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

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.

Inertial Focusing and Ordering in Low Aspect Ratio Microchannels Using Reference Frame Tracking and Rotation Measurements

Inertial focusing and ordering in microchannel flows refers to the tendency of finite-sized particles to migrate across streamlines and to form linear, equally spaced trains in the direction of flow. This study utilizes a motorized microscope stage moving along the length of a low aspect ratio microchannel at up to 10 cm/s and provides a Lagrangian view of particles to obtain more complete time dependent trajectory and rotation histories from the channel inlet to outlet. We observe monodisperse particle dynamics, rotations, and interactions over time scales significantly longer (exceeding a 30-fold increase) than static reference frames. The results present new insight into particle interactions which show quasi-steady state equilibrium spacing which oscillates at a constant frequency at a fixed flow rate, which is different from the damped oscillatory interactions suggested in the literature. The average spacing shows little dependence on flow rate, but the oscillation frequency is dependent both on flow rate and particle size.

Orbits of Small Spherical Tracers in Monodisperse Particle Beds Liquid-Versus Air-Filled Rotating Tumblers

Sorting of particles of different sizes strongly affects the dynamics of river beds. As a model for the sorting of fine particles on the lee face of an alluvial “dune”, we study the orbits of small spherical tracers in monodisperse particle beds in quasi-two dimensional rotating tumblers, both liquid- and air-filled. In addition to searching for clues on lee-face sorting, another purpose is to provide benchmark data for small-scale “qDNS” of bedload sediment transport. While sorting of fines in a rotating tumbler, and other canonical grain flows, has been studied in air, there is a dearth of corresponding studies in liquid. Compared to the “dry” case, our data show that immersion in liquid yields significant differences in bead trajectories at matched Froude number, in the intermittent avalanching regime at low rotation rate.

ELECTRORHEOLOGY OF MONODISPERSE CORE/SHELL STRUCTURED PARTICLE SUSPENSIONS

As a novel candidate of electrorheological (ER) material, core/shell composite particles (PAPMMA) of poly(methyl methacrylate) (PMMA) core and polyaniline (PANI) shell were prepared and adopted as a dispersed phase. PAPMMA particles, obtained by a dispersion polymerization method, were spherical and possessed a monodisperse particle size distribution, in which the PANI shell was introduced on the surface of PMMA via an in-situ polymerization of aniline by adding an oxidant in an aqueous acidic solution. Yield stress of the PAPMMA suspensions under an applied electric field was observed to be increased with a particle size. In addition, monodisperse acrylic microspheres with aniline moiety on the surface were prepared by a seeded emulsion method, and then composite particles possessing chemically bonded PANI shell (PA-PGMA) were prepared via an in-situ polymerization of aniline. Their ER characteristics were also examined.