In this study, a simple model for the smoke formation in black powder combustion is developed. Smoke formation is modeled as nucleation from gas phase molecules. The precursor molecules for this nucleation process for black powder with 75 wt% of KNO3 are identified as potassium salts such, K2CO3 and K2SO4. This determination is based on the partialequilibrium calculations in which chemical species in the condensed phase are excluded. Standard classical nucleation theory (CNT) is adopted to estimate the radius and formation rate of the critical nuclei of smoke particles. The main components of smoke from black powder are K2CO3 or K2SO4 particles, depending on the sulfur content. The predicted nucleation rates of the particles are very fast. The time variation of the averaged particle radius and volume fraction of smoke is also evaluated by solving the population valance equation (Smoluchowski equation). The volume fraction of smoke produced by black powder combustion is predicted to be of the order of 10-4.
This study also investigates how ammonium perchlorate (NH4ClO4, AP) added to the black powder affects smoke formation, using CNT and the Smoluchowski equation. CNT predicts that the critical radius of K2CO3 and K2SO4 particles can be considerably increased by the addition of AP to black powder. This intervention could thus reduce smoke-particle formation. Although CNT predicts that no KCl particles will form because of the high vapor pressure of KCl, the Smoluchowski equation indicates that KCl particles will be produced with a large amount of added AP. Solutions of the Smoluchowski equation also indicate that the average particle diameter and volume fraction of smoke decrease if the amount of added AP is increased.
black powder, smoke formation, potassium salt, nucleation theory, Smoluchowski equation