Jean-Paul Laurent

Theoretical evidence for `Lichtenecker's mixture formulae' based on the effective medium theory

In order to calculate the electrical permittivity property of a multiphase mixture, a beta function distribution of the geometrical shapes of inclusions is considered. By using the effective medium theory together with the assumption of self-consistency, it is shown that the beta function distribution leads to Lichteneckers formulae. This gives a theoretical model for this mixing formula, which had hitherto been considered empirical. This result is important because the first Lichteneckers is already used for time domain reflectometry (TDR) calibration purposes, namely conversion from permittivity measurement to water content of heterogeneous materials.

Homogenization Modeling and Parametric Study of Moisture Transfer in an Unsaturated Heterogeneous Porous Medium

The classical mass balance equation is usually used to model the transfer of humidity in unsaturated macroscopically homogeneous porous media. This equation is highly non-linear due to the pressure-dependence of the hydrodynamic characteristics. The formal homogenization method by asymptotic expansions is applied to derive the upscaled form of this equation in case of large-scale heterogeneities of periodic structure. The nature of such heterogeneities may be different, resulting in locally variable hydrodynamic parameters. The effective capillary capacity and the effective hydraulic conductivity are defined as functions of geometry and local characteristics of the porous medium. A study of a two-dimensional stone-mortar system is performed. The effect of the second medium (the mortar), on the global behavior of the system is investigated. Numerical results for the Brooks and Corey hydrodynamic model are provided. The sensitivity analysis of the parameters of the model in relation to the effective hydrodynamic parameters of the porous structure is presented.

Thermal effusivity of two-phase wood cement-based composites

This study presents a method for estimating the thermal effusivity of wood cement-based composites used in the dry state. Two models, based on an Ohms law approach, will be displayed herein: the unit cell of the parallel model and the model of Jackson and Black have both been used to predict the effective thermal effusivity of wood composites. Various topological parameters, such as the tortuosity factor and the stereological concept of contiguity, have been introduced in order to take into account the effect of the pore structure on the thermal effusivity. Furthermore, the porosity correction term and the correction term which accounts both for the effect of the randomization of particle distribution and for the effect of the ratio of thermal effusivities have been determined empirically. Measurements of the thermal effusivity have been performed inside a closely controlled climatic cell at ambient temperature (C) using a heat plane source technique. Calculated values of the thermal effusivity of these materials have been compared with experimental results. The values predicted by the two models are all in very close agreement with experimental values.

Is the WBE model appropriate for semi-arid shrubs subjected to clear cutting?

It is crucial to understand the adaptive mechanisms of woody plants facing periodic drought to assess their vulnerability to the increasing climate variability predicted in the Sahel. Guiera senegalensis J.F.Gmel is a semi-evergreen Combretaceae commonly found in Sahelian rangelands, fallows and crop fields because of its value as an agroforestry species. We compared canopy leafing, and allometric measurements of leaf area, stem area and stem length and their relationships with leaf water potential, stomatal conductance (gs) and soil-to-leaf hydraulic conductance (KS-L), in mature and current-year resprouts of G. senegalensis in Sahelian Niger. In mature shrubs, seasonal drought reduced the ratio of leaf area to cross-sectional stem area (AL : AS), mainly due to leaf shedding. The canopy of the current-year resprouts remained permanently leafed as the shrubs produced leaves and stems continuously, and their AL : AS ratio increased throughout the dry season. Their KS-L increased, whereas gs decreased. West, Brown and Enquists (WBE) model can thus describe allometric trends in the seasonal life cycle of undisturbed mature shrubs, but not that of resprouts. Annual clear cutting drives allometric scaling relationships away from theoretical WBE predictions in the current-year resprouts, with scaling exponents 2.5 times greater than those of mature shrubs. High KS-L (twice that of mature shrubs) supports this intensive regeneration process. The adaptive strategy described here is probably common to many woody species that have to cope with both severe seasonal drought and regular disturbance over the long term.

Humidity transfer in unsaturated heterogeneous porous media by homogenization

Abstract In the paper the one-equation model of humidity transfer in unsaturated macroscopically heterogeneous porous media is presented. The homogenization method by two-scale asymptotic expansions is used to derive the upscaled form of the Richard equation, which is commonly used when the medium is considered as macroscopically homogeneous. This equation is highly non-linear due to the pressure-dependence of the hydrodynamic characteristics of the porous medium. The domain of validity of the model is explicitly given, namely: the length-scales separation, the characteristic time scale condition and the ratio of the hydrodynamic characteristics being of the same orders of magnitude. The effective capillary capacity and the effective hydraulic conductivity for an equivalent continuum are defined in terms of geometry and local hydrodynamic characteristics of the porous medium. A procedure of determination of the effective suction curve and the effective hydraulic conductivity curve as functions of the average water content for any type of the macroscopic heteregeneity for which the method can be applied, is provided. Since the problem is non-linear this procedure involves the resolution of a local boundary value problem formulated over a period for each value of suction. In two or three-dimensional cases, this problem can be solved using the numerical methods for any geometry of the medium. In a one-dimensional case it was shown that the analytical solution gives the well-known results of harmonic and arithmetic mean.

Effect of moisture content on the thermal effusivity of wood cement-based composites

The influence of moisture content on the thermal effusivity of wood cement-based composite was investigated. Measurements of thermal effusivity were performed inside a closely controlled climatic cell at ambient temperature (C) in conditions ranging from fully saturated to oven-dry. Shrotriya et als model based on an Ohms law approach was used for predicting the effective thermal effusivity of studied materials. The topological parameters of the model, such as sphericity of particles and resistivity formation factor, have been estimated as a first approximation from both thermal conductivity measurements and formulae proposed in the literature. Test results confirm that moisture content tends to increase the thermal effusivity significantly. It is also found that the Shrotriya et als model yields predictions which agree quite closely with experimental data for wood aggregates-clay-cement composites for different amounts of wood aggregates and degrees of saturation.