Coupled reactions 176 slow equilibration between

In the application of the ILDM method to reactive flow problems, physical processes (e.g., transport) are considered as a disturbance to the chemical reaction system. These disturbances may perturb the system within, or out of the manifold. Only the time-scale of the perturbation is important rather than its size, which may be very large. If the time-scale of the disturbance is of the same order as that along the slow manifold, then the components of the perturbation in the fast subspace will have a negligible effect since the chemistry will relax them back to the manifold. The components in the slow subspace will directly couple with the slow chemistry and, therefore, move the state within the manifold. Therefore, the basic idea for flow systems is to create a projection operator P, which projects any physical perturbation onto a perturbation within the manifold. This means that interaction between the physical processes and the slow time-scale chemistry can be represented, but other processes can be neglected since they are equilibrated by the chemistry in a short time. The nature of the projection operator P will depend on the local characteristics of the manifold. 

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