Multiscale Structures to Describe Porous Media Part I: Theoretical Background and Invasion by Fluids

A porous medium with a broad pore-size distribution is described on the basis of the Multiscale Percolation System concept. The representative structure is the superposition of several constitutive elementary networks, of which mesh sizes are proportional to the diameter of the class of pores considered. To account for the contribution of each class to the connection of the medium, a recurrent building process, involving rescaling and superposition, is defined. This process leads to an equivalent monoscale network, involving elements representative of the various classes. Mercury intrusion at increasing pressure into a finite-size sample of this equivalent network is modelled. The inverse problem is solved, leading to the identification of the representative multiscale structure of a given material from the experimental intrusion curve.     

A thermodynamic approach with internal variables using Lagrange formalism. Part II. Continuous symmetries in the case of the time–temperature equivalence

In the first part of this contribution, the Lie-symmetries of the principle of least action associated to the constitutive equations of the DNLR formalism of relaxation have been presented. We examine in this second part the continuous symmetries corresponding to the simple case of stress relaxation under isothermal conditions. The well-known principle of time/temperature equivalence is discussed in terms of variational symmetry for the Jacobi’s action functional, and connected to the Onsager’s relation near the thermodynamic equilibrium.     

Rheological studies of the gelation of aqueous solutions of acrylamide-acrylic acid copolymers in the presence of chromium chloride

The gelation kinetics of aqueous solutions of acrylamideacrylic acid copolymers in the presence of chromium ions was studied with different rheometers. The gel time is found to vary with the principle of the apparatus because of a low shear dependence of the elongation of the macromolecules. The variations of the gel time with the experimental conditions of the gel preparation were investigated and we conclude that the gelation is governed by the oligornerization kinetics of the chromium ions which are instantaneously, complexated by the carboxylate groups of the polymer. The variation laws of the gel time and of the elastic modulus with chromium and polymer concentrations, temperature and ionic strength are in qualitative agreement with the structure of the temporary network of the semi-dilute solutions of these copolymers.     

The Kinematics of Plate Models: A Geometrical Deduction

We present a deduction of the Kirchhoff–Love and Reissner–Mindlin kinematics of a simply-connected plate by using the formal asymptotic development method applied to the compatibility conditions of Saint-Venant and the formula of Cesàro–Volterra. This formal deduction is purely geometrical because we do not use any information coming from the loading or the constitutive behavior.      

Flow instability and shear localization in a drilling mud

To have a better knowledge of problems occurring with drilling fluids in complex wells, we carried out a detailed rheological analysis of a typical drilling mud at low shear rates using both conventional rheometry and MRI velocimetry. We show the existence of a viscosity bifurcation effect: Below a critical stress value, the mud tends to completely stop flowing, whereas beyond this critical stress, it reaches an apparent shear rate larger than a finite (critical) value, and no stable flows can be obtained between this critical shear rate value and zero. These results are confirmed by MRI velocity profiles, which exhibit a slope break at the interface between the solid and the liquid phases inside the Couette geometry. Moreover, this viscosity bifurcation is a transient phenomenon, the progressive development of which can be observed by MRI. A further examination of MRI data shows that, in the transient regime, the shear rate does not vary monotonously in the rheometer gap and is particularly large along the outer (rough) cylinder, which might be at the origin of the development of a region of constant shear rate in the apparent flow curve.     

Noise radiated by a non-isothermal, temporal mixing layer

The ability of Lighthill's analogy to predict the sound radiated by a transitional mixing layer is evaluated by means of direct numerical simulation (DNS). The specific case of low Mach number flows with density variations is investigated. In order to limit the global computational cost, the acoustic source information is based on numerical results where the sound waves have been removed. It is shown that the low Mach number approximation coupled with the acoustic analogy can lead to very accurate predictions for the radiated sound if the acoustic sources in Lighthill's equation are taken into account carefully. Results for the acoustic intensity deduced from a repeated use of the Lighthill's analogy over a wide range of Mach numbers allow us to discuss the adequacy of scaling laws proposed by previous authors (J. Sound Vib. 28(3), 563–585, 1973; 31(4), 391–397, 1973; 48(1), 95–111, 1976) for the prediction of noise from hot jets.     

Global stability analysis of parametrically excited cylindrical shells through the evolution of basin boundaries

In the present study, the large-amplitude vibrations and stability of a perfect circular cylindrical shell subjected to axial harmonic excitation in the neighborhood of the lowest natural frequencies are investigated. Donnell's shallow shell theory is used and the shell spatial discretization is obtained by the Ritz method. An efficient low-dimensional model presented in previous publications is used to discretize the continuous system. The main purpose of this work is to discuss the use of basins of attraction as a measure of the reliability and safety of the structure. First, the nonlinear behavior of the conservative system is discussed and the basin structure and volume is understood from the topologic structure of the total energy and its evolution as a function of the system parameters. Then, the behavior of the forced oscillations of the harmonically excited shell is analyzed. First the stability boundaries in force control space are obtained and the bifurcation events connected with these boundaries are identified. Based on the bifurcation diagrams, the probability of parametric instability and escape are analyzed through the evolution and erosion of basin boundaries within a prescribed control volume defined by the manifolds. Usually, basin boundaries become fractal. This together with the presence of catastrophic subcritical bifurcations makes the shell very sensitive to initial conditions, uncertainties in system parameters, and initial imperfections. Results show that the analysis of the evolution of safe basins and the derivation of appropriate measures of their robustness is an essential step in the derivation of safe design procedures for multiwell systems.     

Uniqueness and the maximum principle for quasilinear elliptic equations with quadratic growth conditions

In this paper, we show that the maximum principle holds for quasilinear elliptic equations with quadratic growth under general structure conditions.Two typical particular cases of our results are the following. On one hand, we prove that the equation (1) {ie77-01} where {ie77-02} and {ie77-03} satisfies the maximum principle for solutions in H ¹()L(), i.e., that two solutions u ₁, u ₂H¹() L() of (1) such that u ₁u₂ on , satisfy u ₁u₂ in . This implies in particular the uniqueness of the solution of (1) in H ₀ ¹ ()L().On the other hand, we prove that the equation (2) {ie77-04} where fH^–1() and g(u)>0, g(0)=0, satisfies the maximum principle for solutions uH¹() such that g(u)¦Du|{²L¹(). Again this implies the uniqueness of the solution of (2) in the class uH ₀ ¹ () with g(u)¦Du|{²L¹().In both cases, the method of proof consists in making a certain change of function u=(v) in equation (1) or (2), and in proving that the transformed equation, which is of the form (3) {ie77-05}satisfies a certain structure condition, which using ((v₁ -v ₂)⁺)ⁿ for some n>0 as a test function, allows us to prove the maximum principle.     

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     

New Acetogenins from the Seeds of Annona coriacea

From the hexane and MeOH extracts of Annona coriacea Mart . (Annonaceae) seeds, two novel acetogenins, coriapentocins A and B ( 1 and 2 , resp.) were isolated. The known acetogenin bullacin ( 3 ) was also isolated from the hexane extract. The structures of compounds 1 – 3 were elucidated by NMR and MS analysis, and relative configurations were established by comparison with literature data.