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Research Papers

# Effects of Polydispersity on Structuring and Rheology in Flowing Suspensions

[+] Author and Article Information
Eilis Rosenbaum

Department of Civil and Environmental Engineering,
Carnegie Mellon University,
Pittsburgh, PA 15213;
National Energy Technology Laboratory,
626 Cochrans Mill Road, P.O. Box 10940,
Pittsburgh, PA 15236
e-mail: eilis.rosenbaum@netl.doe.gov

National Energy Technology Laboratory,
626 Cochrans Mill Road, P.O. Box 10940,
Pittsburgh, PA 15236

Kaushik Dayal

Department of Civil and Environmental Engineering;Center for Nonlinear Analysis,
Department for Mathematical Sciences;
Department of Materials Science and Engineering,
Carnegie Mellon University,
Pittsburgh, PA 15213
e-mail: kaushik.dayal@cmu.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received December 20, 2018; final manuscript received February 28, 2019; published online April 19, 2019. Assoc. Editor: N.R. Aluru.

J. Appl. Mech 86(8), 081001 (Apr 19, 2019) (11 pages) Paper No: JAM-18-1719; doi: 10.1115/1.4043094 History: Received December 20, 2018; Accepted February 28, 2019

## Abstract

The size and distribution of particles suspended within a fluid influence the rheology of the suspension, as well as strength and other mechanical properties if the fluid eventually solidifies. An important motivating example of current interest is foamed cements used for carbon storage and oil and gas wellbore completion. In these applications, it is desired that the suspended particles maintain dispersion during flow and do not coalesce or cluster. This paper compares the role of mono- against polydispersity in the particle clustering process. The propensity of hard spherical particles in a suspension to transition from a random configuration to an ordered configuration, or to form localized structures of particles, due to flow is investigated by comparing simulations of monodisperse and polydisperse suspensions using Stokesian dynamics. The calculations examine the role of the polydispersity on particles rearrangements and structuring of particles due to flow and the effects of the particle size distribution on the suspension viscosity. A key finding of this work is that a small level of polydispersity in the particle sizes helps to reduce localized structuring of the particles in the suspension. A suspension of monodisperse hard spheres forms structures at a particle volume fraction of approximately $47%$ under shear, but a $47%$ volume fraction of polydisperse particles in suspension does not form these structures.

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## Figures

Fig. 1

Particle pair interactions are shown for four motions of particle a relative to particle b

Fig. 2

The particles are sheared in the direction shown and the images below are shown from the side view and looking through the whole sample

Fig. 3

Particle size distribution of the slightly polydisperse particles

Fig. 4

The results reported previously are shown in black. The results of the simulations reported here are shown in color. When we implemented the correct full expressions for the resistance terms into LAMMPS, the match between our results and those of Ball and Melrose (1997) and Brady and Bossis (1984) was closer, even at higher volume fractions, unlike Bybee (2009) and the original LAMMPS FLD implementation. The dashed-dotted (original FLD implementation in LAMMPS) and dashed lines (simulations with full correct expressions) are second-order polynomial fits through the simulation data. Both simulation sets were run with the same initial particle data sets.

Fig. 5

Results are shown for three different strain rates. The simulation sets were run with the same initial particle configurations.

Fig. 6

Results are shown for hard sphere suspensions of monodisperse (solid circles) and polydisperse (open circles) particles

Fig. 7

Comparison of structuring of monodisperse particles at three different volume fractions. The structuring is indicated by particles aligning along a single line and are seen as a single particle from the view point. The structuring increases with volume fraction. The particle configurations were made by reducing the monodisperse particle size from a 50% volume fraction of particles so that all particles are starting from the same configuration. The final configuration is shown. Particles are shown at half size.

Fig. 8

The radial distribution function is shown at three different times, representing the initial configuration, the configuration at the mid-point, and the configuration at the end of the simulation. The grayscale value corresponds to the particle coordination number. The side shown is the view indicated in Fig. 2.

Fig. 9

The initial and the final configurations of two 47% by volume fraction of particles systems. Monodisperse and polydisperse particle configurations are compared. The color corresponds to the particle size.

Fig. 10

The initial and the final configurations of two 47% by volume fraction of particles systems. Monodisperse and polydisperse particle configurations are compared. The color corresponds to the particle size. The side shown is the view indicated in Fig. 2. The insert shows the particles at half size, where the structuring is more apparent. The circled region indicates one of the regions where structuring occurred in the particles. The particles form a line of particles in the x-direction.

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