Multidimensional Combustion Models

A chemical reaction between the reactant species A _a , A _b , etc., that forms the product species A _c , A _d , etc., is often written as (6.1)% MathType!MTEF!2!1!+- % feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamODamaaBa % aaleaacaWGHbaabeaakiaadgeadaWgaaWcbaGaamyyaaqabaGccqGH % RaWkcaWG2bWaaSbaaSqaaiaadkgaaeqaaOGaamyqamaaBaaaleaaca % WGIbaabeaakiabgUcaRiablAciljabgkziUkaadAhadaWgaaWcbaGa % am4yaaqabaGccaWGbbWaaSbaaSqaaiaadogaaeqaaOGaey4kaSIaam % ODamaaBaaaleaacaWGKbaabeaakiaadgeadaWgaaWcbaGaamizaaqa % baGccqGHRaWkcqWIMaYsaaa!4D9B!$${v_a}{A_a} + {v_b}{A_b} + \ldots \to {v_c}{A_c} + {v_d}{A_d} + \ldots $$ where the v _i are termed the stoichiometric coefficients of the reaction. Since every chemical reaction can generally proceed in both directions, the arrow in Eq. 6.1 may be replaced by an equal sign. The general form of the reaction equation now becomes (6.2)% MathType!MTEF!2!1!+- % feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaabuaeaaca % WG2bWaaSbaaSqaaiaadMgaaeqaaOGaamyqamaaBaaaleaacaWGPbaa % beaaaeaacaWGPbaabeqdcqGHris5aOGaeyypa0JaaGimaaaa!3EC1!$$ \sum\limits_i {{v_i}{A_i}} = 0 $$ where, by convention, the stoichiometric coefficients v _i are positive for the product species and negative for the reactant species.