Singular nature of nonlinear macroscale effects in high-rate flow through porous mediaNature singulière des effets macroscopiques non linéaires dans un écoulement à hautes vitesses en milieux poreux

The quadratic law of laminar flow through porous media at high Reynolds numbers, which is well confirmed by the multiple experimental data, is shown to give rise to three fundamental paradoxes. All them can be resolved by assuming the singular structure of flow. The singularity is produced by the formation of jet brunches which invade the stagnant zones and sharply loss their kinetic energy. The numerical simulation confirms this effect. To cite this article: M. Panfilov et al., C. R. Mecanique 331 (2003).     

Influence of a strong density stratification on the entrainment of a turbulent axisymmetric plume

The effect of entrainment and the role of the interface during the interaction between an axisymmetric turbulent mass plume and a strong stratified layer are investigated. We describe mainly the characteristics of the plume: the change in the profiles of the density, the horizontal component of the velocity and the corresponding intensity of turbulence, the change in the entrainment co-efficient, when the plume goes through the impingement interface, assuming a self-similar Gaussian property of the axial velocity component and of the density difference. The influence of the stratification on the plume angle coefficient is studied, and compared with the results related to a homogeneous environment, obtained elsewhere. Experimental correlation on the mean entrainment coefficient in a given plume cross-section, is formulated.     

Influence of the heterogeneity of the solutions on the parameters of miscible displacement in saturated porous medium

The aim of this study is the investigation of the effects of density and viscosity contrasts on miscible displacements when the regime is stable. It has been possible to quantify these effects by using an empirical model which takes into account both the physical properties of the liquids and the hydrodynamic parameters in different configurations of a miscible displacement involving distilled water and a calcium chloride solution. The introduction of a method for measuring electrical conductivities within the porous medium itself (without disturbing the flow) has enabled us to monitor the change in the mixing zone throughout the entire length of the flow path. A stability criterion based on hydrodynamic parameters has been established that depends on two dimensionless numbers.     

Multiphase Thermohaline Convection in the Earth’s Crust: I. A New Finite Element – Finite Volume Solution Technique Combined With a New Equation of State for NaCl–H2O

We present a new finite element – finite volume (FEFV) method combined with a realistic equation of state for NaCl–H₂O to model fluid convection driven by temperature and salinity gradients. This method can deal with the nonlinear variations in fluid properties, separation of a saline fluid into a high-density, high-salinity brine phase and low-density, low-salinity vapor phase well above the critical point of pure H₂O, and geometrically complex geological structures. Similar to the well-known implicit pressure explicit saturation formulation, this approach decouples the governing equations. We formulate a fluid pressure equation that is solved using an implicit finite element method. We derive the fluid velocities from the updated pressure field and employ them in a higher-order, mass conserving finite volume formulation to solve hyperbolic parts of the conservation laws. The parabolic parts are solved by finite element methods. This FEFV method provides for geometric flexibility and numerical efficiency. The equation of state for NaCl–H₂O is valid from 0 to 750°C, 0 to 4000 bar, and 0–100 wt.% NaCl. This allows the simulation of thermohaline convection in high-temperature and high-pressure environments, such as continental or oceanic hydrothermal systems where phase separation is common.     

Coupled Groundwater Flow and Transport in Porous Media. A Conservative or Non-conservative Form?

A new formulation for the modeling of density coupled flow and transport in porous media is presented. This formulation is based on the development of the mass balance equation by using the conservative form. The system of equations obtained by coupling the flow and transport equations using a state equation is solved by a combination of the mixed hybrid finite element method (MHFEM) and the discontinuous finite element method (DFEM). The former is applied in order to solve the flow equation and the dispersive part of the transport equation, whilst the latter is used to solve the advective part of the transport equation. Although the advantages of the MHFEM are known (efficiency calculation of velocity field and continuity of fluxes from one element to an adjacent one), its application in a classical development form (volumetric fluxes as unknowns) leads to the non-conservative version of the mass balance equation. The associated matrix of the system of equations obtained by hybridization is positive definite but non-symmetrical. By using a new approach (mass fluxes as unknowns) the conservative form of the continuity equation is preserved and the associated matrix of the system of equations obtained by hybridization becomes symmetrical. When applied to Elder's problem involving a strong density contrast, this new approach, with a lower calculation cost, leads to similar or identical results to those found in the specialized literature. The comparison between the conservative and non-conservative formulations solved with the same MHFEM and DFEM combination emphasizes the rigor and the pertinence of this new approach. Furthermore, we show the existence of a limit refinement defining the stability of the numerical solution for Elder's problem.     

Fibrillar Networks of Glycyrrhizic Acid for Hybrid Nanomaterials with Catalytic Features

Self‐assembly of the naturally occurring sweetening agent, glycyrrhizic acid (GA) in water is studied by small‐angle X‐ray scattering and microscopic techniques. Statistical analysis on atomic force microscopy images reveals the formation of ultralong GA fibrils with uniform thickness of 2.5 nm and right‐handed twist with a pitch of 9 nm, independently of GA concentration. Transparent nematic GA hydrogels are exploited to create functional hybrid materials. Two‐fold and three‐fold hybrids are developed by introducing graphene oxide (GO) and in situ‐synthesized gold nanoparticles (Au NPs) in the hydrogel matrix for catalysis applications. In the presence of GO, the catalytic efficiency of Au NPs in the reduction of p‐nitrophenol to p‐aminophenol is enhanced by 2.5 times. Gold microplate single crystals are further synthesized in the GA hydrogel, expanding the scope of these hybrids and demonstrating their versatility in materials design.     

A Gallium‐Substituted Distibene and an Antimony‐Analogue Bicyclo[1.1.0]butane: Synthesis and Solid‐State Structures

RGa {R=HC[C(Me)N(2,6‐iPr₂C₆H₃)]₂} reacts with Sb(NMe₂)₃ with insertion into the Sb? N bond and elimination of RGa(NMe₂)₂ ( 2 ), yielding the Ga‐substituted distibene R(Me₂N)GaSb?SbGa(NMe₂)R ( 1 ). Thermolysis of 1 proceeded with elimination of RGa and 2 and subsequent formation of the bicyclo[1.1.0]butane analogue [R(Me₂N)Ga]₂Sb₄ ( 3 ).     

Facile Protocol for Catalytic Frustrated Lewis Pair Hydrogenation and Reductive Deoxygenation of Ketones and Aldehydes

A series of ketones and aldehydes are reduced in toluene under H₂ in the presence of 5 mol % B(C₆F₅)₃ and either cyclodextrin or molecular sieves affording a facile metal‐free protocol for reduction to alcohols. Similar treatment of aryl ketones resulted in metal‐free deoxygenation yielding aromatic hydrocarbons.