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NASA NTRS1990

Asymptotic analysis of dissipative waves with applications to their numerical simulation

Various problems involving the interplay of asymptotics and numerics in the analysis of wave propagation in dissipative systems are studied. A general approach to the asymptotic analysis of linear, dissipative waves is developed. It was applied to the derivation of asymptotic boundary conditions for numerical solutions on unbounded domains. Applications include the Navier-Stokes equations. Multidimensional traveling wave solutions to reaction-diffusion equations are also considered. A preliminary numerical investigation of a thermo-diffusive model of flame propagation in a channel with heat loss at the walls is presented.

Hagstrom, Thomas↗

NASA NTRS1994

Microwave heating and joining of ceramic cylinders: A mathematical model

A thin cylindrical ceramic sample is placed in a single mode microwave applicator in such a way that the electric field strength is allowed to vary along its axis. The sample can either be a single rod or two rods butted together. We present a simple mathematical model which describes the microwave heating process. It is built on the assumption that the Biot number of the material is small, and that the electric field is known and uniform throughout the cylinder's cross-section. The model takes the form of a nonlinear parabolic equation of reaction-diffusion type, with a spatially varying reaction term that corresponds to the spatial variation of the electromagnetic field strength in the waveguide. The equation is analyzed and a solution is found which develops a hot spot near the center of the cylindrical sample and which then propagates outwards until it stabilizes. The propagation and stabilization phenomenon concentrates the microwave energy in a localized region about the center where elevated temperatures may be desirable.

Booty, Michael R.↗

NASA NTRS1996

Effects of Material Degradation on the Structural Integrity of Composite Materials: Experimental Investigation and Modeling of High Temperature Degradation Mechanisms

It has previously been demonstrated that simple coupled reaction-diffusion models can approximate the aging behavior of PMR-15 resin subjected to different oxidative environments. Based on empirically observed phenomena, a model coupling chemical reactions, both thermal and oxidative, with diffusion of oxygen into the material bulk should allow simulation of the aging process. Through preliminary modeling techniques such as this it has become apparent that accurate analytical models cannot be created until the phenomena which cause the aging of these materials are quantified. An experimental program is currently underway to quantify all of the reaction/diffusion related mechanisms involved. The following contains a summary of the experimental data which has been collected through thermogravimetric analyses of neat PMR-15 resin, along with analytical predictions from models based on the empirical data. Thermogravimetric analyses were carried out in a number of different environments - nitrogen, air and oxygen. The nitrogen provides data for the purely thermal degradation mechanisms while those in air provide data for the coupled oxidative-thermal process. The intent here is to effectively subtract the nitrogen atmosphere data (assumed to represent only thermal reactions) from the air and oxygen atmosphere data to back-figure the purely oxidative reactions. Once purely oxidative (concentration dependent) reactions have been quantified it should then be possible to quantify the diffusion of oxygen into the material bulk.

Cunningham, Ronan A.↗

NASA NTRS1998

Critical Slowing Down in Time-to-Extinction: An Example of Critical Phenomena in Ecology

We study a model for two competing species that explicitly accounts for effects due to discreteness, stochasticity and spatial extension of populations. The two species are equally preferred by the environment and do better when surrounded by others of the same species. We observe that the final outcome depends on the initial densities (uniformly distributed in space) of the two species. The observed phase transition is a continuous one and key macroscopic quantities like the correlation length of clusters and the time-to-extinction diverge at a critical point. Away from the critical point, the dynamics can be described by a mean-field approximation. Close to the critical point, however, there is a crossover to power-law behavior because of the gross mismatch between the largest and smallest scales in the system. We have developed a theory based on surface effects, which is in good agreement with the observed behavior. The course-grained reaction-diffusion system obtained from the mean-field dynamics agrees well with the particle system.

