cladding chemical interaction (FCCI) region in metallic fuels. The use of a Zr interdiffusion barrier may mitigate the transport of lanthanides from the fuel to the cladding, but the efficacy of such a liner is not yet known. In this paper, the stability and vacancy-mediated diffusion of La, Ce, Pr, and Nd in hexagonal close-packed (HCP) Zr is investigated via density functional theory (DFT) calculations and self-consistent mean field (SCMF) analysis. DFT is used to calculate the formation, binding, and migration energies of vacancies and vacancy-solute pairs. The DFT energetics are used in the KineCluE code to calculate the Onsager transport coefficients. La is found to be the fastest diffusing species in HCP Zr and experiences an almost isotropic diffusion behavior. The other three species (Ce, Pr, and Nd) demonstrate anisotropic diffusion where the diffusion in the basal planes is significantly faster than that along the c-axis. Further, the calculated lanthanide diffusivities in HCP Zr are fitted to an Arrhenius relation and the activation energies and prefactors are reported for the first time. Furthermore, the vacancy drag and the segregation tendencies were analyzed using the calculated off-diagonal transport coefficients. According to our vacancy-mediated diffusion model, lanthanides are expected to be enriched at vacancy sinks at low temperatures, while at high temperatures, lanthanides are depleted at sinks and will preferably diffuse into the bulk. The enrichment/depletion transition temperature depends on the diffusion direction (basal or axial) and hence will be controlled by the grain texture and orientation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS1997

Numerical Modeling of HgCdTe Solidification: Effects of Phase Diagram, Double-Diffusion Convection and Microgravity Level

Melt convection, along with species diffusion and segregation on the solidification interface are the primary factors responsible for species redistribution during HgCdTe crystal growth from the melt. As no direct information about convection velocity is available, numerical modeling is a logical approach to estimate convection. Furthermore influence of microgravity level, double-diffusion and material properties should be taken into account. In the present study, HgCdTe is considered as a binary alloy with melting temperature available from a phase diagram. The numerical model of convection and solidification of binary alloy is based on the general equations of heat and mass transfer in two-dimensional region. Mathematical modeling of binary alloy solidification is still a challenging numericial problem. A Rigorous mathematical approach to this problem is available only when convection is not considered at all. The proposed numerical model was developed using the finite element code FIDAP. In the present study, the numerical model is used to consider thermal, solutal convection and a double diffusion source of mass transport.

Bune, Andris V.↗

DOE OSTI2022

Diffusion-assisted molecular beam epitaxy of CuCrO 2 thin films

Using molecular beam epitaxy (MBE) to grow multielemental oxides (MEOs) is generally challenging, partly due to difficulty in stoichiometry control. Occasionally, if one of the elements is volatile at the growth temperature, stoichiometry control can be greatly simplified using adsorption-controlled growth mode. Otherwise, stoichiometry control remains one of the main hurdles to achieving high-quality MEO film growths. Here, in this paper, we report another kind of self-limited growth mode, dubbed diffusion-assisted epitaxy, in which excess species diffuses into the substrate and leads to the desired stoichiometry, in a manner similar to the conventional adsorption-controlled epitaxy. Specifically, we demonstrate that using diffusion-assisted epitaxy, high-quality epitaxial CuCrO 2 films can be grown over a wide growth window without precise flux control using MBE.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Diffusion-Limited Kinetics in Reactive Systems

A proper representation of chemical kinetics is vital to understanding, modeling, and optimizing many important chemical processes. In liquid and surface phases, where diffusion is slow, the rate at which the reactants diffuse together limits the overall rate of many elementary reactions. Commonly, the textbook Smoluchowski theory is utilized to estimate effective rate coefficients in the liquid phase. On surfaces, modelers commonly resort to much more complex and expensive Kinetic Monte Carlo (KMC) simulations. Here, in this study, we extend the Smoluchowski model to allow the diffusing species to undergo chemical reactions and derive analytical formulas for the diffusion-limited rate coefficients for 3D, 2D, and 2D/3D interface cases. With these equations, we are able to demonstrate that when species react faster than they diffuse they can react orders of magnitude faster than predicted by Smoluchowski theory, through what we term “the reactive transport effect”. We validate the derived steady-state equations against particle Monte Carlo (PMC) simulations, KMC simulations, and non-steady-state solutions. Furthermore, using PMC and KMC simulations, we propose corrections that agree with all limits and the computed data for the 2D and 2D/3D interface steady-state equations, accounting for unique limitations in the associated derived equations. Additionally, we derive equations to handle couplings between diffusion-limited rate coefficients in reaction networks. We believe these equations should make it possible to run much more accurate mean-field simulations of liquids, surfaces, and liquid–surface interfaces accounting for diffusion limitations and the reactive transport effect.

