On the theory of the shear-induced isotropic-to-nematic phase transition of side chain liquid-crystalline polymers

The shear-induced isotropic-to-nematic phase transition of side chain liquid-crystalline polymers is studied theoretically. A modification of the previous models of main-chain liquid crystals to the case of side chain liquid-crystalline polymers is proposed. Orientational and rheological properties of the model are studied in plane-shear flow. Predictions of the present model agree qualitatively with experimental results (Pujolle-Robic, Noirez in Nature 409:167, 2001).     

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.     

Étude numérique du couplage de la convection naturelle avec le rayonnement de surfaces en cavité carrée remplie d'airNumerical study of natural convection-surface radiation coupling in air-filled square cavities

A numerical tool is developed for coupling natural convection in cavities with surface radiation and computations are performed for an air-filled square cavity whose four walls have the same emissivity. Compared to the adiabatic case without radiation, the top wall is cooled, the bottom wall is heated, air flow along the horizontal walls are reinforced and thermal stratification in cavity core is reduced. Detailed analysis shows that net radiative heat flux is linear with ΔT if $\mathrm{\Delta }T?T_0$, which is the case at low Rayleigh number, and that radiative Nusselt number is a linear function of the cavity height. Surface radiation induces an early transition to time-dependent flows: for $?=0.2$ and a cavity height of 0.335 m the critical Rayleigh number is equal to $9.3\times {10}^6$ and the corresponding Hopf bifurcation is supercritical. Furthermore, multiple periodic solutions are observed between $\mathit{Ra}=1.2\times {10}^7$ and $1.3\times {10}^7$. To cite this article: H. Wang et al., C. R. Mecanique 334 (2006).     

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.     

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.     

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.