This work is focused on shear thinning behavior of **suspensions** of rigid non-Brownian fibers dispersed in a Newtonian liquid. The work consists in 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 pseudo-plastic 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 of 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 nano-sized CNT particles than between micron-sized PA fibers. A theoretical model considering the coexistence of transient aggregates with free non- aggregated 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**.

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viscosity reported here is actually the apparent viscosity that is the ratio of the shear stress at the rim to the shear rate the rim and not the true viscosity that should have been obtained by deconvoluting the data with various shear stress and rates at the rim. Nevertheless, it clearly appears that **fiber** **suspensions** are shear-thinning when the **fiber** concentration is high enough. The higher the **fiber** concentration and aspect ratio, the more pronounced is the shear-thinning behaviour (see, for instance, [? ]). Such a shear thinning behaviour has often been reported [? ? ? ? ? ] whereas its origin has not received any clear explanation. Most models either theoretical [? ? ] or numerical [? ? ? ] do not report such a shear-thinning behaviour because the eﬀect of short-range hydrodynamic forces and of direct mechanical contacts that are all supposed to be proportional to the shear rate, leading to a linear scaling of the shear stress with the shear rate. Shear thinning can only occur if a characteristic time diﬀerent from 1/ ˙γ is involved in the dynamics of the suspension. In particular, this is the case if the contacts are adhesive or if the friction is not Coulombic (i.e. a non-linear frictional law). The ratio of the characteristic adhesive force F to the characteristic hydrodynamic force can be evaluated [? ]:

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aggregates. Optical microscopy observations [Fig. 1b] revealed a relatively large quantity of these structures in **fiber** **suspensions**, compared to **suspensions** of spherical particles. This could explain an enhanced viscous response of the **fiber** **suspensions**. Of course, the variety of the intricate structures observed in **fiber** **suspensions** could generate a large spectrum of relaxation times, not accounted in our theory. However, our single-relaxation time model is the first necessary step to the understanding of the nonlinear viscoelastic response of magnetic **fiber** **suspensions**. Note that at large oscillation amplitudes, the motion of pivoting and bridging aggregates can be restricted by the neighboring aggregates, so that they could progressively stick to each other and form thick clusters with a reduced mobility. This could cause irreversible changes of the suspension structure provided that the Brownian motion is absent. Nevertheless, our experiments with increasing and decreasing stress ramps did not reveal a significant hysteresis of the shear moduli. This indicates that the structure can be efficiently reformed by the shear flow, at least in the short time scale, or irreversible transformations might have occurred at longer times. Note finally that the chains of different length are expected to oscillate out-of-phase relative to each other. So, the hydrodynamic screening effects, not accounted in our theory, should be more significant than in the case of a steady shear flow, for which the chains are considered to be more or less parallel to each other [12]. A detailed investigation into these points will be conducted in future.

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attributed to the failure of the **fiber** network at a critical strain value. Another theoretical model for the calculations of the static yield stress and the storage modulus of magnetic **fiber** **suspensions** was proposed by de Vicente et al. (2009). These authors considered affine displacement of fibers under a strain applied, and the yield stress was calculated via the magnetic dipolar forces between fibers, which must be overcome in order to separate the particles. These theories predicted successfully the static yield stress at high magnetic fields but were not able to predict the flow curve of the suspension above the yield stress. The effect of the shear rate on the rheology of magnetic **fiber** **suspensions** was always modeled by a pure Bingham regime without consideration of an intermediate regime at low shear rate, which comes from viscous dissipation around elongated aggregates before their first rupture.

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Received: 3 October 2016; Accepted: 15 November 2016; Published: 30 November 2016
Abstract: Fibers are widely used in different industrial processes, for example in paper manufacturing
or lost circulation problems in the oil industry. Recently, interest towards the use of fibers at the microscale has grown, driven by research in bio-medical applications or drug delivery systems. Microfluidic systems are not only directly relevant for lab-on-chip applications, but have also proven to be good model systems to tackle fundamental questions about the flow of **fiber** **suspensions**. It has therefore become necessary to provide **fiber**-like particles with an excellent control of their properties. We present here two complementary in situ methods to fabricate controlled micro-fibers allowing for an embedded fabrication and flow-on-a-chip platform. The first one, based on a photo-lithography principle, can be used to make isolated fibers and dilute **fiber** **suspensions** at specific locations of interest inside a microchannel. The self-assembly property of super-paramagnetic colloids is the principle of the second fabrication method, which enables the fabrication of concentrated **suspensions** of more flexible fibers. We propose a flow gallery with several examples of **fiber** flow illustrating the two methods’ capabilities and a range of recent laminar flow results.

