Reduction to a single partial differential equation

Therefore, the only derivatives of W2 that we need to evaluate for use in equations (100) and (102) are Wy and Wp. Since the quantity in brackets in equation (96) is zero in equilibrium, we find from equation (96) that for small departures from equilibrium, 

The quantity t is clearly a representative reaction time, and 3 will now be shown to be simply related to the difference between the frozen and equilibrium sound speeds. 

In order to relate 3 to the equilibrium sound speed and the frozen sound speed Uy, let us compute l/a = (dpjdp) y=y for the present gas. In view of equation (51), 

Reactions in Flows with Negligible Molecular Transport 

The substitution of equations (109) (111) into equation (108) yields the required relationship 

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