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A rheological constitutive law is developed for a suspension of rigid rods in a Bingham fluid for volume fractions ranging up to the semiconcentrated regime. Based on a cell model approach, which allows expressing the shear stress on the particle surface, the particle stress contribution is derived and involves additional yield stress terms related to an ensemble average orientation distribution of the rods. As a first approach, a von Mises criterion is used to describe the composite flow threshold, which is found to be anisotropic in the sense that it depends on the rod orientation. A rod dynamics equation is also proposed and incorporates some diffusion/perturbation due to yielded regions encountered throughout the suspension. In parallel, an equivalent kinetic theory is also developed. The model provides good agreement with shear stress experiments for kaolin pastes filled with steel fibers of two different aspect ratios. [ABSTRACT FROM AUTHOR]

Transient shear flow data of untreated multiwalled carbon nanotubes (MWCNTs) dispersed in a Newtonian epoxy matrix are analyzed. A sequence of shearing and rest steps was applied to characterize the transient responses of the suspensions. Stress overshoots appeared at very small deformation during forward and reverse flow experiments and their intensity increased with rest time between two consecutive flows, during which the suspension structure was reconstructed. The transient behavior of the MWCNT suspensions is explained with the help of a recently proposed model [G. Natale et al., AIChE J. 60(4), 1476-1487 (2014)]. The MWCNTs are described as rigid rods dispersed in a Newtonian matrix, and the evolution of the system is controlled by hydrodynamics, rod-rod interactions, and Brownian motion. The force due to the interactions is modeled as a nonlinear lubrication force and the total stress tensor is evaluated introducing a fourth-order interaction tensor. The Fokker-Planck equation is numerically solved for transient simple shear flow using a finite volume method, avoiding the need of closure approximations. The model predictions show that interactions slow down the orientation evolution of the rods. For the first time, the effect of shear rate is directly accounted by the model, which predicts that a critical shear rate is necessary to break down the structure and let the rods orient in the flow direction. In addition, we confronted the model predictions with the rheological data of a glass fiberfilled polybutene [M. Sepehr et al., 48(5), 1023-1048 (2004)], demonstrating its ability to describe the behavior of micro and nano-scale particle suspensions. [ABSTRACT FROM AUTHOR]

This work is focused on shear thinning behavior of suspensions of rigid non-Brownian fibers dispersed in a Newtonian liquid. The work consists of developing a new theoretical model and conducting accurate experimental measurements. The shear thinning is expected to be caused by adhesive interactions between fibers. Experiments on polyamide (PA) fibers (present work) and carbon nanotube (CNT) suspensions [Khalkhal et al., J. Rheol. 55, 153-175 (2011)] have revealed the following features: (a) The flow curves exhibit a pronounced pseudoplastic behavior interpreted in terms of the progressive aggregate destruction at the increasing shear rate; (b) the enhancement of the shear thinning with an increasing particle volume fraction is observed and explained by an increase in the strength of effective interactions between particles, as their concentration increases; (c) a weak yield stress of the PA fiber suspensions is detected in a controlled-stress mode and explained by the liquid-solid transition as the concentration of aggregates (constituted by fibers) approaches the close packing limit; (d) the shear thinning is much stronger in CNT suspensions because the adhesive interactions play a more important role between nanosized CNT particles than between micron-sized PA fibers. A theoretical model considering the coexistence of transient aggregates with free nonaggregated fibers has been developed. The model allows viscosity calculations in terms of the aggregation parameter--the ratio of adhesive to hydrodynamic forces. It captures qualitatively the above-mentioned shear thinning behaviors and fits reasonably well to the experimental data on both PA fiber and CNT suspensions. [ABSTRACT FROM AUTHOR]

This work is focused on the modelling of the shear and normal stresses in fibre suspensions that are subjected to a simple shear flow in the presence of short-range lubrication forces, van der Waals and electrostatic forces, as well as solid friction forces between fibres. All of these forces are weighed by the contact probability. The theory is developed for attractive fibres with van der Waals interaction dominating over electrostatic repulsion. The model predicts a simple Bingham law for both the shear stress and the first normal stress difference, with the apparent shear and normal yield stresses proportional to the second and the third power of the particle volume fraction respectively. The model is applied to the experimental data of Rakatekar et al. (Adv. Mater., vol. 21, 2009, pp. 874–878) and Natale et al. (AIChE J., vol. 60, 2014, pp. 1476–1487) on suspensions of carbon nanotubes dispersed in a Newtonian epoxy resin. It reproduces well the quadratic dependence of the apparent yield stress on the particle volume fraction $(\unicode[STIX]{x1D70E}_{Y}\propto \unicode[STIX]{x1D719}^{2})$ for average particle aspect ratios of $r=160$ and 1200, while it underpredicts the power-law exponent for $r=80$ (always predicting $\unicode[STIX]{x1D719}^{2}$ behaviour instead of $\unicode[STIX]{x1D719}^{3.2}$). [ABSTRACT FROM PUBLISHER]

