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Submodels of model of nonlinear diffusion in the inhomogeneous medium involving absorption

We study the five-parameter model, describing the process of nonlinear diffusion in an inhomogeneous medium in the presence of absorption, for which the differential equation of the model admits a continuous Lie group of transformations, acting on the set of its solutions. We found six submodels of the original model of nonlinear diffusion, with different symmetry properties. Of these six submodels, the five submodels with transient absorption, for which the absorption coefficient depends on time according to a power law, represent the greatest interest with a mathematical point of view and with the point of view of physical applications. For each of these nonlinear submodels, we obtained formulas for producing new solutions that contain arbitrary constants, and we found all invariant submodels. All essentially distinct invariant solutions describing these invariant submodels are found in an explicit form or are reduced to finding the solution of nonlinear integral equations. The presence of the arbitrary constants in the integral equations that determine these solutions provide new opportunities for analytical and numerical study of boundary value problems for the received submodels and, thus, for the original model of nonlinear diffusion. For the received invariant submodels, we studied diffusion processes for which at the initial moment of the time at a fixed point is specified as a concentration and its gradient or as a concentration and its velocity. Solving of boundary value problems describing these processes is reduced to the solving of nonlinear integral equations. We established the existence and uniqueness of solutions of these boundary value problems under some additional conditions. The obtained results can be used to study the diffusion of substances, diffusion of conduction electrons and other particles, diffusion of physical fields and propagation of heat in inhomogeneous medium, and also to study a turbulence (Leith model, differential approximation to wave turbulence)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Use of a diffuser for producing texture masks for image processing

The use of a diffuser in synthesizing binary texture-variance masks for applications in image processing is investigated. The binary texture-variance masks are used to separate various objects in an image on the basis of their spatial texture variance. The diffuser is required to reduce the speckling present in the mask. The reduction in speckling is described quantitatively as a reduction of the misclassification probability associated with the separation of the objects into several texture classes. General results are furnished for the statistics of the field scattered by the diffuser, and these are used to obtain expressions for the misclassification probabilities in the presence of a diffuser.

Stark, H.↗

Simulation of Coupled Processes of Flow, Transport, and Storage of CO 2 in Saline Aquifers

