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This study demonstrates a three-step process consisting of primary pre-filtration followed by ultrafiltration (UF) and adsorption with thiol-functionalized microfiltration membranes (thiol membranes) to effectively remove mercury sulfide nanoparticles (HgS NPs) and dissolved mercury (Hg 2+ ) from wastewater. Thiol membranes were synthesized by incorporating either cysteine (Cys) or cysteamine (CysM) precursors onto polyacrylic acid (PAA)-functionalized polyvinylidene fluoride membranes. Carbodiimide chemistry was used to cross-link thiol (−SH) groups on membranes for metal adsorption. The thiol membranes and intermediates of the synthesis were tested for permeability and long-term mercury removal using synthetic waters and industrial wastewater spiked with HgS NPs and a Hg 2+ salt. Results show that treatment of the spiked wastewater with a UF membrane removed HgS NPs to below the method detection level (<2 ppb) for up to 12.5 h of operation. Flux reductions that occurred during the experiment were reversible by washing with water, suggesting negligible permanent fouling. Dissolved Hg 2+ species were removed to non-detection levels by passing the UF-treated wastewater through a CysM thiol membrane. The adsorption efficiency in this long-term study (>20 h) was approximately 97%. Addition of Ca 2+ cations reduced the adsorption efficiencies to 82% for the CysM membrane and to 40% for the Cys membrane. The inferior performance of Cys membranes may be explained by the presence of a carboxyl (−COOH) functional group in Cys, which may interfere in the adsorption process in the presence of multiple cations because of multication absorption. CysM membranes may therefore be more effective for treatment of wastewater than Cys membranes. Focused ion beam characterization of a CysM membrane cross section demonstrates that the adsorption of heavy metals is not limited to the membrane surface but takes place across the entire pore length. Experimental results for adsorptions of selected heavy metals on thiol membranes over a wide range of operating conditions could be predicted with modeling. These results show promising potential industrial applications of thiol-functionalized membranes.

The disturbance flow field for a Mach $6$ flat-plate boundary layer flow with a wall-to-free-stream temperature ratio of $0.5$ is studied using direct numerical simulation (DNS), linear stability theory (LST) and biorthogonal decomposition. In the second-mode instability region, the DNS flow field can be reconstructed using a single LST mode, namely $F^+_1$ . However, when the supersonic mode emerges, none of the discrete modes nor the continuous branches alone can precisely match the DNS data. A superposition of the pair of discrete supersonic modes $F^\pm _1$ and the slow acoustic continuous spectrum is required to reproduce the disturbance amplitude distributions and the amplification rates observed in the DNS. Another finding is that the supersonic mode $F^-_1$ , which should be decaying following LST, in actuality is amplified based on the projected DNS data.

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