This project matured a new understanding (a “modern synthesis”) of the structure and evolution of science and technology. It created an understanding and framework for how Sandia National Labs, the Department of Energy, and the nation, might improve their research productivity, with significant ramifications on national security and economic competitiveness.
This report documents our experience constructing a numerical method for the collisional Boltzmann equation that is capable of accurately capturing the collisionless through strongly collisional limits. We explore three different functional representations and present a detailed account of a numerical method based on a spatially dependent Gaussian mixture model (GMM). The Kullback-Leibler divergence is used as a closeness measure and various expectation maximization (EM) solution algorithms are implemented to find a compact representation in velocity space for distribution functions that exhibit significant non-Maxwellian character. We discuss issues that appear with this representation over a range of Knudsen numbers for a prototypical test problem and demonstrate that the strongly collisional limit recovers a solution to Euler's equations. Looking forward, this approach is broadly applicable to the non-relativistic and relativistic collisional Vlasov equations.
This research effort examined the application of Nafion polymers in alcohol solvents as an anti-ice surface coating, as a mixture with hydrophilic polymers and freezing point depressant salt systems. Co-soluble systems of Nafion, polymer and salt were applied using dip coating methods to create smooth films for frost observation over a Peltier plate thermal system in ambient laboratory conditions. Cryo-DSC was applied to examine freezing events of the Nafion-surfactant mixtures, but the sensitivity of the measurement was insufficient to determine frost behavior. Collaborations with the Fog Chamber at Sandia-Albuquerque, and in environmental SAXS measurements with CINT-LANL were requested but were not able to be performed under the research duration. Since experimental characterization of these factors is difficult to achieve directly, computational modeling was used to guide the scientific basis for property improvement. Computational modeling was performed to improve understanding of the dynamic association between ionomer side groups and added molecules and deicing salts. The polyacrylic acid in water system was identified at the start of the project as a relevant system for exploring the effect of varying counterions on the properties of fully deprotonated polyacrylic acid (PAA) in the presence of water. Simulations were modeled with four different counterions, two monovalent counterions (K+ and Na+) and two divalent counterions (Ca2+ and Mg2+). The wt% of PAA in these systems was varied from ~10 to 80 wt% PAA for temperatures from 250K to 400K. In the second set of simulations, the interpenetration of water into a dry PAA film was studied for Na+ or Ca2+ counterions for temperatures between 300K and 400K. The result of this project is a sprayable Nafion film composite which resists ice nucleation at -20 °C for periods of greater than three hours. It is composed of Nafion polymer, hydrophilic polyethylene oxide polymer and CaCl2 anti-ice crosslinker. Durability and field performance properties remain to be determined.
