A 3-parameter model for packing density prediction of ternary mixes of spherical particles

• Deviations from the linear packing theory have been observed.
• Such deviations are attributed to the newly identified wedging effect.
• With wedging effect incorporated, a 3-parameter model has been developed.
• The 3-parameter model is verified by comparing to experimental results.

The conventional packing models are mostly based on the linear packing theory that for a mixture of several size classes of particles (each size class is a collection of mono-sized particles), the specific volume of the mixture is a linear function of the volumetric fractions of the individual size classes. However, deviations from this theory at certain volumetric fractions leading to significant reduction in packing density have been observed. The authors attribute such deviations to the newly identified wedging effect of the fine particles stuck at the gaps between the coarse particles. Herein, the 3-parameter packing model with the wedging effect incorporated is extended to ternary mixes of spherical particles. In the formulation, the linear packing theory is not followed in the sense that the specific volume is no longer assumed to be a linear function of the volumetric fractions. The extended model is validated by checking against the test results from this study and the literature.

Wedging effect occurs when some isolated fine particles are entrapped in the gaps between the coarse particles instead of filling into the voids or when some gaps between the coarse particles are too narrow to accommodate even one complete layer of fine particles, as shown below. Herein, a 3-parameter model for ternary mixes with the wedging effect incorporated is developed.Figure optionsDownload as PowerPoint slide