Powder flowability is a crucial factor in the handling and processing of powder-based industrial products. For example, in pharmaceutical manufacturing, powder flowability affects processes such as discharge from bins and hoppers, powder mixing, feeding, capsule or die filling, and tableting [1-3]. Powder flowability is impacted by many factors, including but not limited to particle size, particle size distribution, density, surface energy, surface roughness, and shape, to name a few [4-8]. That poses significant challenges in predicting flowability based on key parameters such as particle size, particularly for surface-engineered particles with superimposed nano-roughness via dry coating [5, 9]. Our previous work has shown that the granular Bond number (Bog) [8], a dimensionless scaling parameter defined as the ratio of interparticle cohesion to body forces, can link particle-scale cohesion estimates to bulk properties like flowability both for as-received and surface-engineered powders [9]. Estimating Bond number may be done using van der Waals force-based particle contact models. These models need particle scale information such as characteristic particle size, density, surface energy, and surface roughness [8, 10]. A major question is which characteristic particle size should be used; e.g., a single size parameter such as the number or volume weighted mean or median diameter, area weighted mean diameter, or the entire size distribution? To answer this question, this work assessed the relationship between Bond Number and flowability through three methods of calculating the granular Bond number: (1) using the median particle size (d50), (2) using Sauter mean diameter (d32), and (3) utilizing whole size distributions via the size class-dependent (SCD) Bond number methodology [6, 11]. About 30 different real-world pharmaceutical particles were selected, and their particle-scale properties and flowability, both before and after dry coating, were measured for testing these three approaches. Analysis of prediction intervals associating Bond Number with flowability through a power law relationship showed that both d32 and SCD methods provide greater precision than the d50 method, as they account for surface area to volume ratios. Outliers identified through flowability regime prediction mismatch analysis were further examined, along with the impact of factors not explicitly considered in the particle contact mechanics, such as the particle shape aspect ratio (AR), and deviations between theoretically and experimentally determined specific surface area, SSA(m2/gm). It was observed that non-uniformities associated with particles, such as surface morphology, surface debris, fines content, and high SSA, influenced prediction errors, as also observed in previous studies [6, 9]. A new unified prediction function was proposed to encounter such issues and was found to better predict both as-received and dry-coated materials. Particle scale parameters such as AR and SSA were also found to affect the prediction of dry coating performance. Despite a few limitations, the proposed model using either the d32 or SCD methods can reasonably predict bulk-scale flowability based on particle scale measurements for a wide variety of powders before and after dry coating. Considering that using d32 works as well as using SCD, d32 is recommended as the key particle size parameter as it is less intensive computationally. Its usage, along with the Chen model [10], would be helpful to industry practitioners for predicting powder flowability using a small amount of material, also guiding them regarding potential avenues for flowability enhancements, such as via dry coating.
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