Optimum formulation derivation for the ultimate packing fraction using monodispersed particle sizes when optimizing suspension viscosities

Abstract

Purpose

The importance of maximizing the particle packing fraction in a suspension by maximizing average particle size ratio of D₅/D₁ has been adequately shown to be important as previously reported in the literature. This study aims to extend that analysis to include the best formulation approach to maximize the packing fraction with a minimum number of monodisperse particle sizes.

Design/methodology/approach

An existing model previously developed by this author was modified theoretically to optimize the ratio used between consecutive monodisperse particle sizes. This process was found to apply to a broad range of particle configurations and applications. In addition, five different approaches for maximizing average particle size ratio D̅₅/D̅₁ were addressed for blending several different particle size distributions. Maximizing average particle size ratio D̅₅/D̅₁ has been found to result in an optimization of the packing fraction. Several new concepts were also introduced in the process of maximizing the packing fraction for these different approaches.

Findings

The critical part of the analysis to maximize the packing fraction with a minimum number of particles was the theoretical optimization of the ratio used between consecutive monodisperse particle sizes. This analysis was also found to be effectively independent of the maximum starting particle size. This study also clarified the recent incorrect claim in the literature that Furnas in 1931 was the first to generate the maximum theoretical packing fraction possible for n different particles that was actually originally developed in conjunction with the Sudduth generalized viscosity equation. In addition, the Furnas generated equation was also shown to give significantly different results from the Sudduth generated equation.

Research limitations/implications

Experimental data involving monodisperse particles of different blends with a minimum number of particle sizes that are truly monodisperse are often extremely difficult to obtain. However, the theoretical general concepts can still be applicable.

Practical implications

The expanded model presented in this article provides practical guidelines for blending pigments using a minimum number of monodisperse particle sizes that can yield much higher ratios of the particle size averages D̅₅/D̅₁ and thus potentially achieve significantly improved properties such as viscosity.

Originality/value

The model presented in this article provides the first apparent guidelines to control the blending of pigments in coatings by the optimization of the ratio used between consecutive monodisperse particle sizes. This analysis was also found to be effectively independent of the maximum starting particle size.

Citation

Sudduth, R.D. (2019), "Optimum formulation derivation for the ultimate packing fraction using monodispersed particle sizes when optimizing suspension viscosities", Pigment & Resin Technology, Vol. 48 No. 1, pp. 45-56. https://doi.org/10.1108/PRT-01-2018-0006