Two-field and single-field representations of gas–solid reactive flow with surface reactions

A single-field representation is derived to describe a multi-species gas flow seeded with perfectly rigid, non-porous and partially inert particles. Indeed, the latter are not involved in heterogeneous reactions with the gas phase (no consumption of the solid by the gas), but they are expected to potentially undergo adsorption and recombination of gaseous radicals on their surface, resulting in the desorption of stable species into the gas. In this work, integral balances are first established at the gas–solid interface, consistent with the local single-phase equations for reactive multi-species gas flow. This allows rigorous derivation of the jump equations that apply at the gas–solid interface in the presence of surface reactions. Then, the description in terms of local single-phase equations, completed by the jump equations at the interface, is recast into a set of equations for the full domain in the sense of distributions. The result extends Kataoka's formalism (Kataoka, 1986) to reactive gas–solid flow in the presence of both homogeneous and surface reactions.