Ideally the solid oxidizer particles in a propellant can be considered spheres of uniform size. Three sizes of particles are available: coarse at 500 μm, medium at 50 μm, and fine at 5 μm, all at a specific gravity of 1.95, and a viscoelastic fuel binder at a specific gravity of 1.01. Assume that these materials can be mixed and vibrated so that the solid particles will touch each other, there are no voids in the binder, and the particles occupy a minimum of space similar to the sketch of the cross section shown here. It is desired to put 94 wt % of oxidizer into the propellant mix, for this will give maximum performance.
(a) Determine the maximum weight percentage of oxidizer if only coarse crystals are used or if only medium-sized crystals are used.
(b) Determine the maximum weight of oxidizer if both coarse and fine crystals are used, with the fine crystals filling the voids between the coarse particles. What is the optimum relative proportion of coarse and fine particles to give a maximum of oxidizer?
(c) Same as part (b), but use coarse and medium crystals only. Is this better and, if so, why?
(d) Using all three sizes, what is the ideal weight mixture ratio and what is the maximum oxidizer content possible and the theoretical maximum specific gravity of the propellant? (Hint: The centers of four adjacent coarse crystals form a tetrahedron whose side length is equal to the diameter.)