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Received: 3 October 2016; Accepted: 15 November 2016; Published: 30 November 2016
Abstract: Fibers are widely used in different industrial processes, for example in paper manufacturing
or lost circulation problems in the oil industry. Recently, interest towards the use of fibers at the microscale has grown, driven by research in bio-medical applications or drug delivery systems. Microfluidic systems are not only directly relevant for lab-on-chip applications, but have also proven to be good model systems to tackle fundamental questions about the flow of **fiber** **suspensions**. It has therefore become necessary to provide **fiber**-like particles with an excellent control of their properties. We present here two complementary in situ methods to fabricate controlled micro-fibers allowing for an embedded fabrication and flow-on-a-chip platform. The first one, based on a photo-lithography principle, can be used to make isolated fibers and dilute **fiber** **suspensions** at specific locations of interest inside a microchannel. The self-assembly property of super-paramagnetic colloids is the principle of the second fabrication method, which enables the fabrication of concentrated **suspensions** of more flexible fibers. We propose a flow gallery with several examples of **fiber** flow illustrating the two methods’ capabilities and a range of recent laminar flow results.

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When these calibrated nominal models are unable to reproduce experimental findings, some ad hoc terms are usually added, being then calibrated accordingly (e.g., diffusion term reflecting **fiber** interactions).
Thus, data was traditionally employed for calibrating models derived from physical considerations. However, many times those models failed to address experimental findings even when they were finely calibrated. It is the case of models describing intense **fiber** interactions in semi-concentrated and concentrated **fiber** **suspensions**. This issue motivated numerous works referred to later, and remains even today not totally solved.

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of friction between them, their use in MR **suspensions** could enhance significantly the MR effect [López-López et al. (2007)]. Furthermore, an interesting rheological behavior is expected for such magnetic **fiber** **suspensions**, combining the behaviors observed in nonmagnetic **fiber** **suspensions** and in conventional MR **suspensions**. Some experimental rheological data on the rheology of elongated particle **suspensions** that support this statement are reported in the papers by López-López et al. (2007), Kuzhir et al. (2007), Bell et al. (2008) and Ngatu et al. (2008). A detailed experimental investigation on the shear rheology of magnetic **fiber** **suspensions**, including the concentration dependence of the yield stress and observations of the suspension structures under applied magnetic field, is presented in the companion paper. A two- to three-time increase in the yield stress of magnetic **fiber** **suspensions** compared to **suspensions** of spherical magnetic particles was found. However, no theoretical model explaining this increase has been reported. In the present paper, we introduce the first microstructural models for magnetic **fiber** **suspensions** and explain the enhanced magnetorheological response of these **suspensions** in terms of interfiber solid friction. Our theory covers the quasi-static regime of the shear deformation (before the flow onset) and combines the features of the point-wise interaction theory developed by Toll and Manson (1994) for classical **fiber** **suspensions** and the features of the column structure and zigzag structure models for classical MR **suspensions** [Bossis et al. (1997); Volkova (1998)].

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Eprints ID : 13541
To cite this version : Nguyen, Tien-Cuong and Anne-Archard, Dominique and Coma, Véronique and Pichavant, Frédérique and Cameleyre, Xavier and Lombard, Eric and To, Kim Anh and Fillaudeau, Luc Investigation of hydrolysis of lignocellulosic **fiber** **suspensions** with in-situ and ex-situ multi-scale physical

at low **fiber** concentration (0.1 vol.%), each **fiber** seems to have at least a few contact points
with the neighboring ones. It can also be observed that individual fibers are gathered together
in aggregates, even though, as mentioned in section II, the **suspensions** were carefully
dispersed right before the observations. Such aggregation in the absence of magnetic field

School of Biotechnology and Food Technology, Hanoi University of Science and Technology, Hanoï, VIET-NAM
1. INTRODUCTION
Lignocellulose biomass is one of the most abundant renewable resources and certainly one of the least expensive. It was considered as a glucose source for obtain energetic or chemical molecules by bioconversion. This enzymatic conversion was so complicate therefor a better scientific understanding and, ultimately, good technical control of these critical biocatalytic reactions, which involve complex matrices at high solid contents, is currently a major challenge if biorefining operations are to become commonplace. Amongst the main parameters to be studied, the rheological behaviour of the hydrolysis suspension and the fibre particle size, stand out as a major determinants of process efficiency and determine equipment to be used and the strategies applied. Rheological behaviour of fibre **suspensions** is usually described by an apparent yield stress, a shear viscosity (Hershel-Buckley or Bingham models) and elasticity. During biological hydrolysis, the apparent viscosity of **suspensions** decreases in parallel with a decrease of particle size (Nguyen et al., 2013). This study focuses on the characterisation of cellulose **suspensions** (Microcrystalline cellulose, Whatman paper and extruded paper pulp) during enzymatic hydrolysis using in-situ and ex-situ physical analysis. The complex relationships between fibre structure, degradation, chemical composition and rheological behaviour was scrutinised.

