On the distribution of particles in propellant solids

This article examines the distribution of aluminum and ammonium perchlorate particles in propellants. The volume fraction of solids is determined as a function of the weight fraction of aluminum. For unimodal distribution of closed packed spheres the volume fraction reaches 74%. It is shown that in order to entrain spheres of a smaller size, in a structure with a tetrahedron enclosed by four nearest-neighbor spheres, the diameter of the smaller spheres must be approximately smaller than 22%. When the space is filled with large particles and between them introduced smaller particles, the volume fraction of solids increases by 5%. A relation was developed for the free volume of a propellant composite of N tetrahedra, $N_a$ of which are occupied by secondary particles, and the thermodynamic probability of a distribution was also computed as well as the energy of adhesion. Based on random distribution, a relation between the larger and smaller particles was developed. In the last part of this analysis, a deformation of a composite space is examined, and a relation between the dilatation and the volume fraction of total solids which are dewetted is developed. The stress–strain behavior of a composite propellant material is replaced by new parameters which depend upon the dilatation.