Fast binary reactions in simple flows

Consider the binary chemical reaction A + B — C. The reaction-diffusion-advection equations read, in the case of equal diffusion co- 

The symmetry of this system allows to find conservation laws analogous to the spatially independent case (3.8). For example, the equation for the quantity 4 (x,t) = A(x, t) — B(x,t), analogous to Qs in  

In the context of combustion in non-premixed flames, this is called the Burke-Schumann solution. If the initial condition is such that T(x, t = 0) is not homogeneous in space, solving its advection-diffusion equation to obtain T(x, t) is needed in addition to solving the one for / (x, t) before using (5.8)-(5.9) to obtain C(x, t). 

These solutions are plotted in Fig. 5.1. The reaction rate k does not enter the above expressions in the k — oo limit considered here. We see that a sharp interface between A and B, located at x = 0, remains at all times. Also the product C remains concentrated around this interface, forming, in the complete two-dimensional system, a strip of width [2Dj r- Pe 1/2. The amount of product on a portion of this strip of length L along the transverse direction y is given by M = fLdy dxC(x)dx = LCt, where the amount of product per unit of transverse interface is 

We can also calculate the total rate of product creation per unit of time in the system  

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