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Numerical modeling of multiphase flow generally requires a special procedure at the solid wall in order to be consistent with Young's law for static contact angles. The standard approach in the lattice Boltzmann method, which consists of imposing fictive densities at the solid lattice sites, is shown to be deficient for this task. Indeed, fictive mass transfer along the boundary could happen and potentially spoil the numerical results. In particular, when the contact angle is less than 90 degrees, the deficiencies of the standard model are major. Various videos that demonstrate this behavior are provided (Supporting Information). A new approach is proposed and consists of directly imposing the contact angle at the boundaries in much the same way as Dirichlet boundary conditions are generally imposed. The proposed method is able to retrieve analytical solutions for static contact angles in the case of straight and curved boundaries even when variable density and viscosity ratios between the phases are considered. Although the proposed wetting boundary condition is shown to significantly improve the numerical results for one particular class of lattice Boltzmann model, it is believed that other lattice Boltzmann multiphase schemes could also benefit from the underlying ideas of the proposed method. The proposed algorithm is two‐dimensional, and the D2Q9 lattice is used. Copyright © 2016 John Wiley & Sons, Ltd.     

Poincaré Algebra and Space-Time Critical Dimensions for Paraspinnings Strings

In this paper, we paraquantize the spinning string theory in the Neveu-Shwarz model. Unlike the Ardalan and Mansouri work [Phys. Rev. D, Vol. 9, (1974) 3341], the paraquantum system is such that both the center of mass variables and the excitation modes of the string verify paracommutation relations. The commutators of the Poincaré algebra are satisfied, except the [p ,p ] one, since one can only write [p ,p ]= 0, for Q1. Because of the relation [x ,x ] =,0 and with the sole use of the trilinear relations, we find existence possibilities of spinning strings defined in a noncommutative space-time at space-time dimensions other than D=10.     

Poincaré Algebra and Space-Time Critical Dimensions for Parabosonic Strings

We construct the parabosonic string formalism based on the paraquantization of both the center of mass variables and the excitation modes of the string. A critical study of the different commutators of the Poincaré algebra, based on the redefinition of its generators and the direct treatment using trilinear relations, is done. Space-time critical dimensions D as functions of the paraquantization order Q are obtained.     

Variable permeability effect on convection in binary mixtures saturating a porous layer

The Darcy Model with the Boussinesq approximation is used to study natural convection in a shallow porous layer, with variable permeability, filled with a binary fluid. The permeability of the medium is assumed to vary exponentially with the depth of the layer. The two horizontal walls of the cavity are subject to constant fluxes of heat and solute while the two vertical ones are impermeable and adiabatic. The governing parameters for the problem are the thermal Rayleigh number, R _T, the Lewis number, Le, the buoyancy ratio, φ, the aspect ratio of the cavity, A, the normalized porosity, ε, the variable permeability constant, c, and parameter a defining double-diffusive convection (a = 0) or Soret induced convection (a = 1). For convection in an infinite layer, an analytical solution of the steady form of the governing equations is obtained on the basis of the parallel flow approximation. The onset of supercritical convection, or subcritical, convection are predicted by the present theory. A linear stability analysis of the parallel flow model is conducted and the critical Rayleigh number for the onset of Hopf’s bifurcation is predicted numerically. Numerical solutions of the full governing equations are found to be in excellent agreement with the analytical predictions.     

On the thermal anisotropy affecting transfers in a multilayer porous mediumSur l'effet de l'anisotropie thermique sur les transferts dans un milieu poreux multicouches

An analytical model for studying double-diffusive natural convection within a multilayer anisotropic porous medium is developed and validated with respect to a direct numerical silmulation. The studied domain is composed of two horizontal porous layers where the lower one is thermally anisotropic and is submitted to a uniform horizontal heat flux and a vertical mass flux. The assumption of parallel flow is validated and the effect of anisotropy on dynamic transitions is investigated. To cite this article: R. Bennacer et al., C. R. Mecanique 332 (2004).     