This report is the final scientific one for the award DE- FE0000988 entitled “Simulation of Coupled Processes of Flow, Transport, and Storage of CO 2 in Saline Aquifers.” The work has been divided into six tasks. In task, “Development of a Three-Phase Non-Isothermal CO 2 Flow Module,” we developed a fluid property module for brine-CO 2 mixtures designed to handle all possible phase combinations of aqueous phase, sub-critical liquid and gaseous CO 2 , supercritical CO 2 , and solid salt. The thermodynamic and thermophysical properties of brine-CO 2 mixtures (density, viscosity, and specific enthalpy of fluid phases; partitioning of mass components among the different phases) use the same correlations as an earlier fluid property module that does not distinguish between gaseous and liquid CO 2 -rich phases. We verified the fluid property module using two leakage scenarios, one that involves CO 2 migration up a blind fault and subsequent accumulation in a secondary “parasitic” reservoir at shallower depth, and another investigating leakage of CO 2 from a deep storage reservoir along a vertical fault zone. In task, “Development of a Rock Mechanical Module,” we developed a massively parallel reservoir simulator for modeling THM processes in porous media brine aquifers. We derived, from the fundamental equations describing deformation of porous elastic media, a momentum conservation equation relating mean stress, pressure, and temperature, and incorporated it alongside the mass and energy conservation equations from the TOUGH2 formulation, the starting point for the simulator. In addition, rock properties, namely permeability and porosity, are functions of effective stress and other variables that are obtained from the literature. We verified the simulator formulation and numerical implementation using analytical solutions and example problems from the literature. For the former, we matched a one-dimensional consolidation problem and a two-dimensional simulation of the Mandel-Cryer effect. For the latter, we obtained a good match of temperature and gas saturation profiles, and surface uplift, after injection of hot fluid into a model of a caldera structure. In task, “Incorporation of Geochemical Reactions of Selected Important Species,” we developed a novel mathematical model of THMC processes in porous and fractured saline aquifers, simulating geo-chemical reactions associated with CO 2 sequestration in saline aquifers. Two computational frameworks, sequentially coupled and fully coupled, were used to simulate the reactions and transport. We verified capabilities of the THMC model to treat complex THMC processes during CO 2 sequestration by analytical solutions and we constructed reactive transport models to analyze the THMC process quantitatively. Three of these are 1D reactive transport under chemical equilibrium, a batch reaction model with equilibrium chemical reactions, and a THMC model with CO 2 dissolution. In task “Study of Instability in CO 2 Dissolution-Diffusion-Convection Processes,” We reviewed literature related to the study of density driven convective flows and on the instability of CO 2 dissolution-diffusion-convection processes. We ran simulations that model the density-driven flow instability that would occur during CO 2 sequestration. CO 2 diffused through the top of the system and dissolved in the aqueous phase there, increasing its density. Density fingers formed along the top boundary, and coalesced into a few prominent ones, causing convective flow that forced the fluid to the system bottom. These simulations were in two and three dimensions. We ran additional simulations of convective mixing with density contrast caused by variable dissolved CO 2 concentration in saline water, modeled after laboratory experiments in which supercritical CO2 was circulated in the headspace above a brine saturated packed sand in a pressure vessel. As CO 2 dissolved into the upper part of the saturated sand, liquid phase density increases causing instability and setting off convective mixing. We obtained good agreement with the laboratory experiments, which were characterized by finger development and associated mixing of dissolved CO 2 into the system. We then varied a wide range of parameters and conceptual models in order to analyze the possibility of convective mixing under different conditions, such as various boundary conditions, and chemical reaction conditions. The CO 2 fingers from different simulations showed great differences as time progressed, caused by permeability heterogeneity. The early time diffusive phenomenon was captured by fine grid resolution, and the permeability heterogeneity affected the pattern of the CO 2 fingers. In addition, the fingers from three-dimensional simulations tended to be larger and flatter than the two-dimensional ones. In task “Implementation of Efficient Parallel Computing Technologies,” we made enhancements and modifications to our code in order to substantially increase the grid size that could be run. We installed and ran it on various platforms, including a multi-core PC and a cluster, and verified the numerical implementation and parallel code using an example problem from the literature. This problem, with a grid size of sixty million, utilized the cluster’s entire memory and all of its processors. In task “Implementation of General Fracture Conceptual Models,” we used the MINC approach, a generalization of the double-porosity concept, to model flow through porous and fractured media. In this approach, flow within the matrix is described by subdividing the matrix into nested volumes, with flow occurring between adjacent nested matrix volumes as well as between the fractures and the outer matrix volume. We generalized Hooke’s law to a thermo-multi- poroelastic medium, and derived from the fundamental equations describing deformation of porous and fractured elastic media a momentum conservation equation for thermo-multi- poroelastic media. This equation is a generalization to multi-poroelastic media of the one derived in Task 3.0 for single porosity media. We describe two simulations to provide model verification and application examples. The first, one-dimensional consolidation of a double-porosity medium, is compared to an analytical solution. The second is a match of published results from the literature, a simulation of CO 2 injection into hypothetical aquifer-caprock systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Viscosity dependence of the rates of diffusional processes

It is shown that the rates of diffusion-controlled processes may have a solvent vicosity independent part as well as a viscosity dependent part. Some relevant experiments involving intramolecular polypeptide movements are discussed, and implications for some experiments on diffusion in membranes are outlined.

Weaver, D. L.↗

Materials for Advanced Turbine Engines (MATE). Project 4: Erosion resistant compressor airfoil coating

The ability of coatings to provide at least a 2X improvement in particulate erosion resistance for steel, nickel and titanium compressor airfoils was identified and demonstrated. Coating materials evaluated included plasma sprayed cobalt tungsten carbide, nickel carbide and diffusion applied chromium plus boron. Several processing parameters for plasma spray processing and diffusion coating were evaluated to identify coating systems having the most potential for providing airfoil erosion resistance. Based on laboratory results and analytical evaluations, selected coating systems were applied to gas turbine blades and evaluated for surface finish, burner rig erosion resistance and effect on high cycle fatigue strength. Based on these tests, the following coatings were recommended for engine testing: Gator-Gard plasma spray 88WC-12Co on titanium alloy airfoils, plasma spray 83WC-17Co on steel and nickel alloy airfoils, and Cr+B on nickel alloy airfoils.

