A new formulation of immiscible compressible two-phase flow in porous media

A new formulation is proposed to describe immiscible compressible two-phase flow in porous media. The main feature of this formulation is the introduction of a global pressure. The resulting equations are written in a fractional flow formulation and lead to a coupled system which consists of a nonlinear parabolic (the global pressure equation) and a nonlinear diffusion–convection one (the saturation equation) which can be efficiently solved numerically. To cite this article: B. Amaziane, M. Jurak, C. R. Mecanique 336 (2008).     

Time of complete displacement of an immiscible compressible fluid by water in porous media: Application to gas migration in a deep nuclear waste repository

A system of evolutionary partial differential equations (PDEs) describing the two-phase flow of immiscible fluids, such as water–gas, through porous media is studied. In this formulation, the wetting and nonwetting phases are treated to be incompressible and compressible, respectively. This treatment is indeed necessary when a compressible nonwetting phase is subjected to compression during confinement. The system of PDEs consists of an evolution equation for the wetting-phase saturation and an evolution equation for the pressure in the nonwetting phase. This system is applied to the problem of unsaturated flows to assess gas migration and two-phase flow through engineered and geological barriers for a deep repository for radioactive waste. This paper is primarily concerned with the large time behavior of solutions of this system. Under some realistic assumptions on the data, we derive estimates of the speed of propagation of the gas by water in porous media. Namely, we establish estimates of time stabilization for the water saturation to a constant limit profile. The analysis is based on the energy methods whose main idea involves deriving and studying suitable ordinary differential inequalities. We show that the time of complete displacement of a gas by water may be at most infinite or finite depending essentially on the power parameters defining the capillary pressure and the relative permeabilities. This result is then illustrated with two examples in the context of gas migration in a deep nuclear waste repository. We consider Van Genuchten’s and Brooks–Corey’s models for a two-phase water–gas system.     

Numerical simulation and homogenization of two-phase flow in heterogeneous porous media

A mathematically rigorous method of homogenization is presented and used to analyze the equivalent behavior of transient flow of two incompressible fluids through heterogeneous media. Asymptotic expansions and H-convergence lead to the definition of a global or effective model of an equivalent homogeneous reservoir. Numerical computations to obtain the homogenized coefficients of the entire reservoir have been carried out via a finite element method. Numerical experiments involving the simulation of incompressible two-phase flow have been performed for each heterogeneous medium and for the homogenized medium as well as for other averaging methods. The results of the simulations are compared in terms of the transient saturation contours, production curves, and pressure distributions. Results obtained from the simulations with the homogenization method presented show good agreement with the heterogeneous simulations.     

Evaluation of nanotribological behavior of amorphous polystyrene: The macromolecular weight effect

Tribological testing of polymers is of prime importance in many industrial applications. Silicon nitride AFM tips have been used to mimic the contact between amorphous polystyrene surfaces and a hard asperity, which is useful in understanding of how a multitude of asperities behave in a macroscopic contact. In this study, the adhesion force and the friction force of four PS molecular weights were measured and the average contact pressure was calculated by using the JKR contact theory. The nanotribological behavior of polystyrene showed a dependence on macromolecular weight with varying applied normal force and sliding velocity. The study indicates that the length of polymer chains noticeably influences the tribological behavior of amorphous polystyrenes. Mechanisms governing such behavior differences were ascribed to energy dissipating modes.     

Ab Initio Diabatic energies and dipole moments of the electronic states of RbLi molecule

For all states dissociating below the ionic limit Li^? Rb⁺, we perform a diabatic study for ¹Σ⁺ electronic states dissociating into Rb (5s, 5p, 4d, 6s, 6p, 5d, 7s, 4f) + Li (2s, 2p, 3s). Furthermore, we present the diabatic results for the 1–11 ³σ, 1–8 ^1,3Π, and 1–4 ^1,3Δ states. The present calculations on the RbLi molecule are complementary to previous theoretical work on this system, including recently observed electronic states that had not been calculated previously. The calculations rely on ab‐initio pseudopotential, core polarization potential operators for the core‐valence correlation and full valence configuration interaction approaches, combined to an efficient diabatization procedure. For the low‐lying states, diabatic potentials and permanent dipole moments are analyzed, revealing the strong imprint of the ionic state in the ¹Σ⁺ adiabatic states. The transition dipole moment is used to evaluate the radiative lifetimes of the vibrational levels trapped in the 2 ¹Σ⁺ excited states for the first time. In addition to the bound–bound contribution, the bound–free term has been evaluated using the Franck–Condon approximation and also exactly added to the total radiative lifetime. © 2013 Wiley Periodicals, Inc.     

Structure of human telomeric DNA in crowded solution

G-quadruplex structures formed by DNA at the human telomeres are attractive anticancer targets. Human telomeric sequences can adopt a diverse range of intramolecular G-quadruplex conformations: a parallel-stranded conformation was observed in the crystalline state, while at least four other forms were seen in K(+) solution, raising the question of which conformation is favored in crowded cellular environment. Here, we report the first NMR structure of a human telomeric G-quadruplex in crowded solution. We show that four different G-quadruplex conformations are converted to a propeller-type parallel-stranded G-quadruplex in K(+)-containing crowded solution due to water depletion. This study also reveals the formation of a new higher-order G-quadruplex structure under molecular crowding conditions. Our molecular dynamics simulations of solvent distribution provide insights at molecular level on the formation of parallel-stranded G-quadruplex in environment depleted of water. These results regarding human telomeric DNA can be extended to oncogenic promoters and other genomic G-rich sequences.     

Uncertainty principle for the two-sided quaternion windowed Fourier transform

In this paper, we study the quaternion windowed Fourier transform (QWFT) and prove the Local uncertainty principle, the Logarithmic uncertainty principle and Amrein Berthier for the QWFT, the radar quaternion ambiguity function and the quaternion Wigner transform.     

Electrochemical behavior and analytical detection of Imidacloprid insecticide on a BDD electrode using square-wave voltammetric method

A sensitive square-wave voltammetric method for the determination of Imidacloprid(IMD) was developed using electrochemically pretreated boron-doped diamond(BDD) electrode. Aqueous solutions were prepared with Confidor 200 SL as the commercial formulation of IMD. Sodium sulfate(Na_2SO_4) was used as supporting electrolyte. The influence of operating parameters, such as the p H of the medium, frequency, pulse amplitude, scan increment and the concentration of IMD was investigated. An irreversible cathodic peak, corresponding to the reduction of IMD is observed at 1.21 V(vs. SCE) and the electrode reaction was controlled by adsorption. Under optimized conditions, the square-wave reduction peak current was linear over the concentration range of(30–200 μmol L~(-1)) with a detection and quantification limits of 8.60 μmol L~(-1))and 28.67 μmol L~(-1)), respectively. The results were compared with spectrophotometry and HPLC methods under some conditions and found to be in good agreement.To investigate applicability to real samples, the proposed method was applied to the determination of IMD in plum juice.