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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.

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.

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.

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.

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.

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.

This study aims to introduce a new theoretical approach to blend spherical and non‐spherical particles in a coating to improve its viscosity characteristics.

Theoretical analysis has been used to modify an existing model developed by this author to apply to a broad range of particle configurations.

Non‐spherical particles like fibres or discs in a suspension or coating have been found to have three different viscosity response regions. Consequently, the viscosity of suspensions or coatings with these types of particles appears to have two apparent maximums as a function of concentration. Improved viscosity control of coatings have been found to be directly achievable by blending particles with different shapes based on the concentration relative to this first maximum. This optimisation process has been found to be better understood using a new variable which has been described as the “sphericity”, s. The “sphericity”, s, as described in this study has been defined as the relative ratio of the surface to volume fraction for a non‐spherical particle to that of a sphere of equivalent volume.

Experimental data involving monodisperse particles of different configurations is often extremely difficult to obtain. However, the theoretical general concepts can still be applicable.

The model presented in this paper provides practical guidelines to blending pigments with different particle shapes to control the viscosity of coatings and suspensions.

The model presented in this paper provides the first apparent guidelines to control the blending of pigments in coatings and composites with different particle shapes using the “sphericity” of the pigment particle.

This paper attempted to show the potential relationship between five different interaction coefficients relating solvents and polymers. This review addressed primarily a comparison between the polymer-solvent interaction coefficients obtained from two different types of models. These two primary polymer-solvent interaction coefficients included the Flory-Huggins interaction coefficient developed from thermodynamic colligative properties and the polymer-solvent Sudduth interaction coefficient obtained from the generalized viscosity equation. The other three interaction coefficients included Hildebrand solubility parameter and the interaction coefficients or constants for the Huggins and Kraemers models that are normally generated from viscosity measurements. The paper aims to discuss these issues.

These five different interaction coefficients were compared from theoretical considerations as well as on the basis of available experimental data.

Remarkably the polymer-solvent interaction coefficients for both Flory-Huggins interaction coefficient and the Sudduth interaction coefficient were found to be dimensionless and approximately of the same value. In addition, when both interaction coefficients are negative then both describe solvents. In addition, both interaction coefficients describe a plasticizer when they are in the range of 0 to ½. Finally both interaction coefficients describe a non-solvent or a suspension when both are greater than 1. The Hildebrand solubility parameter was found to be directly related to the Flory-Huggins interaction coefficient. The viscosity constants for the Huggins and Kraemers models were found to be included as subsets of the Sudduth generalized viscosity model.

The strong apparent relationship between these five different interaction coefficients to predict the interaction between polymers and solvents is strongly indicated based on the results from this study. However, approximately half of these interaction coefficients have been derived to be evaluated from colligative properties and half were derived to be evaluated from viscosity measurements.

In general, it is much easier to obtain viscosity measurements compared to the evaluation of the colligative properties. Therefore, if a direct relationship can be shown between these five different interaction coefficients, then it would appear to be much easier to evaluate polymer-solvent interactions from the interaction coefficients obtained from viscosity measurements.

This is the first time that these five interaction coefficients have been compared in such a way that shows their direct relationship even though half of these interaction coefficients have been derived to be evaluated from colligative properties and half were derived to be evaluated from viscosity measurements.

The purpose of this paper is to expand the theoretical meaning and application of the separate components of the interaction coefficient as obtained from the generalized viscosity model.

Both theoretical and experimental analysis have been utilized to better understand the meaning of the separate components of the interaction coefficient obtained from the generalized viscosity model. Analysis of the experimental data of Schaller and Humphrey has been used to successfully isolate the separate components of the interaction coefficient.

The relative unhindered volume is the volume outside the sphere of influence of a particle that is responsible for the viscosity characteristics of a coating. This is the volume available for particles to move in the suspension and still contribute to the viscosity. The smaller the relative unhindered volume the higher the viscosity. As the interaction coefficient, σ, increases the particles increase their interaction with each other and the relative unhindered volume decreases. Using the data of Schaller and Humphrey, it was found that the interaction coefficient agreed best with the theoretical expectation relative to particle size when the ionic strength was low. At high levels of ionic strength, the solvent‐particle component of the interaction coefficient was dominant and the influence of particle size on the interaction coefficient was minimal.

Only one set of experimental data was successfully utilized for illustrative purposes in this study but the resulting analysis has implicated a broad range of practical applications. In addition, the general theoretical concepts elucidated relative to the interaction coefficient should still be applicable independent of the experimental results.

The analysis presented in this paper provides several practical guidelines to separate and control the charge component of pigments in a suspension from their size component using the interaction coefficient as described in this study. Consequently, the results of this study should provide several new practical approaches to use when attempting to control the viscosity of suspensions for a broad range of practical applications and for a broad range of suspension types including coatings.

This is the first time that the theoretical statistical character of the interaction coefficient as indicated in the generalized viscosity model has been specifically elucidated. In addition, the relatively simple experimental separation of the interaction coefficient into its size and electrical components has been shown to be widely applicable in this paper.

The purpose of this paper was to show that the generalised viscosity model can correctly characterise suspension data over both a wide range of concentration as well as a wide range of temperature. A second objective of this study was to show theoretically and experimentally how the interaction coefficient from the generalised viscosity model also appears to have some thermodynamic properties.

In this study, many well‐known suspension equations were shown mathematically to be subsets of the generalised viscosity equation. The generalised viscosity equation was also found to be able to be reduced mathematically to two well‐known dilute solution equations (Huggins and Kramer's equations) as well. The relationship between Huggins and Kramer's constants and the interaction coefficient from the generalised viscosity equation yielded the potential to evaluate the solubility characteristics of the interaction coefficient. The value of the interaction coefficient was then found to be able to be evaluated as a function of temperature to enhance an understanding of the thermodynamic characteristics of the interaction coefficient using the data of Bueche.

In this study, a polymer plasticiser system involving polymethyl methacrylate in the plasticiser diethyl phthalate yielded an interaction coefficient, σ, primarily in the expected plasticiser range from 0< σ<1. It was also found that the generalised viscosity equation fit Bueche's polymer plasticiser data remarkably well over the whole concentration range for temperatures ranging from 30°C to 140°C. This study also appeared to show that the interaction coefficient from the generalised viscosity model can apparently characterise thermal transitions as well as thermodynamic solubility for a polymer solute (i.e. polymethyl methacrylate) when viscosity is evaluated over a wide temperature range. This result was particularly significant since Bueche's data covered 25 decades of viscosity on a log scale.

This is the first paper to successfully explore the thermodynamic characteristics of the interaction coefficient of the generalised viscosity equation. This opens up new avenues for evaluating the solubility and thermodynamic characteristics of various additives in solutions and polymeric formulations.