Gandhi, Amar↗

NASA NTRS1999

Surface Tension and Fingering of Miscible Interfaces

Experiments on miscible, buoyantly unstable reaction-diffusion fronts and non-reacting displacement fronts in Hele-Shaw cells show a fingering-type instability whose wavelengths (lambda*) are consistent with an interfacial tension (sigma) at the front caused by the change in chemical composition, even though the solutions are miscible in all proportions. In conjunction with the Saffman-Taylor model, the relation sigma = K/tau, where tau is the interface thickness and K approximately equal 4 +/- 2 x 10(exp -6) dyne, enables prediction of our measured values of lambda* as well as results from prior experiments on miscible interfaces. These results indicate that even for miscible fluids, surface tension is generally a more significant factor than diffusion in interfacial stability and flow characteristics.

Abib, Mohammed↗

NASA NTRS2001

The Cool Flames Experiment

A space-based experiment is currently under development to study diffusion-controlled, gas-phase, low temperature oxidation reactions, cool flames and auto-ignition in an unstirred, static reactor. At Earth's gravity (1g), 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 via the Arrhenius temperature dependence of the reaction rates. Natural convection is important in all terrestrial cool flame and auto-ignition studies, except for select low pressure, highly dilute (small temperature excess) studies in small vessels (i.e., small Rayleigh number). On Earth, natural convection occurs when the Rayleigh number (Ra) exceeds a critical value of approximately 600. Typical values of the Ra, associated with cool flames and auto-ignitions, range from 104-105 (or larger), a regime where both natural convection and conduction heat transport are important. When natural convection occurs, it alters the temperature, hydrodynamic, and species concentration fields, thus generating a multi-dimensional field that is extremely difficult, if not impossible, to be modeled analytically. This point has been emphasized recently by Kagan and co-workers who have shown that explosion limits can shift depending on the characteristic length scale associated with the natural convection. Moreover, natural convection in unstirred reactors is never "sufficiently strong to generate a spatially uniform temperature distribution throughout the reacting gas." Thus, an unstirred, nonisothermal reaction on Earth does not reduce to that generated in a mechanically, well-stirred system. Interestingly, however, thermal ignition theories and thermokinetic models neglect natural convection and assume a heat transfer correlation of the form: q=h(S/V)(T(bar) - Tw) where q is the heat loss per unit volume, h is the heat transfer coefficient, S/V is the surface to volume ratio, and (T(bar) - Tw ) is the spatially averaged temperature excess. This Newtonian form has been validated in spatially-uniform, well-stirred reactors, provided the effective heat transfer coefficient associated with the unsteady process is properly evaluated. Unfortunately, it is not a valid assumption for spatially-nonuniform temperature distributions induced by natural convection in unstirred reactors. "This is why the analysis of such a system is so difficult." Historically, the complexities associated with natural convection were perhaps recognized as early as 1938 when thermal ignition theory was first developed. In the 1955 text "Diffusion and Heat Exchange in Chemical Kinetics", Frank-Kamenetskii recognized that "the purely conductive theory can be applied at sufficiently low pressure and small dimensions of the vessel when the influence of natural convection can be disregarded." This was reiterated by Tyler in 1966 and further emphasized by Barnard and Harwood in 1974. Specifically, they state: "It is generally assumed that heat losses are purely conductive. While this may be valid for certain low pressure slow combustion regimes, it is unlikely to be true for the cool flame and ignition regimes." While this statement is true for terrestrial experiments, the purely conductive heat transport assumption is valid at microgravity (mu-g). Specifically, buoyant complexities are suppressed at mu-g and the reaction-diffusion structure associated with low temperature oxidation reactions, cool flames and auto-ignitions can be studied. Without natural convection, the system is simpler, does not require determination of the effective heat transfer coefficient, and is a testbed for analytic and numerical models that assume pure diffusive transport. In addition, mu-g experiments will provide baseline data that will improve our understanding of the effects of natural convection on Earth.

Pearlman, Howard↗

NASA NTRS1998

Spiral waves are stable in discrete element models of two-dimensional homogeneous excitable media

The spontaneous breakup of a single spiral wave of excitation into a turbulent wave pattern has been observed in both discrete element models and continuous reaction-diffusion models of spatially homogeneous 2D excitable media. These results have attracted considerable interest, since spiral breakup is thought to be an important mechanism of transition from the heart rhythm disturbance ventricular tachycardia to the fatal arrhythmia ventricular fibrillation. It is not known whether this process can occur in the absence of disease-induced spatial heterogeneity of the electrical properties of the ventricular tissue. Candidate mechanisms for spiral breakup in uniform 2D media have emerged, but the physical validity of the mechanisms and their applicability to myocardium require further scrutiny. In this letter, we examine the computer simulation results obtained in two discrete element models and show that the instability of each spiral is an artifact resulting from an unphysical dependence of wave speed on wave front curvature in the medium. We conclude that spiral breakup does not occur in these two models at the specified parameter values and that great care must be exercised in the representation of a continuous excitable medium via discrete elements.