Al–Cu intermetallic coatings processed by sequential metalorganic chemical vapour deposition and post-deposition annealing

Sequential processing of aluminum and copper followed by reactive diffusion annealing is used as a paradigm for the metalorganic chemical vapour deposition (MOCVD) of coatings containing intermetallic alloys. Dimethylethylamine alane and copper N,N′-di-isopropylacetamidinate are used as aluminum and copper precursors, respectively. Deposition is performed on steel and silica substrates at 1.33 kPa and 493–513 K. Different overall compositions in the entire range of the Al–Cu phase diagram are obtained by varying the relative thickness of the two elemental layers while maintaining the overall thickness of the coating close to 1 μm. As-deposited films present a rough morphology attributed to the difficulty of copper to nucleate on aluminum. Post-deposition annealing is monitored by in situ X-ray diffraction, and allows smoothening the microstructure and identifying conditions leading to several Al–Cu phases. Our results establish a proof of principle following which MOCVD of metallic alloys is feasible, and are expected to extend the materials pool for numerous applications, with innovative thin film processing on, and surface properties of complex in shape parts.     

Analytical and numerical investigation of double diffusion in thermally anisotropy multilayer porous medium

Double-diffusive natural convection within a multilayer anisotropic porous medium is studied numerically and analytically. The domain composed of two horizontal porous layers is subjected to a uniform horizontal heat flux and a vertical mass flux, where only the lower one is thermally anisotropic. Darcy model with classical Boussinesq approximation is used in formulating the mathematical model. The effect of thermal anisotropy and the relative width of the two layers on the flow and transfers is illustrated with characterising the transitions from the diffusive to the convective solution. Results were well compared with respect to a developed analytical approach, based on a parallel flow approximation for thermally anisotropic multilayer media.     

Symmetry breaking of melt flow typically encountered in a Bridgman configuration heated from below

A computational model is developed to investigate three-dimensional fluid flow instability and transition to unsteadiness. The simulated domain corresponds to a parallelepiped configuration which is a restriction to the fluid phase of commonly used configurations in crystal growth (viz. Bridgman configuration). In the present work, this problem is studied using three-dimensional simulations and focuses on symmetry breaking and transition to unsteadiness occurring for a low Prandtl number fluid (Pr = 0.01).     

Silicon-initiated carbonylative carbotricyclization and [2+2+2+1] cycloaddition of enediynes catalyzed by rhodium complexes

The reaction of dodec-11-ene-1,6-diynes or their heteroatom congeners with a hydrosilane catalyzed by Rh(acac)(CO)2 at ambient temperature and pressure of CO gives the corresponding fused 5-7-5 tricyclic products, 5-oxo-1,3a,4,5,7,9-hexahydro-3H-cyclopenta[e]azulenes or their heteroatom congeners, in excellent yields through a unique silicon-initiated cascade carbonylative carbotricyclization (CO-SiCaT) process. It has also been found that the 5-7-5 fused tricyclic products can be obtained from the same type of enediynes and CO through a novel intramolecular [2+2+2+1] cycloaddition process. The characteristics of these two tricyclization processes and the fundamental differences in their reaction mechanisms are discussed. This novel higher-order cycloaddition reaction has also been successfully applied to the tricyclization of undeca-5,10-diyn-1-als, affording the corresponding 5-7-5 fused-ring products bearing a seven-membered lactone moiety. Related [2+2+2] tricyclizations of enediyne and diynal substrates are also discussed. These newly discovered reactions can construct multiple bonds all at once, converting linear starting materials to polycyclic compounds in a single step. Thus, these new processes provide innovative routes to functionalized polycyclic compounds that are useful for the syntheses of natural and unnatural products.     

Analytical development of disturbed matrix eigenvalue problem applied to mixed convection stability analysis in Darcy media

This work consists in evaluating algebraically and numerically the influence of a disturbance on the spectral values of a diagonalizable matrix. Thus, two approaches will be possible; to use the theorem of disturbances of a matrix depending on a parameter, due to Lidskii and primarily based on the structure of Jordan of the no disturbed matrix. The second approach consists in factorizing the matrix system, and then carrying out a numerical calculation of the roots of the disturbances matrix characteristic polynomial. This problem can be a standard model in the equations of the continuous media mechanics. During this work, we chose to use the second approach and in order to illustrate the application, we choose the Rayleigh–Bénard problem in Darcy media, disturbed by a filtering through flow. The matrix form of the problem is calculated starting from a linear stability analysis by a finite elements method. We show that it is possible to break up the general phenomenon into other elementary ones described respectively by a disturbed matrix and a disturbance. A good agreement between the two methods was seen. To cite this article: H.B. Hamed, R. Bennacer, C. R. Mecanique 336 (2008).