Timescales in Reactive Flow Models

In a reactive flow system, the chemical timescales should not be treated in isolation from the relevant timescales of the flow processes which may include diffusion, convection/advection or turbulent mixing (Goussis et al. 2005b). The simple initial value problem expressed in Eq. (2.9) must therefore be extended to a system of partial differential equations. Using the notation of Bykov and Maas (2007), the evolution equation for the scalar field of a reacting flow can be described by 

In the second approach, the spatially homogeneous chemical slow manifold is used, and the method must somehow accoxmt for reaction-transport coupling. For a chemical timescale to be defined as fast in a reactive flow system, the Damkohler number, which is defined as the ratio of the flow timescale tf and the chemical timescale Tc, must be large  

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