Development and validation of a constitutive model for size-segregation during percolation

Segregation is a widely occurring undesirable phenomenon in industries that store, handle and process particulate materials. Size-segregation induced by the percolation mechanism is observed in several important processes that negatively impacts the product quality and mixing. To quantify size-segregation, a constitutive model based on simultaneous convective and diffusive demixing was developed and validated. The primary segregation shear cell (PSSC) was used to measure the fundamental parameters and validate the convective-diffusive segregation model. Glass beads of size ratios of 10.9:1 (1250:115 μm), 8.7:1 (1000:115 μm), and 5.1:1 (1000:196 μm) were used for model parameter determination; whereas, size ratio of 6.4:1 (1250:196 μm) was used for model validation. As shown in a previous study, an effective segregation direction could be measured and used to validate the convective-diffusive segregation model for percolation. This justified the use of an effective segregation direction to model the percolation of fines. When compared to the normalized measured data for size ratios larger than 8.7:1, the convective-diffusive model resulted in standard deviations of 0.035. However, for size ratios smaller than 6.4:1, diffusive demixing was occurring during shear with the absence of a rapid initial discharge phase, i.e., minimal contribution due to convective component. Estimating the percolation for the 6.4:1 size ratio was accomplished by using the mean data of the 5.1:1 size ratio, which resulted in standard deviation of 0.055. The initial rapid discharge present in 10.9:1 and 8.7:1 size ratios suggests that a critical size ratio exists that differentiates free-fall discharge segregation from random mixing segregation. This can be critical to powder manufacturers that could use this critical limit to define size distribution recommendations during manufacturing.