NASA Discipline Cardiopulmonary↗

NASA NTRS2005

New Species of Fire Discovered: Fingering Flamelets Form a Dynamic Population

Poets and artists have long used fire as a metaphor for life. At the NASA Glenn Research Center, recent experiments in a subcritical Rayleigh number flow channel demonstrated that this analogy holds up surprisingly well when tools developed to characterize a biological population are applied to a class of fire that occurs in near-extinction, weakly convective environments (such as microgravity) or in vertically confined spaces (such as our apparatus). Under these conditions, the flame breaks into numerous 'flamelets" that form a Turing-type reaction-diffusion fingering pattern as they spread across the fuel. It is standard practice on U.S. spacecraft for the astronaut crew to turn off the ventilation to help extinguish a fire, both to eliminate the fresh oxygen supply and to reduce the distribution of the smoke. When crew members think that the fire is fully extinguished, they reactivate the ventilation system to clear the smoke. However, some flamelets can survive, and our experiments have demonstrated that flamelets quickly grow into a large fire when ventilation increases.

Olson, Sandra L.↗

DOE OSTI2021

BETO 2021 Peer Review - Biochemical Process Modeling and Simulation (BPMS)

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2023

Biochemical Process Modeling and Simulation (BPMS)

The Biochemical Process Modeling and Simulation project aims to reduce the cost and time of research by applying theory, modeling, and simulation to the most relevant bottlenecks in the biochemical process. We use molecular modeling, quantum mechanics, metabolic modeling, fluid dynamics, and reaction-diffusion methods in close collaboration with pretreatment, hydrolysis, upgrading, and TEA. The project's outcomes are increased yields and efficiency of the biochemical process, added value to products, and reduced price of fuels by specifically targeting catalytic efficiency, reactor design, enzyme efficiency, and microbial design. We work closely with experimental projects to identify problems and iterate with experiments to find and refine solutions. By working with experimentalists, we decide on problems that can be solved with simulation that could otherwise not be solved or would take too long with experiment alone to reach BETO's targets. Over the years, we have produced solutions that have resulted in determining the most likely fatty-acid derivative for passive transport out of bacteria that upgrade biomass, and we have also designed enzyme mutations for enhanced lignin upgrading. Metabolic models have been developed to tune the activity of 2,3 butanediol production for the 2030 target. A computational method to deliver understanding of how complex omics data can be interpreted in the metabolic pathways of organisms used in the Agile Biofoundry. We have found methods to overcome specific barriers and continue to develop those methods. Our reactor studies have guided the design of both the microbes and reactors for aerobic and micro-aerobic production at all scales and have been instrumental in improving the accuracy of techno-economic analysis models. This project is essential in the process of selecting the final processes for 2030 SAF production targets. More specifically, recently, we have: 1) Predicted the strength of the basic structural interactions in commodity plastics to provide guidance for plastics upcycling strategies. 2) Developed computational tool to improve the characterization of lignin-derived compounds 3) Developed new methodologies to enable Machine Learning-based Directed Evolution for protein engineering. 4) Developed Machine Learning methods to predict protein promiscuity and mutations to further improve microbial and enzymatic driven processes and demonstrated the utility of ML approaches to engineering proteins from sparse experimental datasets. 5) Developed new methods to enable high-fidelity simulation of aerobic fermentation at industrial scale and resolving mismatch of time scales through subcycling/operator splitting 7) Identified the difficulty in preventing local high-oxygen conditions in industrial bubble columns, which leads to less-desirable acetoin production, suggesting future research directions in alternative reactor configurations (e.g loop reactors, shallow-channel reactors).

