Emmanuelle Abisset-Chavanne

Kinetic Theory Microstructure Modeling in Concentrated Suspensions

When suspensions involving rigid rods become too concentrated, standard dilute theories fail to describe their behavior. Rich microstructures involving complex clusters are observed, and no model allows describing its kinematics and rheological effects. In previous works the authors propose a first attempt to describe such clusters from a micromechanical model, but neither its validity nor the rheological effects were addressed. Later, authors applied this model for fitting the rheological measurements in concentrated suspensions of carbon nanotubes (CNTs) by assuming a rheo-thinning behavior at the constitutive law level. However, three major issues were never addressed until now: (i) the validation of the micromechanical model by direct numerical simulation; (ii) the establishment of a general enough multi-scale kinetic theory description, taking into account interaction, diffusion and elastic effects; and (iii) proposing a numerical technique able to solve the kinetic theory description. This paper focuses on these three major issues, proving the validity of the micromechanical model, establishing a multi-scale kinetic theory description and, then, solving it by using an advanced and efficient separated representation of the cluster distribution function. These three aspects, never until now addressed in the past, constitute the main originality and the major contribution of the present paper.

On the use of interaction tensors to describe and predict rod interactions in rod suspensions

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.

A multi-scale description of orientation in simple shear flows of confined rod suspensions

The multi-scale description of dilute or semi-dilute suspensions involving rods has been successfully accomplished and applied in many scenarios of industrial interest. Many processes involve, however, the flow of rod suspensions in very narrow gaps whose thickness is much smaller than the rod length. In these conditions, the evolution of rod orientation is expected to be affected by confinement effects. In the present work, we propose a multi-scale description of rod orientation in confined conditions and simple shear flows.

Direct simulation of concentrated fiber suspensions subjected to bending effects

When fiber suspensions become concentrated, standard mesoscale theories do not allow a precise description of the fine physics involved at the microscopic level. Thus one way of studying the kinematics and the rheological effects of such suspensions is to make a direct numerical simulation (or DNS for abbreviation). In previous works authors proposed DNS for these types of suspensions. However when it was carried out the elasticity associated with fibers was not introduced in the suspensions; fibers were considered purely rigid and free of bending when they were subjected to interaction forces. In this work a DNS of fiber suspensions in transient and steady shear flows is presented. The suspensions are considered along with interactions between fibers and the statistical evolutions of a population of fibers (such as orientation components and number of interactions between fibers) have been described. Then in the frame of a beam theory approach, the elasticity of the suspensions is introduced by considering that the forces acting of each fiber lead to the bending of the fibers. Thus this bending results in a physical elastic behavior illustrated quantitatively by an elastic energy stored within the suspensions. These added aspects on the DNS of concentrated fiber suspensions constitute the main originality of this paper.

Orientation kinematics of short fibres in a second-order viscoelastic fluid

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.

Fractional modelling of functionalized CNT suspensions

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.

Towards a kinetic theory description of electrical conduction in perfectly dispersed CNT nanocomposites

Nanocomposites composed of carbon nanotubes – CNTs – in a polymer matrix exhibit a significant enhancement of electrical conductivity, mechanical and thermal properties [COL 06, XU 06]. Due to the large length to diameter aspect ratios (from 100 to 10,000), they create conducting networks at low volume fractions [OUN 03].

Fluid-Long Fiber Interaction Based on a Second Gradient Theory

Most suspension descriptions nowadays employed are based on the Jefferys model andsome phenomenological adaptations of it that do not take into account size effects, that is, the kinematicsand stresses do not introduce a micro-mechanical characteristic length and thus, the rheologicalproperties become independent of the rod length. New models able to enrich first gradient kinematicsas well as to activate rod-bending mechanisms (needed for explaining the mild elasticity experimentallynoticed) are needed. In this paper we propose a second gradient description able to activate rods bending.

On the multi‑scale description of electrical conducting suspensions involving perfectly dispersed rods

Nanocomposites allow for a significant enhancement of functional properties, in particular electrical conduction. In order to optimize materials and parts, predictive models are required to evaluate particle distribution and orientation. Both are key parameters in order to evaluate percolation and the resulting electrical networks. Many forming processes involve flowing suspensions for which the final particle orientation could be controlled by means of the flow and the electric field. In view of the multi-scale character of the problem, detailed descriptions are defined at the microscopic scale and then coarsened to be applied efficiently in process simulation at the macroscopic scale. The first part of this work revisits the different modeling approaches throughout the different description scales. Then, modeling of particle contacts is addressed as they determine the final functional properties, in particular electrical conduction. Different descriptors of rod contacts are proposed and analyzed. Numerical results are discussed, in particular to evaluate the impact of closure approximations needed to derive a macroscopic description.

Two-Scales Kinetic Theory Model of Short-Fibers Aggregates

This paper proposes a first attempt to define a two scales kinetic theory to describe concentrated suspensions involving short fibers, nano-fibers or nanotubes. In this case, fiber-fiber interactions can not be neglected and rich microstructures issued from these interactions can be observed, involving a diversity of fibers clusters or aggregates with complex kinematics, and different sizes and shapes. These clusters can interact to create larger clusters and also break because the flow induced hydrodynamic forces. In this paper we propose a double-scale model to describe such microstructure: at the finest scale we study the cluster kinematic based on the behaviour of the rods that constitute it, at a coarser scale, we use clusters distribution to derive the effect of the clusters presence on the suspensions properties.