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• The driven cavity flow problem.
Finally, we consider the complex flow generated in a driven cavity that involves a short **fiber** suspension characterized by the same material parameters that in the pre- vious tests. The velocity is prescribed on the domain boundary according to: v(x = 0, y) = 0, v(x = 1, y) = 0, v(x, y = 0) = 0 and v(x, y = 1) = (16v max x 2 (1 − x) 2 , 0). The velocity field is then solved by assuming a Newtonian behavior and by applying a standard mixed finite element formulation where the velocity and pressure approx- imations verify the LBB stability condition. The Fokker-Planck equation governing the evolution of the **fiber** orientation distribution function is then solved along some closed streamlines, where the periodicity condition of that distribution function was imposed as described in Ammar and Chinesta [3]. From the computed orientation distribution function, the characteristic modes are extracted by using the technique previously described based on the application of the Karhunen-Lo`eve decomposition, allowing to fit the empirical snapshot natural closure strategy previously introduced. Now, the evolution equation associated with the second order orientation tensor is solved by assuming different closure relations: linear, quadratic, hybrid, natural and the empirical natural one.

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L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r]

The passage from the governing equations of Stokesian dynamics of N fibers to kinetic equations consists of, first, writing the Liouville equation that corresponds to the time evolution [r]

The passage from the governing equations of Stokesian dynamics of N ﬁbers to kinetic equations consists of, ﬁrst, writing the Liouville equation that corresponds to the time evolution eq[r]

Results for ﬁber **suspensions** and two choices of microstructural state variables.
Given a microstructural equation there are, in general, inﬁnitely many corre- sponding to it formulas for the extra stress tensor that look very diﬀerently but are equivalent in the sense that they all imply the same predicted stresses. By a predicted stress we mean the stress obtained by evaluating the expression for the stress tensor at solutions to the microstructural equation. Predicted stresses are the stresses measured in rheological observations. The reason why there are, in general, inﬁnitely many equivalent formulas for the extra stress tensor is that there are, in general, inﬁnitely many partial solutions to the microstructural equation. Let us see the process of getting solution to the microstructural equa- tion as a gradual process in which the space in which the solutions are searched is being gradually restricted. Partial solutions are, in our terminology, the mi- crostructural state variables restricted to such submanifolds. From the physical point of view, the gradual process of restrictions leading to partial solutions can be interpreted as the process of a descend to more macroscopic (i.e. less detailed) levels of description. The submanifolds are also called closures (see more in Section 2.4 and in Grmela (2010)).

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Deux types de matière organique dissoute ont été utilisés, la première provient d'eau prélevée dans le fleuve du Rhône (R124, mission Mai 1992), et la seconde provient d'eau prélevée e[r]

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L’objet de cet article est de présenter les avantages et les limitations de la spectroscopie acoustique pour l’analyse de systèmes dispersés denses de particules de taille micronique ou colloïdale. L’étude expérimentale, menée sur deux matériaux différents, est basée sur la mesure de l’atténuation acoustique d’une onde ultrasonore à différentes fréquences à travers la suspension. Dans le cas de **suspensions** denses de calcite de quelques dizaines de microns, l’exploitation des spectres d’atténuation acoustique permet d’accéder aisément à la distribution de taille des particules en suspension. L’utilisation d’une plage de fréquence réduite peut être envisagée pour réduire le temps d’analyse sans limiter pour autant la précision des résultats. Au contraire, les interactions particulaires existant au sein de **suspensions** denses de silice colloidale perturbent la réponse acoustique du milieu dispersé et ne permettent pas une exploitation directe des spectres d’atténuation. Des méthodes de correction sont proposées pour parvenir à une détermination correcte des distributions de taille. Enfin, en se fondant sur des mesures effectuées avec des mélanges de produits, l’utilisation de la spectroscopie acoustique pour caractériser les propriétés de **suspensions** de particules polydisperses est discutée.

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moderate to high volume fractions ( φ > 0.1). This constitutes a significant improvement compared to current statistical models, either arising from two-fluid modeling or kinetic theory of granular media, and sheds light on the nature of pseudoturbulence in concentrated **suspensions** and in particular on the role of concentration fluctuations. Future work should focus on validating the model over different ranges of Reynolds number and density ratio. Furthermore, the modeling of diffusion mechanisms in such systems should be revisited in light of the proposed paradigm.

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