Most suspension descriptions used nowadays are based on Jeffery's model or some phenomenological modifications of it that do not take into account size effects: the kinematics and stresses do not involve a micro-mechanical characteristic length and thus, the predicted rheological properties are necessarily independent of rod length. More sophisticated models able to enrich first-gradient kinematics as well as to activate rod-bending mechanisms are needed, in particular to explain the mild elasticity observed experimentally. In this paper we propose a second-gradient theory for dilute suspensions of flexible rods in a Newtonian fluid that is indeed able to activate rod bending and predict viscoelastic behaviour. [ABSTRACT FROM AUTHOR]

In this work, the rheo-optical response of multiwalled carbon nanotube (MWCNT) suspensions was analyzed. Dichroism was obtained using a polarization-modulation technique in parallel disks and for the first time for these particles in a Couette flow geometry. MWCNTs were dispersed in a Newtonian epoxy matrix, at different concentrations covering the dilute and semidilute regimes. Measurements of dichroism were performed as functions of shear rate and nanotube concentration. Surprisingly, the ultimate average orientation angle with respect to the flow direction was far from zero degree, even at high Peclet (Pe) numbers in very dilute suspensions. To explain this peculiar behavior, a new model for flexible rods, valid in the dilute regime, is proposed. It is based on the development of Strautins and Latz [Rheol. Acta 46, 1057-1064 (2007)] that considers flexible rods made of beads and connectors. We modified their bending potential that allows only straight rods at equilibrium with a harmonic cosine expression. This simple modification changes drastically the behavior of these flexible particles that exhibit a non-negligible orientation in the vorticity direction under steady state. [ABSTRACT FROM AUTHOR]

To explain the shear-thinning behavior of untreated carbon nanotube (CNT) suspensions in a Newtonian matrix, a new set of rheological equations is developed. The CNTs are modeled as rigid rods dispersed in a Newtonian matrix and the evolution of the system is controlled by hydrodynamic and rod-rod interactions. The particle-particle interactions is modeled by a nonlinear lubrication force, function of the relative velocity at the contact point, and weighted by the contact probability. The stress tensor is calculated from the known fourth-order orientation tensor and a new fourth-order interaction tensor. The Fokker-Planck equation is numerically solved for steady simple shear flows using a finite volume method. The model predictions show a good agreement with the steady shear data of CNTs dispersed in a Newtonian epoxy matrix as well as for suspensions of glass fibers in polybutene,1 demonstrating its ability to describe the behavior of micro- and nanoscale particle suspensions. © 2013 American Institute of Chemical Engineers AIChE J, 60: 1476-1487, 2014 [ABSTRACT FROM AUTHOR]

A set of rheological equations is developed for semiconcentrated suspensions of rigid fibers in a Newtonian fluid taking into account hydrodynamic and fiber-fiber interactions. The force generated by the fiber interactions is modeled using a linear hydrodynamic friction coefficient proportional to the relative velocity at the contact point, and weighted by the probability for contacts to occur. The equation of evolution of the second-order orientation tensor, containing advection and diffusion terms due to fiber interactions, is derived to predict fiber orientation under flow. The well known fourth-order orientation tensor, related to the hydrodynamic contribution, and a newly proposed fourth-order interaction tensor are used to evaluate the total stress in the composite. A linear and a quadratic closure approximation are proposed to describe the fourth-order interaction tensor. Results are presented using the quadratic form, which is found to be more accurate than the linear one. The model is shown to describe well simple shear data of suspensions of glass fibers in a Newtonian polybutene. Moreover, fiber orientation and the average number of contacts per fiber are predicted. The newly proposed interaction coefficient varies with fiber orientation, which appears to be realistic. [ABSTRACT FROM AUTHOR]