The interaction of self-heating and branched-chain reaction in the vicinity of the second and third explosion limits of the H2 + 02 reaction is studied numerically. We assume the vessel walls are reflective and use Baldwin's scheme appropriate to an aged boric acid coating. We confirm the dominance of chain branching at the second limit. An unexpected feature, however, is the bistability of the stationary-state radical concentration (i.e., there are two solutions for each vessel temperature below the limit). As Ta is increased, the two solutions move closer together and coalesce at the point of ignition. This allows the limit to be identified mathematically as a limit-type bifurcation.
The computations reveal that at higher pressures, self-heating shifts the point of explosion to lower vessel temperatures. Self-heating influences the reaction rate mainly via the kinetics of hydrogen peroxide decomposition. A simplified scheme of the leading reactions responsible for reaction near the third limit can be represented in the form of a closed cycle with (i) initiation; (ii) branching and progation steps; (iii) termination accompanied by significant heat release; and (iv) formation of HzO2. There is feedback in this cycle as the heat evolved in (iii) increases the rate of thermal initiation (i) which occurs principally by H202 decomposition.
These kinetics lead to critical conditions analogous to the Semenov criterion for thermal explosion and give a value of the apparent activation energy for the third limit of 242 KJ mol-~. The numerical calculations involving the complete Baldwin scheme of reactions lead to an apparent activation energy very close to that determined from the simplified scheme of reactions.