Simulation of random packing of binary sphere mixtures by mechanical contraction

Abstract

The mechanical contraction simulation for random dense packings is extended to binary mixture of spheres. The volume packing density as a function of sphere composition follows a characteristic triangular shape and resembles previous experiments on length scales from colloidal particles to metal shots. An excluded volume argument, which qualitatively explains trends in random packing densities of monodisperse particles, is insufficient to account for this triangular shape. The coordination number, or the average number of contacts on a sphere, shows a remarkable dip from 6 to 4 at the crossover from many small spheres to many large spheres, which has not been reported earlier. An explanation is given in terms of caging effects. r

Discrete element modelling of the packing of spheres and its application to the structure of porous metals made by infiltration of packed beds of NaCl beads

“…Data are near identical when a smaller "sensor" region was used to mimic the exact size of the machined casting (33 mm) as only one large particle diameter is removed from the overall cross section. The packing behaviour is in broad agreement with observations from other researchers [15,23,28] who, for a particle size ratios between 2 and 3, found maximum packing fractions were achieved with between 25 and 30vol.% additions of small particles. Figure 7 shows horizontal sections at the mid-plane for the modelled particle distributions (for 35mm vessels) and for CT images from corresponding samples (33 mm in diameter after the surface is machined) and the simulation can be seen to replicate, quite accurately, the typical features for the packing of these beads (for example regions with locally high packing and others with voids).…”

“…Despite the very high coordination number for the large particles, their low number fraction means that the average coordination number increases very little with increasing additions (from 6.3 to 7.0 over the full range of addition). This observation is similar to that observed in [23,28]. It is also reported that the maximum number of small particles that might be randomly placed on a large sphere (the so-called parking number [28,29]) can be determined for a particular particle size ratio, for this system it is 35.…”

“…This observation is similar to that observed in [23,28]. It is also reported that the maximum number of small particles that might be randomly placed on a large sphere (the so-called parking number [28,29]) can be determined for a particular particle size ratio, for this system it is 35. For 50vol.% additions the L-S coordination number is 26±4.5, below this upper limit.…”

“…It is worth noting that if the condition of exactly contacting spheres is used, i.e. rc = 0, the "true" coordination number for monosized spheres is 5.6 ±1.45 which is in good agreement with that expected for loose packing [14,16,23,26,28].…”

Geometrical cluster ensemble analysis of random sphere packings

“…In a stable random packing the majority of spheres are arrested at their position, whereas a minority of about 1%-3% of spheres can rattle 17 when the whole packing is shaken. The generated clusters must also have most of the spheres arrested.…”