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Most theoretical fibre suspension models currently used for predicting the flow-induced evolution of microstructure in the processing of reinforced thermoplastics are based on the Jeffery model of dilute suspensions in a Newtonian suspending fluid or phenomenological adaptations of it that account for fibre-fibre interactions. An important assumption of all these models is the Newtonian character of the fluid in which the fibres are suspended. In industrial practice, the considered fluids are in general molten thermoplastics that exhibit a viscoelastic behaviour. Even though few counterparts of the Jeffery theory exist for second-order fluids, they have been rarely considered and, to our knowledge, never taken into account at the macroscopic scale. In this paper, we address the modelling of short fibre suspensions in second-order fluids throughout the different description scales, from microscopic to macroscopic. We propose a simplified modelling framework that allows one to extend to viscoelastic suspending fluids the standard Folgar and Tucker model widely used in industrial simulation software.

Experimental findings and rheological modelling of chemically treated single-wall carbon nanotubes suspended in an epoxy resin were addressed in a recent publication (Ma et al., J Rheol 53:547–573, 2009). The shear-thinning behaviour was successfully modelled by a Fokker-Planck-based orientation model. However, the proposed model failed to describe linear viscoelasticity using a single mode as well as the relaxation after applying a finite step strain. Both experiments revealed a power-law behaviour for the storage and relaxation moduli. In this paper, we show that a single-mode fractional diffusion model is able to predict these experimental observations.

International audience; Recently, Férec et al. (2009a) proposed a model for nondilute rod-like suspensions, where particle interactions are taking into account via a micromechanical approach. The derived governing equation used the well-known second-and fourth-order orientation tensors (a2 and a4) and novel second-and fourth-order interaction tensors (b2 and b4). To completely close the model, it is necessary to express a4, b2, and b4 in terms of a2. This paper gives the general framework to elaborate these new relations. Firstly, approximations for b2 are developed based on linear combinations of a2 and a4. Moreover, a new closure approximation is also derived for b4 , based on the orthotropic fitted closure approach. Unknown parameters are determined by a least-square fitting technique with assumed exact solutions constructed from the probability distribution function (PDF). As numerical solutions for the PDF are difficult to obtain given the nonlinearity of the problem, a combination of steady state solutions is used to generate PDF designed to cover uniformly the entire domain of possible orientations. All these proposed approximations are tested against the particle-based simulations in a variety of flow fields. Improvements of the different approximations are observed, and the couple iORW-CO4P3 gives efficient results.

Commonly isolated carbon nanotubes in suspension have been modelled as a perfectly straight structure. Nevertheless, single-wall carbon nanotubes (SWNTs) contain naturally side-wall defects and, in consequence, natural bent configurations. Hence, a semi-flexile filament model with a natural bent configuration was proposed to represent physically the SWNT structure. This continuous model was discretized as a non-freely jointed multi-bead-rod system with a natural bent configuration. Using a Brownian dynamics algorithm the dynamical mechanical contribution to the linear viscoelastic response of naturally bent SWNTs in dilute suspension was simulated. The dynamics of such system shows the apparition of new relaxation processes at intermediate frequencies characterized mainly by the activation of a mild elasticity. Storage modulus evolution at those intermediate frequencies strongly depends on the flexibility of the system, given by the rigidity constant of the bending potential and the number of constitutive rods.

International audience; Rheological model of fluids involving Brownian relaxation, reptation, diffusion, and scission–recombination processes as relaxation mechanisms is formulated. Numerical solution of a particular example of the model displays the S-shape form of the shear rate versus shear stress curves observed in worm-like micellar solutions.

This paper reports the application of a recently developed filament stretching protocol for the study of the extensional rheology of both treated and untreated carbon nanotubes (CNT) suspended within an epoxy resin. It was experimentally observed that filaments formed by treated and untreated CNT suspensions behaved differently after initial stretching. The filament thinning process of the base epoxy was consistent with a simple Newtonian fluid, whilst the filament of treated CNT suspensions also thinned in a Newtonian way but with an enhanced extensional viscosity. Filaments formed with untreated CNT suspensions behaved in a non-uniform way with local fluctuation in filament diameter, and it was not possible to obtain reliable extensional viscosity data. Irregularity of the untreated CNT filaments was consistent with coupled optical images, where spatial variation in CNT aggregate concentration was observed. In the case of treated CNT suspensions, the enhanced extensional viscosity was modelled in terms of the alignment of CNTs in the stretching direction, and the degree of alignment was subsequently estimated using a simple orientation model.

The development of flow kinematics and fiber orientation distribution from the parabolic velocity profile and isotropic orientation at the channel inlet was computed in multi-disperse suspension flow through a parallel plate channel and their predictions were compared with those of mono- and bi-disperse suspensions. A statistical scheme (orientations of a large number of fibers are evaluated from the solution of the Jeffery equation along the streamlines) was confirmed to be very useful and feasible method to analyze accurately the orientation distribution of fibers in multi-disperse fiber suspension flow as well as mono- and bi-dispersions, instead of direct solutions of the orientation distribution function of fibers or the evolution equation of the orientation tensor which involves a closure equation. It was found that the flow kinematics and the fiber orientation depend completely on both the fiber aspect-ratio and the fiber parameter for multi-disperse suspension when the fiber–fiber and fiber-wall interactions are neglected. Furthermore, the addition of large aspect-ratio fibers as well as an increase in the fiber parameter related to the large aspect-ratio fibers could suppress the complex velocity field and stress distributions which are observed in suspensions containing small aspect-ratio fibers. From a practical point of view, therefore, the mechanical and physical properties of fiber composites should be improved with an increase in the volume fraction of large aspect-ratio fibers.