Changements de structure provoqués par l'écoulement

Résumé De même que la structure conditionne les propriétés rhéologiques, l'état d'écoulement d'un système peut être un facteur déterminant de sa structure par suite des réarrangements moléculaires qu'il provoque. On étudie le cas d'un liquide pur à fortes interactions intermoléculaires et celui des suspensions colloïdales et solutions macromoléculaires. Les calculs sont développés dans des cas types où l'écoulement entraîne des changements de phase ou des variations de l'état d'agrégation. L'étude rhéologique ou rhéooptique de tels systèmes permet la détermination expérimentale des énergies d'interaction intermoléculaires. On en donne des exemples.

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Zusammenfassung Ebenso wie die Struktur die Theologischen Eigenschaften beeinflußt, kann der Fließzustand eines Systems ein maßgebender Faktor seiner Struktur als Folge der molekularen Umordnung, die er erzeugt, sein. Es wird der Fall einer reinen Flüssigkeit mit starken intermolekularen Wechselwirkungen sowie der kolloiden Suspensionen und makromolekularen Lösungen untersucht. Die Rechnungen sind für typische Fälle durchgeführt, bei denen das Fließen Phasenänderungen und Änderungen des Aggregatzustandes hervorruft. Die rheologische und rheooptische Untersuchungen solcher Systeme erlaubt eine experimentelle Bestimmung der zwischenmolekularen Wechselwirkungsenergien, wie an Beispielen gezeigt wird.

     

Analyse mathématique de l'équation de Galbrun en écoulement uniforme

We consider Galbrun's equation, used in linear aeroacoustics. For a simple case (rigid duct with uniform flow) in the time harmonic regime, we show that an approach based on a regularized variational formulation of the problem ensures the convergence of a nodal finite-element method.     

Vérification expérimentale de la relation de réciprocité d'Onsager pour l'électro-osmose et l'électro-filtration dans une argile naturelle

This Note is devoted to the experimental verification of the Onsager's reciprocal relations in the particular case of electro-osmosis and electro-filtration. A special set up has been designed to carry out the measurements of both the electro-osmotic permeability and the streaming potential. This has been performed by using a natural material i.e., saturated kaolinite. To cite this article: K. Beddiar et al., C. R. Mecanique 330 (2002) 893–898.     

Étude thermodynamique de l'évolution sous chargement dynamique de structures délaminées

In order to study the evolution of damage in a delaminated structure, the assemblage of plates is considered under dynamic loading. Using a general result of the thermodynamic coupling approach, with the Hamiltonian formulation in the general case, the energy release rate associated with the propagation of the delamination is presented as a heat source.     

Taux de restitution de l'énergie pour une poutre courbe mince

Let a thin two-dimensional domain be in a plane strains state. It is made of two materials separated by a regular curvilinear interface along of which a crack is assumed to propagate. The expression of the energy release rate is derived in local coordinates using the so-called θ-method. It is shown that there are complementary terms related to the derivation of the local metric.     

Théories multicouches pour l'écoulement de Falkner–Skan

In this paper, for the case of Falkner–Skan flow, we investigate indentations which can provoke boundary layer separation, without deeply modifying the base flow. Using the asymptotic method of matched expansions, we show that these perturbations lead to double or triple deck structures depending on the size of the indentation.     

Fonction de distribution pour les gaz polyatomiques dans la couche de Knudsen. Solution approchée de l'équation de Boltzmann

Polyatomic gases in strong non equilibrium vibrational state are studied in the Knudsen layer. A kinetic equation is derived from the Boltzmann equation for a stationary gas without macroscopic velocity. The simplification are basically deduced from the order of magnitude of adimmensional gradient terms. The approximate solution of this equation is deduced from a recurrent algorithm on the adimensional space variable power. Furthermore, the boundary condition allows us to obtain density and temperature jumps at the wall.     

Impact non-pénétrant sur le thorax : une contribution à l'étude de la propagation des ondes

The stress wave generated by a nonpenetrating impact on the thorax is likely to cause severe injury to the lung. Theoretical studies are necessary to help the understanding of injury mechanisms. Within the framework of elastodynamics, we study the transmission of a wave at the interface between two weakly coupled semi-infinite media representing the thoracic wall and the lung. By using an appropriate method, we describe the distribution of energy carried by the shear and pressure waves in the medium representing the lung. These results should contribute to a better interpretation of the experimental results.     

Homogénéisation d'équations et d'inéquations à paramètres oscillants. Application à l'étude d'écoulement de faible épaisseur en régime transitoire

Double scale homogenization is used to average stationary equation or inequalities in which both highly oscillating variables and parameters appear. We demonstrate how the limit is obtained using a two-stage procedure , firstly by carrying out a classical homogenization process by freezing the oscillating parameter, then by averaging the result with respect to this parameter. These results allow us to average the pressure for a newtonian fluid in a narrow gap between two rough unstationnary surfaces.     

