Modifying the Linear Packing Model for Predicting the Porosity of Nonspherical Particle Mixtures

Abstract

Based on the similarity analysis between the spherical and nonspherical particle packings, a mathematical model, modified from the previous linear packing model for spherical particles, is proposed for predicting the porosity of nonspherical particle mixtures. The background for this development is discussed in detail. The applicability of the proposed model is validated by the good agreement between the measured and calculated results for various packing systems including binary, ternary, and multicomponent packing of spherical and/or nonspherical particles.

Particulate Binary Mixtures: Dependence of Packing Porosity on Particle Size Ratio

“…In Figure 1a, the experimentally determined porosity of a binary glass bead mixture of D/d ) 10.22 (indicated by the data points, which were taken from Mota et al 2 ) is shown, together with the calculated porosity using different correction functions. 2,22,35,36 In Figure 1b, a normalized porosity ( / 0 ) is shown for data sets of Yu et al, 13 where 0 ) D 0 ) d 0 are values of 0 that correspond to those referenced in the quoted literature. It can be seen that, with decreasing δ, the smooth transition of minimum porosity (curves 1-3) may become an intersection point (data sets 4 and 5), because the filling mechanism of packing becomes predominant.…”

“…4,[8][9][10][11][12][13][14][15][16][17][18][19] However, deviations of experimental data from theoretical prediction induce the development of research to seek the causes of these deviations. A linear mixture model, which is applied for binary packing when the ratio of small particle size (d) to large particle size (D) is δ ) d/D f 0, is used in numerous works.…”

“…A linear mixture model, which is applied for binary packing when the ratio of small particle size (d) to large particle size (D) is δ ) d/D f 0, is used in numerous works. [8][9][10][11][12][13]17,20 The overall porosity ( ) is presented in the form of the product of fractional porosities:…”

“…[8][9][10]13,17,22 Equations 9 and 10 represent the two branches of the model, as depicted in Figure 1.…”

“…Based on this approach, the linear-mixture packing model was developed with the incorporation of interaction functions, generally represented by experimentally determined polynomial or power-law functions. 13,35,36 This brief outline leads shows that, generally, two types of model dependence of on x D are proposed: the discontinuity model, when the minimum porosity min is obtained by the intersection of eqs 9 and 10, and the continuity model, with a smooth porosity transition in the region of min . The choice of a continuity or discontinuity model will result in a smooth or broken curve with an intersection point in the region of minimum porosity (see Figure 1).…”