Particle packing modeling incorporating the wedging effect

Abstract

The packing of solid particles is an important research topic in particle mechanics and powder technology. However, it is difficult to predict and measure the packing density of particles. Although theoretical models for prediction and test methods for measurement have been developed, the predicted values and measured results do not always agree with each other. Through in-depth review of the theoretical predictions by the existing 2-parameter model and the respective measured results, it is postulated in this thesis that the discrepancies between the predicted values and measured results are mainly due to the wedging effect – a new interaction effect that has not been considered in previous packing models. The wedging effect occurs when some isolated fine particles are entrapped at the gaps between the coarse particles or when the gaps between the coarse particles are not wide enough for the formation of complete layers of fine particles. Such wedging effect would reduce the packing density and therefore should be considered in particle packing modeling.

To provide additional measured results covering a wider range of size ratio than those published by others, a comprehensive experimental study of measuring the packing densities of binary mixes of mono-sized and rounded particles has been conducted. The wedging effect was further explained and more importantly quantified in the light of these experimental results. And, by incorporating the wedging effect, a 3-parameter packing model has been developed. The 3-parameter model was calibrated by fitting the theoretical predictions with the measured results of the comprehensive study conducted herein. After calibration, the theoretical predictions agree very well with the measured results, with the prediction error generally within 1.43%.

Further, some of the particle packing models were evaluated by comparing with published test results. The particle packing models so evaluated include the 2-parameter model (with the loosening and wall effects incorporated), the compressible model (with the loosening, wall and compaction effects incorporated) and the 3-parameter model (with the loosening, wall and wedging effects incorporated). It was found that the accuracy of the models varies with both the size ratio and volumetric fractions of the binary mix. In general, when the size ratio is larger than 0.65, all the packing models are sufficiently accurate. However, when the size ratio is smaller than 0.65, the 2-parameter model and the compressible model would either over- or under-estimate the packing density with the prediction errors generally larger at around the volumetric fractions giving maximum packing density. On the other hand, within the whole range of size ratio from 0.02 to 0.74 covered by the test results used for evaluation of the packing models, the packing density prediction by the 3-parameter model are accurate to within an absolute error of 0.020. Overall, the better performance of the 3-parameter model may be attributed to the incorporation of the wedging effect. With the wedging effect incorporated, the 3-parameter model is the most accurate and generally applicable to the whole range of size ratio from 0 to 1.