Modeling Carbon Condensation in Detonation of High Explosives: A Tale of Two Approximations

Detonation of carbon-rich high explosives produces significant amounts of carbon soot. This soot consists of nanometer-size carbon particles (e.g., nanodiamonds), often aggregated into large fractal structures. The mechanism of formation of this soot is believed to consist of two steps where, first, molecules of high explosive decompose into gaseous molecules (H₂O, CO₂, N₂ etc.) and the so-called excess carbon in the form of small (few atoms) carbon-rich fragments. During the second step - the so-called carbon condensation or clustering - those small fragments undergo the slow (compared to the first step) diffusion-limited coagulation into successively larger carbon clusters and particles. Accordingly, modeling of the condensation kinetics has traditionally been done within the paradigm of the Smoluchowski coagulation with the two standard approximations: (i) the volume fraction of the excess carbon in detonation products is taken to be low, and (ii) the time scale of coalescence of carbon particles upon collision is assumed very short, rendering the overall process diffusion-limited. In this work, we consider the ramifications of lifting these two approximations on modeling of the kinetics of carbon condensation and compare modeling results with recent experimental observations.