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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]

Various industries, such as automotive and leisure, show a great interest in foaming thermoplastic polyurethane (TPU) with physical blowing agents. Hence, this study aims to investigate the effects of absorption of carbon dioxide and nitrogen by melt TPU on solubility and interfacial tension. Using a pressure–volume–temperature apparatus for high pressure and temperature combined with a magnetic suspension balance, the solubility of carbon dioxide and nitrogen in thermoplastic polyurethane melt was measured at temperatures from 190 °C to 220 °C and at pressures to 25 MPa. The solubility of both supercritical fluids (SCF) in the TPU melt was then compared with semiempirical data and theoretical values calculated from the Sanchez–Lacombe equations of state (S-L EOS). The surface tension of the TPU/SCF interface was measured using the axisymmetric drop shape analysis profile. It was observed that the dependency of interfacial tension on temperature at high pressures decreases because of a reduction in SCF solubility at high temperatures. The relationship between the interfacial tension and the density difference of polymer-supercritical fluid was also examined using the generalized Macleod's equation. [ABSTRACT FROM AUTHOR]

Following Leal who gave the motion of a slender axisymmetric rod in a second-order fluid, we derived a complete rheological constitutive equation for dilute and semidilute slender rod suspensions in a viscoelastic solvent based on a cell model. Numerical solutions for the Fokker–Planck equation are obtained for simple shear flows at low and large Peclet numbers using a finite volume method, hence avoiding the need for closure approximations. The second normal stress difference coefficient of the solvent plays a non-negligible role in the particle contribution to the stress as well as on the rod orientation dynamics: a spread of the particle orientation in the flow-vorticity plane and an enhancement of the alignment along the vorticity direction are predicted when increasing the second normal stress difference coefficient. Brunn extended the Leal analysis to dumbbells and tri-dumbbells, for which both normal stress difference coefficients have to be considered. The original Pipkin diagram is finally modified to help guide the choice of relevant constitutive equations for particles in viscoelastic fluids. [ABSTRACT FROM AUTHOR]

A model is developed for suspensions of rigid fibers in a non-Newtonian fluid exhibiting a yield stress by taking into account hydrodynamic and fiber–fiber interactions. To be applied to fiber-reinforced viscoplastic fluids such as cementitious pastes or mortars, the matrix behavior is described by a Herschel–Bulkley law. The model is able to predict shear thinning and shear thickening behaviors as well as anisotropic yield stress depending on the fiber orientation. The extra stress term involves structural tensors, where exact analytical solutions have been proposed for an isotropic fiber orientation in simple shear flow. The model predictions show a good agreement with the yield stress values of steel fibers dispersed in kaolin pastes. [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]

Abstract: The probability distribution function for fiber orientation under flow (Fokker–Planck equation) is numerically solved using a finite volume method. Different time and spatial schemes have been tested to reduce considerably the computational time and to cover a wide range of the Peclet (Pe) number. For Pe ≤103, the results are compared with data available in the literature and for Pe ≥103, the numerical schemes are assessed using an analytical solution. Excellent agreement was observed and the method allowed us to describe the evolution of the fourth-order orientation tensor components of fibers in transient simple shear (forward and reverse) flows, and compare with the predictions of an orthotropic closure approximation. In addition, the Folgar–Tucker–Lipscomb (FTL) model was used with no closure approximation to predict the rheological behavior of a short fiber-filled polypropylene in simple shear flow. The accuracy of commonly used closure approximations is discussed, and key aspects of the FTL model that still need to be improved are highlighted in the scope of this work. [Copyright &y& Elsevier]

Abstract: Small and large amplitude oscillatory shear measurements (SAOS and LAOS) were used to investigate the rheological behavior of short glass fibers suspended in polybutene and molten polypropylene. Raw torque and normal force signals obtained from a strain-controlled instrument (ARES rheometer) were digitized using an analog to digital converter (ADC) card to allow more precise data analysis. The fiber concentration did not affect the torque signal in the SAOS mode, except for its magnitude, whereas the normal force signal was too low to be measurable. With increasing strain amplitude, the magnitude of the torque became a function of time. Depending on the applied frequency and strain rate, the stress in the filled polybutene increased with time, whereas for reinforced polypropylene (viscoelastic matrix), the behavior was opposite, i.e. the stress decreased with time. These effects were more pronounced at high fiber content. In addition the primary normal stress differences were no longer negligible at large deformation amplitude and exhibited a non-sinusoidal periodic response. Fast Fourier transform (FFT) analysis was performed and the resulting spectra, along with Lissajous figures of the shear stress and the primary normal stress differences, are explained in terms of fiber orientation. The experimental results for the suspensions in polybutene are well predicted by the Folgar-Tucker-Lipscomb (FTL) model. [Copyright &y& Elsevier]

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]

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]

The motion of an ellipsoidal particle immersed in a flow of a Newtonian fluid was obtained in the pioneering work of Jeffery in 1922. Suspensions of industrial interest usually involve particles with a variety of shapes. Moreover, suspensions composed of rods (a limit case of an ellipsoid) aggregate, leading to clusters with particular shapes that exhibit, when immersed in a flow, an almost rigid motion. In this work, we propose a framework for describing dilute suspensions of rigid particles and derive an expression for calculating the motion of rigid clusters of general shape immersed in a flow of a Newtonian fluid. We show that the cluster’s rotary velocity only depends on a symmetric tensor c with unit trace that can be considered as the appropriate conformation tensor for describing cluster kinematics. [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]

• Modeling of thermo-expandable microcapsules expansion in term of temperature. • Simulation of non-isothermal foaming in thermoplastics during extrusion process. • Die swell and compressible fluid are considered. • Two thermoplastics with different viscositiy produce the same cell size. • Thermoplastic viscosity affects the foaming location and velocity. A numerical simulation for foaming a melted thermoplastic by extrusion process is conducted, where thermo-expandable microcapsules are used as a blowing agent. Firstly, a growth model for an encapsulated bubble is developed to match experimental results. Then, the growth model is used to numerically solve a 2D non-isothermal die-swell problem, making possible to simulate the extrusion foaming process. In particular, the model is able to predict the foaming location. Numerical results are compared with experimental data obtained by optical microscopy observations and density measurements on extruded samples. The effects of thermoplastic melt rheology on foaming and the die swell induced by foaming are also investigated. This simulation helps to estimate process parameters such as extrusion speed and to predict die swell and sample porosity in whole, to finally optimize the industrial process. [ABSTRACT FROM AUTHOR]