Rashid, J. M.↗

Solubility and diffusion of hydrogen in IN-100 and Waspaloy

The solubility of hydrogen, at a fixed hydrogen pressure, was measured in two different heat treatment conditions in both IN-100 and Waspaloy by equilibrium and analysis. The diffusion coefficients were determined by measuring the rate of hydrogen evolution in a vacuum. Hydrogen evolution appeared to be a diffusion-controlled process in all cases. For hydrogen diffusion in Waspaloy, Delta H was 38.5 kJ and D0 was 2.6 x 10 to the -7th sq/s. For IN-100, Delta H was 68.2 kJ and D0 was 59 x 10 to the -7th sq/s. The values for Waspaloy are close to those for pure nickel. The values for IN-100 are more similar to high nickel alloys that show trapping or surface layer impedance.

Khan, A. S.↗

Development of vapor phase hydrogen peroxide sterilization process for spacecraft applications

This paper will present test data and discussion on the work we are conducting at JPL to address the following issues: 1) efficacy of sterilization process; 2) diffusion of hydrogen peroxide under sterilization process conditions into hard to reach places; 3) materials and components compatibility with the sterilization process and 4) development of methodology to protect sensitive components from hydrogen peroxide vapor.

hydrogen peroxide sterilization spacecraft↗

Quantitative Evaluation of Radial Diffusion and Local Acceleration Processes During GEM Challenge Events

We simulate the radiation belt electron flux enhancements during selected Geospace Environment Modeling (GEM) challenge events to quantitatively compare the major processes involved in relativistic electron acceleration under different conditions. Van Allen Probes observed significant electron flux enhancement during both the storm time of 17–18 March 2013 and non–storm time of 19–20 September 2013, but the distributions of plasma waves and energetic electrons for the two events were dramatically different. During 17–18 March 2013, the SYM-H minimum reached -130 nT, intense chorus waves (peak B w ~140 pT) occurred at 3.5 < L < 5.5, and several hundred keV to several MeV electron fluxes increased by ~2 orders of magnitude mostly at 3.5 < L < 5.5. During 19–20 September 2013, the SYM-H remained higher than -30 nT, modestly intense chorus waves (peak B w ~80 pT) occurred at L > 5.5, and electron fluxes at energies up to 3 MeV increased by a factor of ~5 at L > 5.5. The two electron flux enhancement events were simulated using the available wave distribution and diffusion coefficients from the GEM focus group Quantitative Assessment of Radiation Belt Modeling. By comparing the individual roles of local electron heating and radial transport, our simulation indicates that resonant interaction with chorus waves is the dominant process that accounts for the electron flux enhancement during the storm time event particularly near the flux peak locations, while radial diffusion by ultralow-frequency waves plays a dominant role in the enhancement during the non–storm time event. Incorporation of both processes reasonably reproduces the observed location and magnitude of electron flux enhancement.

