A phenomenological model of electrorheological fluids

The fundamental assumption of the paper is that the extra stress tensor src="/content/njf80kprf62xtbvd/xxlarge964.gif" alt="tau" align="BASELINE" BORDER="0"> of an electrorheological fluid is an isotropic tensor valued function of the rate of strain tensor D and the vector n (which characterizes the orientation src="/content/njf80kprf62xtbvd/s00397-003-0320-0etIEq1.gif" alt="$${\mathbf{\hat{n}}}$$" align="middle" border="0"> and length N of the fibers formed by application of an electric field). The resulting constitutive equation for src="/content/njf80kprf62xtbvd/xxlarge964.gif" alt="tau" align="BASELINE" BORDER="0"> is supplemented by the solution of the previously studied time evolution equation for n. Plastic behavior for the shear and normal stresses is predicted. Anticipating that the action of increasing shear rate src="/content/njf80kprf62xtbvd/s00397-003-0320-0etIEq14.gif" alt="$$ \dot{\gamma } $$" align="middle" border="0"> is i) to orient the fibers more and more in the direction of flow and ii) simultaneously to break up the fibers leads to the conclusion that for src="/content/njf80kprf62xtbvd/s00397-003-0320-0etIEq15.gif" alt="$$ \dot{\gamma } \to \infty $$" align="middle" border="0"> the same behavior is encountered as without an electric field. Using realistically possible approximation formulas for the dependence of src="/content/njf80kprf62xtbvd/s00397-003-0320-0etIEq2.gif" alt="$${\mathbf{\hat{n}}}$$" align="middle" border="0"> and N on src="/content/njf80kprf62xtbvd/s00397-003-0320-0etIEq16.gif" alt="$$ \dot{\gamma } $$" align="middle" border="0"> leads to the Bingham behavior for src="/content/njf80kprf62xtbvd/s00397-003-0320-0etIEq17.gif" alt="$$ \dot{\gamma } \to 0 $$" align="middle" border="0"> and power law behavior for large shear rates.ss="Contact">

Dispersion de Taylor généralisée à un fluide à propriétés physiques variablesGeneralized Taylor dispersion for heterogeneous fluid

The investigation of non-reactive miscible solute dispersion in a vertical Hele–Shaw cell is considered. An asymptotic method is used to extend Taylor model to the case of the fluid density, the dynamic viscosity and the molecular diffusion coefficient are solute concentration-dependent. It is demonstrated that the averaged variables over the gap are governed by a convection–dispersion equation in which the dispersion tensor is concentration-dependent. <strong>To cite this article: C. Felder et al., C. R. Mecanique 332 (2004).strong>     

The generalized-kinetics-based equilibrium distribution function for composite particlesLa fonction de distribution d'équilibre pour des particules composées basée sur la cinétique généralisée

This work is devoted to the equilibrium distribution function for a fluid of mutually non-interacting identical composite point particles in three-dimensional physical space. The distribution function is derived within the generalized-kinetics (GK) vision from the proposed probabilistic model based on quantum-mechanical bosons and fermions. The first GK advantage is that the derivation does not involve any assumption on the interpolation between bosons and fermions whereas the resulting function provides this interpolation. The second GK advantage is that composons, the particles described with the GK-based distribution function, are considerably less schematic and more consistent physically than quons. Composons correspond to a specific case of Isakov's general q-commutation relation involving an infinite number of the q-coefficients. Connection of the composon concept to previous results in the literature is pointed out. A few directions for future research on the topic are formulated. The results of the work can be used in the composite-particle fluid problems where the Maxwell–Boltzmann description is not valid, for instance, in dense populations of not too massive point-like particles of a complex, composite nature at not too high temperatures. <strong>To cite this article: N. Bellomo et al., C. R. Mecanique 331 (2003).strong>     

Recovery of small electromagnetic inhomogeneities from partial boundary measurementsIdentification de petites inhomogénéités diélectriques à partir de mesures partielles

We consider for the inverse problem of identifying locations and certain properties of the shapes of small dielectric inhomogeneities in a homogeneous background medium from boundary measurements on part of the boundary or dynamic boundary measurements for a finite time interval. Using as weights particular background solutions we develop asymptotic methods based on appropriate averaging of the data. <strong>To cite this article: H. Ammari, A.G. Ramm, C. R. Mecanique 330 (2002) 199–205.strong>     

A linearization technique for multi-species transport problems

We study a one-dimensional multi-species system of dispersive-advective contaminant transport equations coupled by nonlinear biological (kinetic reactions) and physical (adsorption) processes. To deal with the nonlinearities and the coupling, and to avoid additional computational costs, we propose a linearization technique based on first-order Taylor’s series expansions. A stabilized finite element in space, combined with an Euler implicit finite difference discretization in time, is used to approximate the dispersive-advective transport problem. Three computational tests are performed with different boundary conditions, retardation factors and kinetic parameters for a nonlinear reactive multi-species transport model. The proposed methodology is shown to be accurate and decrease computational costs in the numerical implementation of nonlinear reactive transport problems.     

