Carbon clustering in detonations

The clustering of carbon in the detonation regime is studied with the assumption of a diffusion-limited clustering process. The diffusion constants are determined from modified Enskog theory and the Stokes–Einstein relation. With the size dependence of the cluster energy treated with a surface term, the energy difference between clusters and bulk carbon has an asymptotic time dependence of t−1/3. That is, for any given time it takes 1000 times as long to release the next 90% of the carbon energy. This leads to a very slow ‘‘reaction rate’’ which can couple to the reaction zone to produce nonideal time-dependent detonations on the scale of microseconds and centimeters. In addition, any ‘‘bottleneck’’ in the clustering process due to a sticking coefficient of less than one leads to a temporary delay in energy release that persists out to times several orders of magnitude larger than the time scale of the initial effect of the ‘‘bottleneck.’’