Sharpness of wavefront

As a measure of the sharpness of the wavefront, we can consider two quantities (i) the magnitude of the maximum (negative) gradient, — (dh/dr)max, which occurs at b = ja0 and (ii) the distance Ar between the points corresponding to 25 per cent and 75 per cent conversion (see Fig. 11.4) In dimensionless terms and with travelling coordinates, these two quantities are simply 

Sharp fronts correspond to high gradients and small distances Ar (and either one of these two conditions implies the other). The results given in (11.28) also imply the following dependences  

with the simple cubic autocatalytic rate law, we have been able to find an analytical expression for the time and space dependence of a steady reaction-diffusion wave and make various quantitative and qualitative comments about the behaviour of the wave in terms of the kinetic and diffusion parameters. We now turn to the apparently simpler kinetics of a quadratic autocatalysis, hoping for similar rewards. 

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