An average model for disordered sphere packings

In this paper, an assembly of disordered packings is considered as a suitable set of packing cells of ordered spheres. In consequence, any of its parameters can be obtained by averaging the values of the set. Namely, the density of a packing of ordered spheres is described by two variables: the angle of the base, and the angle of the inclined edge of the associated parallelepiped. Then, the density of a packing of disordered spheres is obtained by averaging the angle of the base, and the subsequent averaging of the other angle, according to the kind of strain induced by the experiment. The average packing yields the density limits of loose sphere assemblies achieved by a process of fluidization and sedimentation in air, in water, and in viscous liquid at zero gravitational force. It also models the close sphere assemblies shaped by gentle tapping, vertical shaking, horizontal and multidirectional vibrations. The theory allows to elucidate the mechanism of each of the limits, as, for example, the metastable columns of spheres in the loosest packing, as well as the random close packing, and crystallization. The limits obtained coincide very well with the published experimental, numerical and theoretical data.

The Effect of Particle Size Ratio on Porosity of a Particles Deposition Process

Porosity plays an important role on a particle deposition process which determines the strength of material. The structure of a material from deposition process can be viewed as a random close packed. References show that random close packing structure of uniform-sized particles gives a porosity of around 36%. In this work we simulate the deposition process using a particle method to study the effect of particle size ratio into a porosity of a material with the ratio of particles’ radius is ranged from 1:1 to 1:5. From the simulation we get an interesting result that shows the porosity is decreased when the size ratio is increased in range from 1:1 to 1:1.5 with its minimum porosity is 31.92% at ratio 1:1.5. Then as the ratio increases from 1:1.5 to 1:5, the porosity is also increasing.