Contrôle par jet pulsé de l'écoulement dans un divergent court à grand angle

This experimental study investigates the control of flow in a short diffuser with a 2×45° divergence angle, using wall synthetic jets. Measurements are made by particle image velocimetry. Velocity profiles, velocity fields, and vorticity maps show that the flow, initially separated as a free jet, undergoes a global excitation which creates periodic oscillating structures producing large fluid motions in the vicinity of the wall. This results in an increased mixing of the primary separated jet with the surrounding fluid.     

Comportement thermomécanique de l'argile de Boom

Special attention has been recently paid on temperature effects on the behaviour of deep saturated clays, in relation with nuclear deep waste storage. However, few experimental data are presently available, and existing constitutive models need to be completed. This note is aimed at completing, both experimentally and theoretically, the understanding of the effects of the overconsolidation ratio on the thermal volume changes of Boom clay (Belgium). The experimental data obtained here are in a good agreement with existing data. As a complement to existing data, they are used to develop a new elastoplastic model. The adoption of a second coupled plastic mechanism provides good simulations on a complex thermo-mechanical path.     

Mécanique de la rupture fragile en présence de plasticité : définition d'un taux de restitution d'énergie

This study aims at defining an energetic parameter which characterises progressive crack growth in a brittle elastoplastic medium. First, Francfort and Marigo's elastic fracture theory, based on a minimum energy principle, is recalled. Then, a link with the framework of generalised standard materials is exhibited and allows to introduce the new energetic contributions due to plasticity.     

Inversion d'un écoulement plan de Stokes – application à l'écoulement à débit moyen nul entre deux plans parallèles

We present the interest and some characteristics of the inverse transformation of a 2D Stokes flow. This method is applied to the cellular flow between two parallel plates induced by a rotating cylinder to obtain the flow around two circular cylinders in contact placed in the centre of a rotating circular cylinder.     

Interprétation de la double structure observée dans l'onde de détonation du nitrométhane gazeux

Calculations of the reaction zone of the detonation of gaseous nitromethane, either pure or diluted with oxygen, in the range of equivalence ratio Φ between 0.1 and 1.75, show that for 1.75⩾Φ⩾1.3 the chemical energy is released in two main successive reaction steps characterized by very different induction times. These results corroborate the experimental observations of two levels of cellular structures in the same range of equivalence ratios. To our knowledge this work is the first which deals with the problem of nonmonotonous chemical energy release behind the leading shock of a detonation wave.     

Modèles discrets de structures tissées : Analyse de stabilité et de drapé

A discrete model of a woven fabric structure is established, whereby nodes endowed with a mass and a rotational rigidity are connected by rigid bars to form a two-dimensional truss. The set of four bars that delineate a quadrilateral area is further endowed with a torsion deformation mode. The kinematics of the truss reproduces the large rotations and displacements encountered for real tissues. The equilibrium shape of such a structure is obtained as the minimum of its total potential energy versus the whole set of kinematic translational and rotational variables, accounting for eventual kinematic constraints due to contact with a rigid surface by the Lagrange multipliers method. A stability analysis is conducted, and the potentiality of the model is illustrated by fabric draping simulations. To cite this article: B. Ben Boubaker et al., C. R. Mecanique 330 (2002) 871–877.     

Calcul numérique de la déformation mécanique d'un modèle de cellule endothéliale

Mechanical forces influence endothelial cell's (EC) morphology and functions. In this work it was proposed a numerical analysis of steady laminar flows near a modeled monolayer of elastic ECs in order to determine the local distributions of mechanical forces on the surface and inside of the cell. The numerical results showed that the flow induced mechanical stresses led to a cell deformation and that the distributions of these stresses were not uniform on cell surface. It will be interesting to study eventual correlations between the distributions of biological receptors (cytoskeleton, adhesion molecules, etc.) and that of the non-uniform mechanical forces.     

Étude numérique des instabilités de la phase fluide et de l'interface de solidification en croissance dirigée horizontale

Convective instabilities of low Prandtl number fluids are subject to various studies. The purpose here is an extension to hydrodynamic transitions in the fluid phase with a free or rigid surface under phase change and to construct the corresponding bifurcation diagram. Investigations interesting the process control by using the latent heat and the solid/liquid thermal conductivity difference are considered. The solution methodology is based on a front localisation approach showing a very good ability to describe convection regimes coupled to the phase change transition in the case of vertical solidification with confinement. To cite this article: E.A. Semma et al., C. R. Mecanique 331 (2003).