Families of two-dimensional, unsteady shock-induced vortical flows are simulated numerically. The flows consist of one or more regions of light gas, surrounded by heavy gas, being overtaken by a normal shock wave. The interaction of the density gradient at each light/heavy interface with the pressure gradient from the shock wave generates vorticity. This causes the light gas regions to roll up into one or more counter-rotating vortex pairs, which stir and mix the light and heavy gases. The mixing is characterized by an asymptotic stretching rate. The effects of shock strength, light/heavy gas density ratio, and geometry on the mixing are investigated. These two-dimensional, unsteady flows are analogous to three-dimensional, steady flows that may be used in SCRAMJET combustors demanding rapid and efficient mixing of fuel and oxidizer. For such applications, 1) the fuel injectors should be elongated in the direction of the shock; 2) multiple smaller injectors are preferable to a single larger injector; 3) injectors should be arranged in groups of closely spaced pairs, rather than uniformly; and 4) multiple shock waves should be utilized, if possible.

Polymer membranes perform innumerable separations with far-reaching environmental implications. Despite decades of research, design of new membrane materials remains a largely Edisonian process. To address this shortcoming, we demonstrate a generalizable, accurate machine learning (ML) implementation for the discovery of innovative polymers with ideal performance. Specifically, multitask ML models are trained on experimental data to link polymer chemistry to gas permeabilities of He, H 2 , O 2 , N 2 , CO 2 , and CH 4 . We interpret the ML models and extract valuable insights into the contributions of different chemical moieties to permeability and selectivity. We then screen over 9 million hypothetical polymers and identify thousands that lie well above current performance upper bounds, including hundreds of never-before-seen ultrapermeable polymer membranes with O 2 and CO 2 permeability greater than 10 4 and 10 5 Barrers, respectively. High-fidelity molecular dynamics simulations confirm the ML-predicted gas permeabilities of the promising candidates, which suggests that many can be translated to reality.

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State-of-the-art polymeric membranes are unable to perform the high-precision ion separations needed for technologies essential to a circular economy and clean energy future. Coordinative interactions are a mechanism to increase sorption of a target species into a membrane, but the effects of these interactions on membrane permeability and selectivity are poorly understood. We use a multilayered polymer membrane to assess how ion-membrane binding energies affect membrane permeability of similarly sized cations: Cu 2+ , Ni 2+ , Zn 2+ , Co 2+ , and Mg 2+ . We report that metals with higher binding energy to iminodiacetate groups of the polymer more selectively permeate through the membrane in multisalt solutions than single-salt solutions. In contrast, weaker binding species are precluded from diffusing into the polymer membrane, which leads to passage proportional to binding energy and independent of membrane thickness. Our findings demonstrate that selectivity of polymeric membranes can markedly increase by tailoring ion-membrane binding energy and minimizing membrane thickness.

This work investigates the two-dimensional flow of a shock wave over a circular lightgas inhomogeneity in a channel with finite width. The pressure gradient from the shock wave interacts with the density gradient at the edge of the inhomogeneity to deposit vorticity around the perimeter, and the structure rolls up into a pair of counter-rotating vortices. The aim of this study is to develop an understanding of thc scaling laws for the flow field produced by this interaction at times long after the passage of the shock across the inhomogeneity. Numerical simulations are performed for various initial conditions and the results are used to guide the development of relatively simple algebraic models that characterize the dynamics of the vortex pair, and that allow extrapolation of the numerical results to conditions more nearly of interest in practical situations. The models are not derived directly from the equations of motion but depend on these equations and on intuition guided by the numerical results. Agreement between simulations and models is generally good except for a vortex-spacing model which is less satisfactory.A practical application of this shock-induced vortical flow is rapid and efficient mixing of fuel and oxidizer in a SCRAMJET combustion chamber. One possible injector design uses the interaction of an oblique shock wave with a jet of light fuel to generate vorticity which stirs and mixes the two fluids and lifts the burning jet away from the combustor wall. Marble proposed an analogy between this three-dimensional steady flow and the two-dimensional unsteady problem of the present investigation. Comparison is made between closely corresponding three-dimensional steady and twodimensional unsteady flows, and a mathematical description of Marble's analogy is proposed.