58 GEOSCIENCES↗

Using Diffusion Bonding in Making Piezoelectric Actuators

A technique for the fabrication of piezoelectric actuators that generate acceptably large forces and deflections at relatively low applied voltages involves the stacking and diffusion bonding of multiple thin piezoelectric layers coated with film electrodes. The present technique stands in contrast to an older technique in which the layers are bonded chemically, by use of urethane or epoxy agents. The older chemical-bonding technique entails several disadvantages, including the following: It is difficult to apply the bonding agents to the piezoelectric layers. It is difficult to position the layers accurately and without making mistakes. There is a problem of disposal of hazardous urethane and epoxy wastes. The urethane and epoxy agents are nonpiezoelectric materials. As such, they contribute to the thickness of a piezoelectric laminate without contributing to its performance; conversely, for a given total thickness, the performance of the laminate is below that of a unitary piezoelectric plate of the same thickness. The figure depicts some aspects of the fabrication of a laminated piezoelectric actuator by the present diffusion- bonding technique. First, stock sheets of the piezoelectric material are inspected and tested. Next, the hole pattern shown in the figure is punched into the sheets. Alternatively, if the piezoelectric material is not a polymer, then the holes are punched in thermoplastic films. Then both faces of each punched piezoelectric sheet or thermoplastic film are coated with a silver-ink electrode material by use of a silkscreen printer. The electrode and hole patterns are designed for minimal complexity and minimal waste of material. After a final electrical test, all the coated piezoelectric layers (or piezoelectric layers and coated thermoplastic films) are stacked in an alignment jig, which, in turn, is placed in a curved press for the diffusion-bonding process. In this process, the stack is pressed and heated at a specified curing temperature and pressure for a specified curing time. The pressure, temperature, and time depend on the piezoelectric material selected. At the end of the diffusion-bonding process, the resulting laminated piezoelectric actuator is tested to verify the adequacy of the mechanical output as a function of an applied DC voltage.

Sager, Frank E.↗

Solid-state synthesis of Li{sub 4}Ti{sub 5}O{sub 12} whiskers from TiO{sub 2}-B

Highlights: • The Li{sub 4}Ti{sub 5}O{sub 12} whiskers were synthesized from TiO{sub 2}-B whiskers via a solid state reaction. • The TiO{sub 2}-B crystal structure for lithium diffusion is easier than anatase. • The separated diffusion and reaction process is crucial for the solid-state syntheses of Li{sub 4}Ti{sub 5}O{sub 12} whiskers. - Abstract: In this work, Li{sub 4}Ti{sub 5}O{sub 12} (LTO) was synthesized from the precursors of TiO{sub 2}-B and anatase whiskers, respectively. The synthesized LTO whiskers from TiO{sub 2}-B whiskers via a solid state reaction at 650 °C have a high degree of crystallinity with an average diameter of 300 nm. However, when anatase whiskers were used as the precursor, only particle morphology LTO was produced at 750 °C. The further analysis of the precursors, the intermediate products and the final products reveal that the crystal structure of the anatase hinders the diffusion of lithium, leading to a typical reaction–diffusion process. Under this condition, only particle morphology LTO can be produced. However, the crystal structure of the TiO{sub 2}-B is easy for lithium diffusion and the process is performed in two separated steps (i.e., diffusion and reaction), which makes it possible to decrease the solid-state reaction temperature down to 650 °C and then maintain the morphologies of whiskers.

36 MATERIALS SCIENCE↗

Double Diffusive Convection in Materials Processing

A great number of crystals grown in space are plagued by convective motions which contribute to structural flaws. The character of these instabilities is not well understood but is associated with density variations in the presence of residual gravity (g-jitter). As a specific example, past HgCdTe crystal growth space experiments by Lehoczky and co-workers indicate radial compositional asymmetry in the grown crystals. In the case of HgCdTe the rejected component into the melt upon solidification is HgTe which is denser than the melt. The space grown crystals indicate the presence of three dimensional flow with the heavier HgTe-rich material clearly aligned with the residual gravity (0.55-1.55 micro g) vector. This flow stems from double-diffusive convection, namely, thermal and solutal buoyancy driven flow in the melt. The study of double-diffusive convection is multi-faceted and rather vast. In our investigation, we seek to focus on one specific aspect of this discipline that is of direct relevance to materials processing especially crystal growth, namely, the side ways heating regime. This problem has been widely studied, both experimentally and numerically, in the context of solar ponds wherein the system is characterized by a linear salt (solutal) gradient with an imposed lateral temperature gradient. The induced flow instabilities arise from the wide disparity between the fluid thermal diffusivity and the solute diffusivity. The extension of the analysis to practical crystal growth applications has however not been rigorously made and understood. One subtle but important difference in crystal growth systems is the fact that die system solute gradient is non-linear (typically exponential). Besides, the crystal growth problem has the added complexities of solidification, both lateral and longitudinal thermal gradients and segregation phenomena in systems where binary and ternary compounds are being grown. This paper treats the side ways heating problem alone in a model fluid system. Results from detailed numerical calculations, mainly two dimensional are provided. The interactions between a non-linear solute gradient and an imposed transverse thermal gradient are investigated. The buoyancy effects are treated in the traditional Boussinesq approximation and also in a more complete density formulation to address recent concerns of the first approach especially in simulations of the system response in a reduced gravity environment. Detailed flow, temperature and solute field plots along with heat and mass transfer results are presented in the paper. Implications to practical crystal growth systems as discerned from the modeling results are also explored and reported.

