211 research outputs found
Flow of low pressure gas through dual-porosity media
Using the theory of homogenization we derive macroscopic models for describing flow of gas at low pressure in dual-porosity media. The case of a fractured porous medium is under consideration for the study, and the existence of a representative elementary volume that consists of open connected fractures surrounded by porous matrix blocks is assumed. The local flow is governed by either Klinkenberg's law or Knudsen's diffusion law in the matrix while either a non-slip flow or a slip flow occurs in the fractures. Six new models are derived by homogenization, which are compared to the three models which were obtained for Darcy's regime in an earlier work. Each of these nine models is characterized by its macroscopic flow regime and by the type of macroscopic behavior it describes. Besides Darcy's and Klinkenberg's macroscopic flow regimes, a transition regime between Klinkenberg's and Knudsen's regimes is identified. The types of macroscopic behaviors include a dual and a single porosity description and an intermediate behavior that describes a single-porosity behavior, but in which the porosity of the entire fractured porous medium is accounted for
Ecoulement de Klinkenberg et diffusion de Knudsen en milieu à double porosité : mise en évidence des effets d'échelles
Analysis of coupled heat and moisture transfer in masonry structures
Evaluation of effective or macroscopic coefficients of thermal conductivity
under coupled heat and moisture transfer is presented. The paper first gives a
detailed summary on the solution of a simple steady state heat conduction
problem with an emphasis on various types of boundary conditions applied to the
representative volume element -- a periodic unit cell. Since the results
essentially suggest no superiority of any type of boundary conditions, the
paper proceeds with the coupled nonlinear heat and moisture problem subjecting
the selected representative volume element to the prescribed macroscopically
uniform heat flux. This allows for a direct use of the academic or commercially
available codes. Here, the presented results are derived with the help of the
SIFEL (SIimple Finite Elements) system.Comment: 23 pages, 11 figure
Nonlocal boundary conditions for corrugated acoustic metasurface with strong near field interactions
The propagation of long-wavelength sound in the presence of a metasurface made by arranging acoustic resonators periodically upon or slightly above an impervious substrate is studied. The method of two-scale asymptotic homogenization is used to derive effective boundary conditions, which account for both the surface corrugation and the low-frequency resonance. This method is applied to periodic arrays of resonators of any shape operating in the long-wavelength regime. The approach relies on the existence of a locally periodic boundary layer developed in the vicinity of the metasurface, where strong near-field interactions of the resonators with each other and with the substrate take place. These local effects give rise to an effective surface admittance supplemented by nonlocal contributions from the simple and double gradients of the pressure at the surface. These phenomena are illustrated for the periodic array of cylindrical Helmholtz resonators with an extended inner duct. Effects of the centre-to-centre spacing and orientation of the resonators' opening on the nonlocality and apparent resonance frequency are studied. The model could be used to design metasurfaces with specific effective boundary conditions required for particular applications
Homogenization of Biomechanical Models for Plant Tissues
In this paper homogenization of a mathematical model for plant tissue
biomechanics is presented. The microscopic model constitutes a strongly coupled
system of reaction-diffusion-convection equations for chemical processes in
plant cells, the equations of poroelasticity for elastic deformations of plant
cell walls and middle lamella, and Stokes equations for fluid flow inside the
cells. The chemical process in cells and the elastic properties of cell walls
and middle lamella are coupled because elastic moduli depend on densities
involved in chemical reactions, whereas chemical reactions depend on mechanical
stresses. Using homogenization techniques we derive rigorously a macroscopic
model for plant biomechanics. To pass to the limit in the nonlinear reaction
terms, which depend on elastic strain, we prove the strong two-scale
convergence of the displacement gradient and velocity field
Acoustics of multiscale sorptive porous materials
This paper investigates sound propagation in multiscale rigid-frame porous materials that support mass transfer processes, such as sorption and different types of diffusion, in addition to the usual visco-thermo-inertial interactions. The two-scale asymptotic method of homogenization for periodic media is successively used to derive the macroscopic equations describing sound propagation through the material. This allowed us to conclude that the macroscopic mass balance is significantly modified by sorption, inter-scale (micro- to/from nanopore scales) mass diffusion, and inter-scale (pore to/from micro- and nanopore scales) pressure diffusion. This modification is accounted for by the dynamic compressibility of the effective saturating fluid that presents atypical properties that lead to slower speed of sound and higher sound attenuation, particularly at low frequencies. In contrast, it is shown that the physical processes occurring at the micro-nano-scale do not affect the macroscopic fluid flow through the material. The developed theory is exemplified by introducing an analytical model for multiscale sorptive granular materials, which is experimentally validated by comparing its predictions with acoustic measurements on granular activated carbons. Furthermore, we provide empirical evidence supporting an alternative method for measuring sorption and mass diffusion properties of multiscale sorptive materials using sound waves
Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?
A wide variety of techniques have been developed to homogenize transport equations in multiscale and multiphase systems. This has yielded a rich and diverse field, but has also resulted in the emergence of isolated scientific communities and disconnected bodies of literature. Here, our goal is to bridge the gap between formal multiscale asymptotics and the volume averaging theory. We illustrate the methodologies via a simple example application describing a parabolic transport problem and, in so doing, compare their respective advantages/disadvantages from a practical point of view. This paper is also intended as a pedagogical guide and may be viewed as a tutorial for graduate students as we provide historical context, detail subtle points with great care, and reference many fundamental works
Participation of interleukin-5, interleukin-8 and leukotriene B4 in eosinophil accumulation in two different experimental models
Modulation of microglia by Wolfberry on the survival of retinal ganglion cells in a rat ocular hypertension model
The active component of Wolfberry (Lycium barbarum), lycium barbarum polysaccharides (LBP), has been shown to be neuroprotective to retinal ganglion cells (RGCs) against ocular hypertension (OH). Aiming to study whether this neuroprotection is mediated via modulating immune cells in the retina, we used multiphoton confocal microscopy to investigate morphological changes of microglia in whole-mounted retinas. Retinas under OH displayed slightly activated microglia. One to 100 mg/kg LBP exerted the best neuroprotection and elicited moderately activated microglia in the inner retina with ramified appearance but thicker and focally enlarged processes. Intravitreous injection of lipopolysaccharide decreased the survival of RGCs at 4 weeks, and the activated microglia exhibited amoeboid appearance as fully activated phenotype. When activation of microglia was attenuated by intravitreous injection of macrophage/microglia inhibitory factor, protective effect of 10 mg/kg LBP was attenuated. The results implicated that neuroprotective effects of LBP were partly due to modulating the activation of microglia
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