On the redox reactions between allyl radicals and NOx

NO_x mitigation is a central focus of combustion technologies with increasingly stringent emission regulations. NO_x can also enhance the autoignition of hydrocarbon fuels and can promote soot oxidation. The reaction between allyl radical (C₃H₅) and NO_x plays an important role in the oxidation kinetics of propene. In this work, we measured the absolute rate coefficients for the redox reaction between C₃H₅ and NO_x over the temperature range of 1000–1252 K and pressure range of 1.5–5.0 bar using a shock tube and UV laser absorption technique. We produced C₃H₅ by shock heating of C₃H₅I behind reflected shock waves. Using a Ti:Sapphire laser system with frequency quadrupling, we monitored the kinetics of C₃H₅ at 220 nm. Unlike low-temperature chemistry, the two target reactions, C₃H₅ + NO → products (R1) and C₃H₅ + NO₂ → products (R2), exhibited a strong positive temperature dependence for this radical-radical type reaction. However, these reactions did not show any pressure dependence over the pressure range of 1.5–5.0 bar, indicating that the measured rate coefficients are close to the high-pressure limit. The measured values of the rate coefficients resulted in the following Arrhenius expressions (in unit of cm³/molecule/s):$k_1\left({\mathrm{C}}_3{\mathrm{H}}_5+\text{NO}\right)=1.49\times {10}^{?10}\exp \left(?6083.6\frac{\mathrm{K}}{T}\right)\left(1017?1252K\right)$$k_2\left({\mathrm{C}}_3{\mathrm{H}}_5+\mathrm{N}{\mathrm{O}}_2\right)=1.71\times {10}^{?10}\exp \left(?3675.7\frac{\mathrm{K}}{T}\right)\left(1062?1250K\right)$To our knowledge, these are the first high-temperature measurements of allyl + NO_x reactions. The reported data will be highly useful in understanding the interaction of NO_x with resonantly stabilized radicals as well as the mutual sensitization effect of NO_x on hydrocarbon fuels.     

Almost automorphic solutions to logistic equations with discrete and continuous delay

We obtain sufficient conditions for the existence and uniqueness of a positive compact almost automorphic solution to a logistic equation with discrete and continuous delay. Moreover, we provide a counterexample to some results in literature which deal with the uniqueness of almost periodic solutions to logistic type equations.