Ramachandra, Narayanan↗

Revealing the Rate-Limiting Li-Ion Diffusion Pathway in Ultrathick Electrodes for Li-Ion Batteries

Increasing the loading of active materials by thickening the battery electrode coating can enhance the energy density of a Li-ion cell, but the trade-off is the much reduced Li + transport kinetics. To reach the optimum energy and power density for thick electrodes, the effective chemical diffusion coefficient of Li + (D Li ) must be maximized. However, the diffusion of Li + inside an electrode is a complex process involving both microscopic and macroscopic processes. Fundamental understandings are needed on the rate-limiting process that governs the diffusion kinetics of Li + to minimize the negative impact of the large electrode thickness on their electrochemical performance. In this study, lithium Ni–Mn–Co oxide (NMC) cathodes of various thicknesses ranging from 100 to 300 μm were used as a model system to study the rate-limiting diffusion process during charge/discharge. The rate-limiting diffusion coefficient of Li + was investigated and quantified, which was correlated to the electrochemical performance degradation of thick electrodes. Lastly, it is revealed here that the under-utilization of the active material was caused by the limited diffusion of Li + inside the porous electrode, leading to a critical electrode thickness, beyond which the specific capacity was significantly reduced.

25 ENERGY STORAGE↗

Influence of Ink Formulation and Drying Conditions on Ionomer Distribution in High-Performance Roll-to-Roll-Coated Gas-Diffusion Electrodes

To enable mass production of fuel cell membrane electrode assemblies (MEAs) catalyst layers production will require continuous roll-to-roll (R2R) coating processes. Gas diffusion electrodes (GDEs) are advantageous for mass production because the catalyst layer can be directely coated on the microporous layer of the gas diffusion media without the need for a decal-transfer process. It is known that the water-to-alcohol ratio in the catalyst ink influences the interactions of the ionomer with the catalyst leading to different distributions of ionomer in spray-coated catalyst layers. It is also known that during drying of colloidal mixtures, like fuel cell inks, factors such as drying rate, particle size, and agglomeration influence how the materials distribute themselves throughout the thickness of the dired film. Thus far there have only been limited studies to understand how process conditions such as ink formulation and drying temperature influence the distribution of ionomer and catalyst coated using scalable methods. This understanding is especially important for GDEs since it is known that having a sufficient amount of ionomer at the catalyst layer-membrane interface is critical for high performance. In this study we have focused on determining how the ratio of water to 1-propanol in the catalyst ink ink and drying temperature influence the distribution of ionomer throughout the thickness of the catalyst layer. Using a combination of Kelvin probe and x-ray photoelectron spectroscopy we show that an ionomer-rich surface is promoted by a higher drying rate and a water-rich catalyst ink. In contrast, a 1-propanol catalyst ink leads to a lower concentration of ionomer on the top surface. Using x-ray computed tomography, we are able to characterize the ionomer distribution throughout the thickness of the layer. We find that, in addition to promoting an ionomer-rich top surface, water-rich inks lead to a more homogenous distribution of ionomer, whereas a 1-propanol-rich ink leads to a more irregular distribution. It is found that MEA performance is improved by selecting conditions and ink formulations that promote ionomer enrichment at the top surface to facilitate a good interface with the membrane. MEAs prepared with a 75 wt% water catalyst ink with a 0.9 I/C have equivalent performance to spray-coated GDEs. Critically, these R2R-coated GDEs do not need an additional ionomer overlayer like the spray-coated GDEs do, reducing the number of processing steps in a manufacturing setting. This work shows that with the appropriate selection of materials, ink formulation, and processing conditions gas-diffusion electrodes are a viable pathway for fuel cell manufacturing.

ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION↗

Dynamics in the Plastic Crystalline Phases of Cyclohexanol and Cyclooctanol Studied by Quasielastic Neutron Scattering

Plastic crystals are a promising candidate for solid state ionic conductors. In this work, quasielastic neutron scattering is employed to investigate the center of mass diffusive motions in two types of plastic crystalline cyclic alcohols: cyclohexanol and cyclooctanol. Two separate motions are observed which are attributed to long-range translational diffusion (α-process) and cage rattling (fast β-process). Residence times and diffusion coefficients are calculated for both processes, along with the confinement distances for the cage rattling. In addition, a binary mixture of these two materials is measured to understand how the dynamics change when a second type of molecule is added to the matrix. Furthermore, it is observed that, upon the addition of the larger cyclooctanol molecules into the cyclohexanol solution, the cage size decreases, which causes a decrease in the observed diffusion rates for both the α- and fast β-processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Assessment of ion kinetic effects in shock-driven inertial confinement fusion implosions using fusion burn imaging

The significance and nature of ion kinetic effects in D{sup 3}He-filled, shock-driven inertial confinement fusion implosions are assessed through measurements of fusion burn profiles. Over this series of experiments, the ratio of ion-ion mean free path to minimum shell radius (the Knudsen number, N{sub K}) was varied from 0.3 to 9 in order to probe hydrodynamic-like to strongly kinetic plasma conditions; as the Knudsen number increased, hydrodynamic models increasingly failed to match measured yields, while an empirically-tuned, first-step model of ion kinetic effects better captured the observed yield trends [Rosenberg et al., Phys. Rev. Lett. 112, 185001 (2014)]. Here, spatially resolved measurements of the fusion burn are used to examine kinetic ion transport effects in greater detail, adding an additional dimension of understanding that goes beyond zero-dimensional integrated quantities to one-dimensional profiles. In agreement with the previous findings, a comparison of measured and simulated burn profiles shows that models including ion transport effects are able to better match the experimental results. In implosions characterized by large Knudsen numbers (N{sub K} ∼ 3), the fusion burn profiles predicted by hydrodynamics simulations that exclude ion mean free path effects are peaked far from the origin, in stark disagreement with the experimentally observed profiles, which are centrally peaked. In contrast, a hydrodynamics simulation that includes a model of ion diffusion is able to qualitatively match the measured profile shapes. Therefore, ion diffusion or diffusion-like processes are identified as a plausible explanation of the observed trends, though further refinement of the models is needed for a more complete and quantitative understanding of ion kinetic effects.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Atomistic processes of surface-diffusion-induced abnormal softening in nanoscale metallic crystals

Abstract Ultrahigh surface-to-volume ratio in nanoscale materials, could dramatically facilitate mass transport, leading to surface-mediated diffusion similar to Coble-type creep in polycrystalline materials. Unfortunately, the Coble creep is just a conceptual model, and the associated physical mechanisms of mass transport have never been revealed at atomic scale. Akin to the ambiguities in Coble creep, atomic surface diffusion in nanoscale crystals remains largely unclear, especially when mediating yielding and plastic flow. Here, by using in situ nanomechanical testing under high-resolution transmission electron microscope, we find that the diffusion-assisted dislocation nucleation induces the transition from a normal to an inverse Hall-Petch-like relation of the strength-size dependence and the surface-creep leads to the abnormal softening in flow stress with the reduction in size of nanoscale silver, contrary to the classical “alternating dislocation starvation” behavior in nanoscale platinum. This work provides insights into the atomic-scale mechanisms of diffusion-mediated deformation in nanoscale materials, and impact on the design for ultrasmall-sized nanomechanical devices.

36 MATERIALS SCIENCE↗