BIOMASS FUELS↗

DOE OSTI2025

Morphogenic Growth 3D Printing

Inspired by nature's morphogenesis, a new 3D printing process –growth printing (GP)– takes advantage of a self‐propagating curing front to produce 3D polymeric parts following a growth‐like development plan. The propagation of the curing front is driven by the exothermic polymerization of dicyclopentadiene (DCPD), which transforms the liquid resin into a stiff polymer as it propagates at 1 mm s −1 . GP is triggered when a heated initiator contacts the uncured liquid resin in an open container. The initiator nucleates the frontal polymerization reaction and the isotropic radial propagation of the growth front. Simultaneously, the initiator is moved up across the free surface of the resin, pulling the cured object out of the uncured resin. The motion trajectory of the initiator with respect to the free resin surface controls the growth morphology of the 3D part. An inverse design algorithm is developed to produce 3D parts by modeling the reaction‐diffusion‐driven solidification process. This process has substantial energy savings and high printing speeds.

3D printing↗

DOE OSTI2023

Virtual Volumetric Additive Manufacturing (VirtualVAM)

Abstract Tomographic volumetric additive manufacturing (VAM) produces arbitrary 3D geometries by exposure of a rotating volume of photopolymer resin to tomographically‐patterned illumination. This enables high speed, layer‐less printing of parts from a wide range of photopolymers not amenable to layer‐by‐layer processes. Since the entire geometry is produced at once over the course of a few seconds to minutes, molecular diffusion length scales become significant to the printing process. Understanding these molecular reaction and diffusion processes is imperative for advancing VAM to a usable technology. These processes are experimentally very difficult to monitor and measure. Herein, VirtualVAM ‐ a simulation framework for modeling the tomographic VAM process, is developed and experimentally validated. VirtualVAM simulates reaction, diffusion, and heat generation processes over the course of a print with single‐voxel resolution. From a few experimentally‐determined input parameters and a set of images for projection, VirtualVAM is able to generate a large spatio‐temporal data set for any given tomographic VAM print. Using VirtualVAM, a number of experimentally‐unattainable aspects of the VAM process are investigated such as single‐voxel conversion profiles, effect of molecular oxygen, and stopping time determination. VirtualVAM also enables the optimization of exposure patterns to further improve contrast between in‐part and out‐of‐part delivered dose.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Reaction–Diffusion Coupling Facilitates the Sequential Precipitation of Metal Ions from Battery Feedstock Solutions

Here, the development of new technologies for chemical separations is urgently needed to meet the surging demand for critical materials that has strained resources and caused environmental challenges. Inspired by the classic Liesegang experiment, we demonstrated the separation of critical metal ions based on the coupling of ion diffusion and precipitation kinetics. For this purpose, a model feedstock solution simulating dissolved battery electrodes was placed on top of a hydrogel loaded with a precipitating agent, namely sodium hydroxide. As the lithium, manganese, cobalt, and nickel ions diffused into the gel, a gradient of precipitates formed along the length of the reactor. Elemental analysis of the spatially distributed precipitates showed the enrichment of nickel near the gel-solution interface, followed by the formation of an almost pure (>96%) manganese product further along the reactor. Optimization experiments revealed that a sodium hydroxide concentration of 10 mM and a gel/solution volume ratio of 2:1 favored efficient separations. The robustness of the method was demonstrated in four out of five feedstock compositions of typically used battery cathodes. Our proof-of-concept experiments present a paradigm for critical materials separations that does not require specialty chemicals, binding agents, membranes, or toxic solvents.

25 ENERGY STORAGE↗

DOE OSTI2023

Reversible Reactions, Mesh Size, and Segmental Dynamics Control Penetrant Diffusion in Ethylene Vitrimers

The diffusion of two aromatic dyes with nearly identical sizes was measured in ethylene vitrimers with precise linker lengths and borate ester cross-links using fluorescence recovery after photobleaching (FRAP). One dye possessed a reactive hydroxyl group, while the second was inert. The reaction of the hydroxyl group with the network is slow relative to the hopping times of the dye, resulting in a large slowdown by a factor of 50 for a reactive probe molecule. A kinetic model was fit to the fluorescence intensity data to determine rate constants for the reversible reaction of the dye from the network, which confirms the role of slow reaction kinetics. A second network cross-linker was also investigated with a substituted boronic ester showing ∼10,000 times faster exchange kinetics. In this system, the two dyes show the same diffusion coefficient, as the reaction is no longer the rate-limiting step. The role of dense meshes on small and large dyes is also discussed in the context of the existing theories. Finally, these results highlight the potential of dynamic networks to control penetrant transport through synergistic effects of the mesh size, dynamic bond kinetics, and penetrant–network interactions.