Johnson, Matthew Sean↗

NASA NTRSDate not supplied

Comparisons of Mixing Efficiency for the Strut Fuel Injector Obtained from Large-Eddy and Reynolds-Averaged Simulations, and Experiments

Mixing efficiency is obtained for a strut fuel injector at hypervelocity flow conditions by using large-eddy simulations (LES), Reynolds-averaged simulations (RAS), and experiments. The injector and flow conditions have been previously investigated by using RAS and experiments as a part of the Enhanced Injection and Mixing Project (EIMP) at the NASA Langley Research Center (LaRC). Because the fidelity of LES is a strong function of the grid, the mixing efficiency is obtained on two grids, the coarser of which is a factor of two coarser in each of the three dimensions with respect to the fine grid. The RAS uses the two-equation linear eddy viscosity and diffusivity modeling of Menter. In RAS, the species diffusivity model exhibits a strong dependence on the turbulent Schmidt number, which is often adjusted until some metric of engineering interest, such as the mixing efficiency, matches the experimental data. In the absence of experimental data, scale-resolving simulations, such as LES, have been proposed as surrogates for experiments that could provide the data needed to “calibrate” the turbulent Schmidt number in the RAS models. This approach is followed because LES requires significantly more computational resources (CPU, data storage, and time) than RAS, making it prohibitive for use in many engineering applications and specifically for parameter exploration or optimization. Here we examine the mixing efficiency obtained from several RAS with different values of the turbulent Schmidt number, and compare the results with those obtained from the LES and experiments. In addition, the least squares fitting approach was used to demonstrate how to obtain an estimate for the turbulent Schmidt number from LES analytically. These estimates were then used together with prior knowledge about RAS model sensitivity to select a turbulence model that was expected to best match the LES data.

LES↗

NASA NTRSDate not supplied

Comparisons of Mixing Efficiency for the Strut Fuel Injector Obtained from Large-Eddy and Reynolds-Averaged Simulations, and Experiments

LES↗

NASA NTRS1994

Multicomponent Gas Diffusion and an Appropriate Momentum Boundary Condition

Multicomponent gas diffusion is reviewed with particular emphasis on gas flows near solid boundaries-the so-called Kramers-Kistemaker effect. The aim is to derive an appropriate momentum boundary condition which governs many gaseous species diffusing together. The many species' generalization of the traditional single gas condition, either as slip or stick (no-slip), is not obvious, particularly for technologically important cases of lower gas pressures and very dissimilar molecular weight gases. No convincing theoretical case exists for why two gases should interact with solid boundaries equally but in opposite flow directions, such that the total gas flow exactly vanishes. ln this way, the multicomponent no-slip boundary requires careful treatment The approaches discussed here generally adopt a microscopic model for gas-solid contact. The method has the advantage that the mathematics remain tractable and hence experimentally testable. Two new proposals are put forward, the first building in some molecular collision physics, the second drawing on a detailed view of surface diffusion which does not unphysically extrapolate bulk gas properties to govern the adsorbed molecules. The outcome is a better accounting of previously anomalous experiments. Models predict novel slip conditions appearing even for the case of equal molecular weight components. These approaches become particularly significant in view of a conceptual contradiction found to arise in previous derivations of the appropriate boundary conditions. The analogous case of three gases, one of which is uniformly distributed and hence non-diffusing, presents a further refinement which gives unexpected flow reversals near solid boundaries. This case is investigated alone and for aggregating gas species near their condensation point. In addition to predicting new physics, this investigation carries practical implications for controlling vapor diffusion in the growth of crystals used in medical diagnosis (e.g. mercuric iodide) and semiconductors.

