Solutions of the Time-Harmonic Wave Equation in Periodic Waveguides: Asymptotic Behaviour and Radiation Condition

In this paper, we give the expression and the asymptotic behaviour of the physical solution of a time harmonic wave equation set in a periodic waveguide. This enables us to define a radiation condition and show well-posedness of the Helmholtz equation set in a periodic waveguide.     

A Reissner-type plate theory for monoclinic material derived by extending the uniform-approximation technique by orthogonal tensor decompositions of <Emphasis Type="Italic">n</Emphasis>th-order gradients

The uniform-approximation approach is an a-priori assumption free structured approach for the derivation of hierarchies of lower-dimensional theories for thin structures with increasing approximation accuracy. In this publication, we derive a second-order consistent plate theory for monoclinic material and investigate several theories that arise from the original theory by a pseudo-reduction approach which aims to reduce the number of PDEs that are to solve. A one-variable model that governs only the interior solution is presented and, in addition, an extended two-variable model that also covers edge effects. Since the second introduced variable is a rotation of a vector field, we have to uniquely identify the rotation dependent parts in general gradients of the vector field, which is resolved by the introduction of an orthogonal decomposition. The final two-variable model is equivalent to the Reissner–Mindlin theory for the special case of isotropic material, whereas the one-variable model is equivalent to the first Reissner PDE. In contrast to this special case, the two-variable model is a coupled system of two PDEs for general monoclinic material.     

Model equations for the Eiffel Tower profile: historical perspective and new results

Model equations for the shape of the Eiffel Tower are investigated. One model purported to be based on Eiffel's writing does not give a tower with the correct curvature. A second popular model not connected with Eiffel's writings provides a fair approximation to the tower's skyline profile of 29 contiguous panels. Reported here is a third model derived from Eiffel's concern about wind loads on the tower, as documented in his communication to the French Civil Engineering Society on 30 March 1885. The result is a nonlinear, integro-differential equation which is solved to yield an exponential tower profile. It is further verified that, as Eiffel wrote, “in reality the curve exterior of the tower reproduces, at a determined scale, the same curve of the moments produced by the wind”. An analysis of the actual tower profile shows that it is composed of two piecewise continuous exponentials with different growth rates. This is explained by specific safety factors for wind loading that Eiffel & Company incorporated in the design of the free-standing tower. To cite this article: P. Weidman, I. Pinelis, C. R. Mecanique 332 (2004).     

Competitive Absorption of Polar and Non-Polar Liquids into Latex Bound Porous Structures of Fine Ground Calcium Carbonate

Fine calcium carbonate is frequently used as coating pigment, e.g. in paints, paper and board. Emulsion polymer latex provides a typical binder incorporated in such coatings. Exposure of the resulting porous structure to liquid, depending on latex concentration level, results in ab- and adsorption as the liquid is drawn into the structure by capillarity and the nature of the relative surface chemistry of the pores. Previous work has shown that typical coating structures act to separate oil components according to their surface energy characteristics and solubility index in respect to pigment surface and intra-latex diffusion. This study considers water and alkane (hexadecane) as model liquids. Absorption rate into compressed tablets of ground calcium carbonate is observed with and without the presence of latex. Polyacrylate dispersant used in manufacture renders the pigment surface both hydrophilic and hygroscopic and, therefore, controls the differential dynamic wetting characteristics of the porous structure for either polar or non-polar liquid. In competition with hexadecane saturating the pore structure of a latex-free sample, polar water is seen to displace the non-polar liquid instantaneously, causing disintegration of the packed porous structure. In the presence of latex binder, however, the structurally destructive pressure this creates is contained, and retardation of the polar water is observed. The required pre-wetting action of water vapour diffusion on the polyacrylate pigment surface is considered to be an integral part of the successful competition between oil and water in the offset printing process, as non-polar oil absorbs steadily into a water pre-saturated structure.     

Cellular-level near-wall unsteadiness of high-hematocrit erythrocyte flow using confocal μPIV

In hemodynamics, the inherent intermittency of two-phase cellular-level flow has received little attention. Unsteadiness is reported and quantified for the first time in the literature using a combination of fluorescent dye labeling, time-resolved scanning confocal microscopy, and micro-particle image velocimetry (μPIV). The near-wall red blood cell (RBC) motion of physiologic high-hematocrit blood in a rectangular microchannel was investigated under pressure-driven flow. Intermittent flow was associated with (1) the stretching of RBCs as they passed through RBC clusters with twisting motions; (2) external flow through local obstacles; and (3) transitionary rouleaux formations. Velocity profiles are presented for these cases. Unsteady flow clustered in local regions. Extra-cellular fluid flow generated by individual RBCs was examined using submicron fluorescent microspheres. The capabilities of confocal μPIV post-processing were verified using synthetic raw PIV data for validation. Cellular interactions and oscillating velocity profiles are presented, and 3D data are made available for computational model validation.     

The constitutive equations of finite strain poroelasticity in the light of a micro-macro approach

After recalling the constitutive equations of finite strain poroelasticity formulated at the macroscopic level, we adopt a microscopic point of view which consists of describing the fluid-saturated porous medium at a space scale on which the fluid and solid phases are geometrically distinct. The constitutive equations of poroelasticity are recovered from the analysis conducted on a representative elementary volume of porous material open to fluid mass exchange. The procedure relies upon the solution of a boundary value problem defined on the solid domain of the representative volume undergoing large elastic strains. The macroscopic potential, computed as the integral of the free energy density over the solid domain, is shown to depend on the macroscopic deformation gradient and the porous space volume as relevant variables. The corresponding stress-type variables obtained through the differentiation of this potential turn out to be the macroscopic Boussinesq stress tensor and the pore pressure. Furthermore, such a procedure makes it possible to establish the necessary and sufficient conditions to ensure the validity of an ‘effective stress’ formulation of the constitutive equations of finite strain poroelasticity. Such conditions are notably satisfied in the important case of an incompressible solid matrix.