confinement↗

DOE OSTI2021

Controlling radiolysis chemistry on the nanoscale in liquid cell scanning transmission electron microscopy

When high-energy electrons from scanning transmission electron microscope (STEM) are interacting with the liquid, the vast majority of the chemical reactions that are observed are induced by the radiolysis breakdown of the liquid molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

The scaling of kinetic and transport behaviors in the solution-phase chemistry of a plasma–liquid interface

The reactions at a plasma–liquid interface often involve species such as the solvated electron or the hydroxyl radical, which initiate the reduction or oxidation of solution-phase reactants (so-called scavengers) or are consumed by their own second-order recombination. Here, the mathematical scaling of the reaction–diffusion equations at the interface is used to obtain a characteristic time that can be used to determine the transition from highly efficient scavenger reduction or oxidation to lower efficiencies due to transport limitations. The characteristic time (tc) is validated using numerical solutions of the reaction–diffusion equations. When the scavenger kinetics are faster than second-order recombination, this characteristic transition time scales proportionally with the scavenger diffusivity (Ds) and the square of the scavenger bulk concentration (SB) and inversely proportional to the electron flux (J) squared; that is, t c = D s S B 2 F 2 /J 2 , where F is Faraday’s constant. However, when the scavenger kinetics are comparable or slower than second-order recombination, this scaling does not hold. Extending this analysis to three-dimensional systems shows that the profile of the electron flux on the surface affects the spatial location where reactions are most effective. Finally, the assessment of the implications of these behaviors for the reactor design highlights how effectively controlling the electron flux and solution transport may be necessary to improve the efficiency of scavenger reactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Resonant amplification of enzymatic chemical oscillations by oscillating flow

Using theory and simulation, we analyzed the resonant amplification of chemical oscillations that occur due to externally imposed oscillatory fluid flows. The chemical reactions are promoted by two enzyme-coated patches located sequentially on the inner surface of a pipe that transports the enclosed chemical solution. In the case of diffusion-limited systems, the period of oscillations in chemical reaction networks is determined by the rate of the chemical transport, which is diffusive in nature and, therefore, can be effectively accelerated by the imposed fluid flows. In this work, we first identify the natural frequencies of the chemical oscillations in the unperturbed reaction–diffusion system and, then, use the frequencies as a forcing input to drive the system to resonance. We demonstrate that flow-induced resonance can be used to amplify the amplitude of the chemical oscillations and to synchronize their frequency to the external forcing. In particular, we show that even 10% perturbations in the flow velocities can double the amplitude of the resulting chemical oscillations. Particularly, effective control can be achieved for the two-step chemical reactions where during the first half-period, the fluid flow accelerates the chemical flux toward the second catalytic patch, while during the second half-period, the flow amplifies the flux to the first patch. The results can provide design rules for regulating the dynamics of coupled reaction–diffusion processes and can facilitate the development of chemical reaction networks that act as chemical clocks.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Understanding copper diffusion in CuInSe 2 with first-principles based atomistic and continuum models

We investigate the diffusion of copper in CuInSe 2 using thermodynamic and kinetic models based on density functional theory calculations, attempting to reconcile large differences in reported experimental diffusivities. We find that observations of rapid chemical diffusion can be explained by large thermodynamic factors, which we calculate using a compositionally constrained model of intrinsic point defect formation. We further characterize how copper diffusion coefficients depend on material synthesis conditions and exhibit their variation across the CuInSe 2 secondary phase diagram. In doing so, we identify stable off-stoichiometries that are dominated by either vacancy- or interstitial-mediated diffusion mechanisms. These results are employed in the development of a continuum reaction–diffusion model, which we use to simulate experimental depth profiles.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