Evaluating Mixture Rules for Multi-Component Pressure Dependence: H + O2 (+M) = HO2 (+M)

A substantial fraction of the reactions that take place in combustion are complex-forming (i.e. pressure-dependent) reactions, which depend on the collisional energy transfer characteristics of the surrounding mixture (“bath gas”). In contrast to the single-component bath gases used in nearly all fundamental investigations of these reactions, significant fractions of multiple species of disparate collisional energy transfer characteristics are usually present in combustion environments. Calculations of the rate constant for multi-component mixtures thereafter inevitably relies on a “mixture rule” based on rate constants for the individual single-component bath gases. Failure to implement a mixture rule, which is actually quite common in many implementations of kinetic models within combustion codes, can yield errors up to a factor equal to the number of separate expressions for each component. Even still, as demonstrated herein, rate constants evaluated through various proposed mixture rules can differ by over 60% for exactly the mixture compositions of interest to combustion modeling. Therefore, evaluating the suitability of various mixture rules for accurately representing multi-component pressure dependence for combustion modeling purposes appears particularly worthwhile, given that these differences now exceed achievable accuracies for single-component bath gases and, additionally, given that inverse uncertainty quantification procedures almost always rely on starting with an accurate model structure, including mixture rules. The present study evaluates various existing and new mixture rules for representations of multi-component pressure dependence for H+O2(+M)=HO2(+M) through comparison with master equation calculations. The results indicate that mixture rules based on the reduced pressure provide a considerably more accurate description than those based on pressure (reaching accuracies of 2% compared to ∼60%). Recommendations are made for incorporation of these new mixture rules within combustion codes. Until then, potential errors in the full condition-dependence for H+O2(+M)=HO2(+M) of up to ∼90% are essentially unavoidable merely due to available representation options within combustion codes.