Filtration Law in Porous Media with Poor Separation of Scales

We investigate the validity of Darcysrc="/content/r33x4665j3546046/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0">s law when the separation of scales is poor. We use the method of multi-scale asymptotic expansions which gives the macroscopic behaviour from the pore scale description. The first order approximation is the Darcysrc="/content/r33x4665j3546046/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0">s law. When the separation of scales is poor, eventual correctors to Darcysrc="/content/r33x4665j3546046/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0">s law are obtained by investigating the following orders of approximation, thus enabling us to study its robustness. We investigate the two first correctors. Thus, the accuracy of the macroscopic flow law is improved from src="/content/r33x4665j3546046/11242_2004_Article_3649_TeX2GIFIEq1.gif" alt="$${\cal O}$$" align="middle" border="0"> (src="/content/r33x4665j3546046/xxlarge949.gif" alt="epsi" align="BASELINE" BORDER="0">) to src="/content/r33x4665j3546046/11242_2004_Article_3649_TeX2GIFIEq2.gif" alt="$${\cal O}$$" align="middle" border="0"> (src="/content/r33x4665j3546046/xxlarge949.gif" alt="epsi" align="BASELINE" BORDER="0"><sup>3sup>), where src="/content/r33x4665j3546046/xxlarge949.gif" alt="epsi" align="BASELINE" BORDER="0"> is the separation of scale parameter. The second corrector shows a Brinkmansrc="/content/r33x4665j3546046/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0">s term. For macroscopically homogeneous porous media, the first corrector cancels out, that points out the robustness of Darcysrc="/content/r33x4665j3546046/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0">s law in this case.     

Dynamic Analysis of an Infinite Cylindrical Hole in a Saturated Poroelastic Medium

In this paper, the dynamic response of an infinite cylindrical hole embedded in a porous medium and subjected to an axisymmetric ring load is investigated. Two scalar potentials and two vector potentials are introduced to decouple the governing equations of Biot’s theory. By taking a Fourier transform with respect to time and the axial coordinate, we derive general solutions for the potentials, displacements, stresses and pore pressures in the frequency-wave-number domain. Using the general solutions and a set of boundary conditions applied at the hole surface, the frequency-wave-number domain solutions for the proposed problem are determined. Numerical inversion of the Fourier transform with respect to the axial wave number yields the frequency domain solutions, while a double inverse Fourier transform with respect to frequency as well as the axial wave number generates the time-space domain solution. The numerical results of this paper indicate that the dynamic response of a porous medium surrounding an infinite hole is dependant upon many factors including the parameters of the porous media, the location of receivers, the boundary conditions along the hole surface as well as the load characteristics.     

Acoustics with wall-slip flow of gas-saturated porous media

This work is aimed at deriving and at analyzing the dynamic filtration law that describes the acoustics of a gas saturated porous medium, when a wall-slip flow occurs due to low gas pressure. The dynamic filtration law is derived by upscaling the pore-scale description that consists of the equations of linear acoustics and a wall-slip condition on the pore wall. We have shown that the effective dynamic permeability depends on the Knudsen number and can be approximated by the generalized Klinkenberg’s law at low Knudsen numbers. Analysis of these results on a simple geometry proves that this approximation fails at reproducing the macroscopic inertial effects at high pulsations.     

The mucosal immune system: From dentistry to vaccine development

The oral cavity is the beginning of the aero-digestive tract, which is covered by mucosal epithelium continuously under the threat of invasion of pathogens, it is thus protected by the mucosal immune system. In the early phase of our scientific efforts for the demonstration of mucosal immune system, dental science was one of major driving forces due to their foreseeability to use oral immunity for the control of oral diseases. The mucosal immune system is divided functionally into, but interconnected inductive and effector sites. Intestinal Peyer’s patches (PPs) are an inductive site containing antigen-sampling M cells and immunocompetent cells required to initiate antigen-specific immune responses. At effector sites, PP-originated antigen-specific IgA B cells become plasma cells to produce polymeric IgA and form secretory IgA by binding to poly-Ig receptor expressed on epithelial cells for protective immunity. The development of new-generation mucosal vaccines, including the rice-based oral vaccine MucoRice, on the basis of the coordinated mucosal immune system is a promising strategy for the control of mucosal infectious diseases.     

Nonfickian effect in time and space for diffusion processes

Diffusion processes are usually simulated using the classical diffusion equation. In certain scenarios, such equation induces anomalous behavior and consequently several improvements were introduced in the literature to overcome them. One of the most popular was the replacement of the diffusion equation by an integro‐differential equation. Such equation can be established considering a modification of Fick's mass flux where a delay in time is introduced. In this article, we consider mathematical models for diffusion processes that take into account a memory effect in time and space. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1589–1602, 2015