Noever, David A.↗

NASA NTRS2003

Cool Flames in Propane-Oxygen Premixtures at Low and Intermediate Temperatures at Reduced-Gravity

The Cool Flame Experiment aims to address the role of diffusive transport on the structure and the stability of gas-phase, non-isothermal, hydrocarbon oxidation reactions, cool flames and auto-ignition fronts in an unstirred, static reactor. These reactions cannot be studied on Earth where natural convection due to self-heating during the course of slow reaction dominates diffusive transport and produces spatio-temporal variations in the thermal and thus species concentration profiles. On Earth, reactions with associated Rayleigh numbers (Ra) less than the critical Ra for onset of convection (Ra(sub cr) approx. 600) cannot be achieved in laboratory-scale vessels for conditions representative of nearly all low-temperature reactions. In fact, the Ra at 1g ranges from 10(exp 4) - 10(exp 5) (or larger), while at reduced-gravity, these values can be reduced two to six orders of magnitude (below Ra(sub cr)), depending on the reduced-gravity test facility. Currently, laboratory (1g) and NASA s KC-135 reduced-gravity (g) aircraft studies are being conducted in parallel with the development of a detailed chemical kinetic model that includes thermal and species diffusion. Select experiments have also been conducted at partial gravity (Martian, 0.3gearth) aboard the KC-135 aircraft. This paper discusses these preliminary results for propane-oxygen premixtures in the low to intermediate temperature range (310- 350 C) at reduced-gravity.

Pearlman, Howard↗

NASA NTRS1992

Numerical simulations of turbulent premixed H2/O2/N2 flames with complex chemistry

Premixed stoichiometric H2/O2/N2 flames propagating in two-dimensional turbulence were studied using direct numerical simulation (simulations in which all fluid and thermochemical scales are fully resolved) including realistic chemical kinetics and molecular transport. Results are compared with earlier zero-chemistry (flame sheet) and one-step chemistry simulations. Consistent with the simpler models, the turbulent flame with realistic chemistry aligns preferentially with extensive strain rates in the tangent plane and flame curvature probability density functions are close to symmetric with near-zero means. By contrast to simple-chemistry results with non-unity Lewis numbers (ratio of thermal to species diffusivity), local flame structure does not correlate with curvature but rather with tangential strain rate. Turbulent straining results in substantial thinning of the flame relative to the steady unstrained laminar case. Heat release and H2O2 contours remain thin and connected ('flamelet-like') while species including H-atom and OH are more diffuse. Peak OH concentration occurs well behind the peak heat-release zone. The feasibility of incorporating realistic chemistry into full turbulence simulations to address issues such as pollutant formation in hydrocarbon-air flames is suggested.

Baum, M.↗

DOE OSTI2024

A finite difference informed random walker (FDiRW) solver for strongly inhomogeneous diffusion problems

In nature, many complex multi-physics coupling problems exhibit strong diffusivity inhomogeneity. For instance, in the context of radionuclide absorption by porous wasteform materials within a flowing waste stream, the difference of species’ diffusivity in solid and liquid phases spans by 3~8 orders of magnitude. To solve the diffusion equations with strongly inhomogeneous diffusivity, traditional discretization-based methods, such as the Finite Difference Method (FDM), require infinitesimally small time steps (<10 -10 ) as high spatial resolutions are employed in most microstructure evolution processes, leading to prohibitively high computational costs. Here, this work developed an integrated numerical approach (FDiRW: Finite Difference informed Random Walk) to tackle this challenge. The idea is that utilizing the Random Walk concept, the fast diffusion is modeled as a superposition of point source’s solution for a concentration distribution while FDM is used to obtain the point source’s solution at each node. A mesh-coarsening algorithm is developed to generate an exclusive coarse mesh for FDiRW approach to maximize its efficiency. The effectiveness of the coarse mesh-based FDiRW approach is validated by benchmarking Finite Difference solutions. Numerical results demonstrated that FDiRW achieves a remarkable 1000x computational efficiency improvement over FDM while preserving desired accuracy for a medium-sized model of 192 × 192 × 192 grids. Finally, as models scale up, a floating-point operations (PLOPs) analysis of the FDiRW algorithm reveals that its computational complexity grows quadratically in terms of the number of nodes employed in computation.

36 MATERIALS SCIENCE↗