Results for “Reaction-diffusion models” — Page 4

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↗

DOE OSTI2022

A model of spatio-temporal regulation within biomaterials using DNA reaction–diffusion waveguides

In multi-cellular organisms, cells and tissues coordinate biochemical signal propagation across length scales spanning micrometres to metres. Designing synthetic materials with similar capacities for coordinated signal propagation could allow these systems to adaptively regulate themselves across space and over time. Here, we combine ideas from cell signalling and electronic circuitry to propose a biochemical waveguide that transmits information in the form of a concentration of a DNA species on a directed path. The waveguide could be seamlessly integrated into a soft material because there is virtually no difference between the chemical or physical properties of the waveguide and the material it is embedded within. We propose the design of DNA strand displacement reactions to construct the system and, using reaction–diffusion models, identify kinetic and diffusive parameters that enable super-diffusive transport of DNA species via autocatalysis. Finally, to support experimental waveguide implementation, we propose a sink reaction and spatially inhomogeneous DNA concentrations that could mitigate the spurious amplification of an autocatalyst within the waveguide, allowing for controlled waveguide triggering. Chemical waveguides could facilitate the design of synthetic biomaterials with distributed sensing machinery integrated throughout their structure and enable coordinated self-regulating programmes triggered by changing environmental conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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 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↗