Utilizing the Discrete Element Method for the Modeling of Viscosity in Concentrated Suspensions Martin Kroupa, Michal Vonka, Miroslav Soos, and Juraj Kosek* Department of Chemical Engineering, University of Chemistry and Technology Prague, Technicka 5, 16628 Prague 6, Czech Republic * S Supporting Information ABSTRACT: The rheological behavior of concentrated suspensions is a complicated problem because it originates in the collective motion of particles and their interaction with the surrounding fluid. For this reason, it is difficult to accurately model the effect of various system parameters on the viscosity even for highly simplified systems. We model the viscosity of a hard-sphere suspension subjected to high shear rates using the dynamic discrete element method (DEM) in three spatial dimensions. The contact interaction between particles was described by the Hertz model of elastic spheres (soft-sphere model), and the interaction of particles with flow was accounted for by the two-way coupling approach. The hydrodynamic interaction between particles was described by the lubrication theory accounting for the slip on particle surfaces. The viscosity in a simple-shear model was evaluated from the force balance on the wall. The obtained results are in close agreement with literature data for systems with hard spheres. Namely, the viscosity is shown to be independent of shear rate and primary particle size for monodisperse suspensions. In accordance with theory and experimental data, the viscosity grows rapidly with particle volume fraction. We show that this rheological behavior is predominantly caused by the lubrication forces. A novel approach based on the slip of water on a particle surface was developed to overcome the divergent behavior of lubrication forces. This approach was qualitatively validated with literature data from AFM measurements using a colloidal probe. The model presented in this work represents a new, robust, and versatile approach to the modeling of viscosity in suspensions with the possibility to include various interaction models and study their effect on viscosity. ■ INTRODUCTION Suspensions of particles in a liquid are common in a large variety of applications such as food, blood, and polymer latexes to name only a few. An essential property of these systems is their viscosity because it largely affects their behavior. Conversely, the viscosity of a suspension is generally affected by its properties. The rheological behavior can be very complex, and for this reason, simplified systems are often preferred because they reduce the number of influencing parameters. The simplest system in this context is the hard-sphere model. 1 However, even for this simple system the rheological behavior for high particle volume fractions ϕ is still not completely understood. Experimental measurements of the viscosity in hard-sphere suspensions are often complicated by various effects including the deviation from a strictly monodisperse suspension, which introduces a strong effect on the viscosity. 2 Furthermore, the presence of interparticle forces (e.g., the van der Waals attraction) introduces additional complexity into the system. 1,2 Therefore, benchmark studies of hard-sphere rheology usually used dispersions of silica particles or measurements of charge- stabilized latexes mapping the hard-sphere behavior. 3−7 For low values of the particle volume fraction, the viscosity η of a hard-sphere suspension follows Einstein’s equation, 8 which predicts a linear dependence of η on ϕ. This relation breaks down for ϕ larger than approximately 5%. The reason for this is that below this threshold the movement of each particle can be treated individually and then added to obtain the behavior of the whole suspension. For larger values of particle volume fraction, the particles inevitably start to influence each other, and the dependence of η on ϕ becomes nonlinear. In this region, phenomenological equations are widely used, such as that of Krieger and Dougherty 9 η η ϕ ϕ = − ϕ − ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ 1 f m 2.5 m (1) or Maron and Pierce 10 η η ϕ ϕ = − − ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ 1 f m 2 (2) where η f is the fluid dynamic viscosity and ϕ m is the maximum packing fraction. Received: June 23, 2016 Revised: July 29, 2016 Published: August 1, 2016 Article pubs.acs.org/Langmuir © 2016 American Chemical Society 8451 DOI: 10.1021/acs.langmuir.6b02335 Langmuir 2016, 32, 8451−8460 This is an open access article published under an ACS AuthorChoice License, which permits copying and redistribution of the article or any adaptations for non-commercial purposes. Downloaded via 171.243.67.90 on June 1, 2023 at 03:14:55 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
Utilizing the Discrete Element Method for the Modeling of Viscosity in Concentrated Suspensions
Jun 03, 2023
The rheological behavior of concentrated suspensions is a complicated problem because it originates in the collective motion of particles and their interaction with the surrounding fluid. For this reason, it is difficult to accurately model the effect of various system parameters on the viscosity even for highly simplified systems. We model the viscosity of a hard-sphere suspension subjected to high shear rates using the dynamic discrete element method (DEM) in three spatial dimensions.
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Suspensions of particles in a liquid are common in a large
variety of applications such as food, blood, and polymer latexes
to name only a few. An essential property of these systems is
their viscosity because it largely affects their behavior.
Conversely, the viscosity of a suspension is generally affected
by its properties. The rheological behavior can be very complex,
and for this reason, simplified systems are often preferred
because they reduce the number of influencing parameters. The
simplest system in this context is the hard-sphere model.1
However, even for this simple system the rheological behavior
for high particle volume fractions ϕ is still not completely
understood.
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