A new first-principles approach for the catenary

This paper reports on findings relating to catenaries since the publication in Expositiones Mathematicae of Denzler and Hinz’s pioneering 1999 paper, Catenaria Vera – the True Catenary. New governing differential equations and explicit solutions are derived for the catenary in positive and negative radial potentials with physical constants incorporated in the derivations. In keeping with precedent by Denzler and Hinz, a measure of historical perspective is offered as homage to Gottfried Wilhelm Leibniz, Christiaan Huygens and Johann Bernoulli, the original first-solvers of the catenary.     

Lumineszenzdatierung als Schlüssel zur Vergangenheit

In this article, we describe the basic principles of luminescence dating, for which knowledge and methods of solid state physics and radiochemistry play a major role. The type of dated event – the last heating or daylight exposure – opens up a broad spectrum of applications of this method for periods ranging from 10² up to several 10⁵ years. Through the cooperation of dating specialists with geoscientists and archaeologists, luminescence dating is nowadays an essential tool for addressing problems in Earth‐science and human history.     

Hydrodynamic formation of stable anisotropic structures in Couette flow of dilute suspensionFormation hydrodynamique pour structures anisotropiques stables dans un flux de Couette d'une suspension diluée

The problem of rotary motion of rigid axially symmetric elongated particles in the Couette flow of dilute suspension with anisotropic carrier fluid is solved. It is shown that the stable stationary solutions of the dynamical set of ordinary differential equations describing the particles rotary motion are possible in the case of forming the stationary anisotropy in the carrier fluid of the suspension. It allows us to detect the stationary orientation of suspended particles and formation of stable anisotropic liquid-crystalline structures in the considered suspension under the action of hydrodynamic forces. The study of rheological properties of such a structured suspension shows that it behaves as a viscoelastic quasi-Newtonian anisotropic liquid medium. To cite this article: E.Yu. Taran et al., C. R. Mecanique 332 (2004).     

Méthode d'homogénéisation auto-cohérente en calcul à la ruptureSelf-consistent homogeneization method in yield design

This work is aimed towards determining the macroscopic strength criterion of a heterogeneous material with a random microstructure. We use the self-consistent concept by considering a reference material, which is of same nature as the constituents of the heterogeneous material. We deduce that the estimates of the macroscopic strength domain are the solutions to self-consistent equations and we give their derivation procedure. To cite this article: S. Turgeman, B. Guessab, C. R. Mecanique 330 (2002) 623–626.     

Influence of aspect ratio on the flow above the free end of a surface-mounted finite cylinder

The flow above the free end of a surface-mounted finite-height cylinder was studied in a low-speed wind tunnel using particle image velocimetry (PIV). Velocity measurements were made in vertical and horizontal measurement planes above the free end of finite cylinders of aspect ratios AR = 9, 7, 5 and 3, at a Reynolds number of Re = 4.2 × 10⁴. The relative thickness of the boundary layer on the ground plane was δ/D = 1.7. Flow separating from the leading edge formed a prominent recirculation zone on the free-end surface. The legs of the mean arch vortex contained within the recirculation zone terminate on the free-end surface on either side of the centreline. Separated flow from the leading edge attaches onto the upper surface of the cylinder along a prominent attachment line. Local separation downstream of the leading edge is also induced by the reverse flow and arch vortex circulation within the recirculation zone. As the cylinder aspect ratio is lowered from AR = 9 to AR = 3, the thickness of the recirculation zone increases, the arch vortex centre moves downstream and higher above the free-end surface, the attachment position moves downstream, and the termination points of the arch vortex move upstream. A lowering of the aspect ratio therefore results in accentuated curvature of the arch vortex line. Changes in aspect ratio also influence the vorticity generation in the near-wake region and the shape of the attachment line.     

Impact of a bead on a rotating wall

We study experimentally the impact of a plastic bead on a rotating wall made of steel (velocity Ω; radial position x₀). The results show that the restitution coefficient is directly function of the impact velocity x₀Ω and is invariant by changing frame reference. The influence of the height of release of the particle on its angular velocity after impact is also studied. We observe an increase of the angular velocity with height followed by a saturation. We propose an interpretation for this evolution considering that the particle may roll without sliding during all the impact. This physical feature is not always taken into account in existing models of impact between rigid bodies. To cite this article: F. Rioual et al., C. R. Mecanique 336 (2008).     

Rheological properties of dense granular flows

Recent progresses in understanding the behavior of dense granular flows are presented. After presenting a bulk rheology of granular materials, I focus on the new developments to account for non-local effects, and on ongoing research concerning the surface rheology and the evolution of mechanical properties for heterogeneous systems.     

New rheological developments for reactive processing of poly(ε-caprolactone)

This short review aims to show how an integrated activity on reactive processing have been developed these last years in our laboratory. We can say that the originality of this approach is based on combining developments in chemistry, in line instrumentation, and rheology aspects. Our rheological works can be divided into four important contributions: rheo-physics, rheo-chemistry, rheo-mixing and rheo-processing. These different parts are illustrated from the ε-caprolactone polymerisation in bulk and dispersed media. Rheo-physics studies allowed us to calculate the molecular weight distribution and chain structures of in situ polymerised poly(ε-caprolactone) samples. From rheo-chemistry works, we are now able to predict the variation of the complex shear modulus versus the extent of the polymerisation. The developments of new rheological tools such as rheo-mixer enable us to investigate complex mixing situations encountered in reactive polymer blends and formulations. Lastly, a rheo-processing approach based on the in-line measurement of the viscosity in a slit rheometer at the die exit of the extruder allows us to envisage its application to the experimental control of the reactive processing in extruder. To cite this article: P. Cassagnau et al., C. R. Chimie 9 (2006).