Numerical studies of gravity destabilized percolation in 2D porous media

Two dimensional simulations of percolation are realized on square networks of pore throats with a random capillary pressure distribution. We analyse the influence of a destabilizing gravity field (g) and of the standard deviation of the distribution of the capillary pressure thresholds (W_t). The fragmentation process is not taken into account in this study. For an increase of g or/and when W_t decreases, two transitions are analyzed with three different regimes displacement patterns: Invasion percolation, invasion percolation in a gradient, and invasion in a pure gradient. The transitions are controlled both by the ratio g/W_t and by the sample size (L). A scaling law between the saturation at the percolation threshold and g/W_t allows delineating the three regimes in agreement with theoretical argument of the percolation in a gradient.     

Dechiralisation lines–induced unwinding in confined SmC* liquid crystals

Equilibrium and dynamic behaviours of dechiralisation lines occurring below SmC* cell boundaries in planar geometry constitute a polemic topic for several decades. We report new observations in the SmC* phase of the strongly polarised liquid crystal CFL08. They are compared with vortex motions in superfluids and type-II superconductors, and we propose a simple heuristic model attempting to explain the intriguing mismatch between bulk helix pitch and inter-lines distance. It results from opposite effects of the helix pitch and surface lines charge value on the equilibrium lines distance. The model assumes that the lines electric interactions dominate the cell equilibrium state. In particular the unwinding transition of the bulk helix is provoked by field-induced displacements of the lines lattices. It permits to relate the lines density and critical fields to intrinsic energy parameters, and to explain the pitch/distance mismatch, together with its almost constant value across the transition. We foresee the helix pitch and unwinding field variations versus sample width.     

Convective heat loss of water in a circular pipe cooled at constant rate

A numerical study is made of the heat loss by natural convection of water within a horizontal circular cylinder with wall temperature decreasing at a constant rate. The particular situation of water with maximum density at 4 °C is formulated in dimensionless relations based on a linear relationship between the water thermal expansion coefficient and the temperature. Such an approach leads to an exhaustive solution in terms of a non linear Rayleigh number. The link is also established with the standard situation where the hypothesis of a linear relationship between density and temperature is applicable. In particular it is shown that the quasi steady state results obtained for a standard situation become equilibrium curves to which the system tends with increasing difference between the temperature of the boundary and 4 °C. A complete numerical solution is obtained for non linear Rayleigh numbers ranging between 0 and 10⁷. Previous numerical and experimental results on the horizontal circular cylinder are also discussed and recast in terms of the present dimensional approach.     

Assessment of the Full Compatibility of Copper(I)-Catalyzed Alkyne-Azide Cycloaddition and Oxime Click Reactions for bis-Labelling of Oligonucleotides

The conjugation of oligonucleotides with reporters is of great interest for improving their intrinsic properties or endowing new ones. In this context, we report herein a new procedure for the bis-labelling of oligonucleotides through oxime ligation (Click-O) and copper(I)-catalyzed alkyne–azide cycloaddition (Click-H). 5′-Azido and 3′-aldehyde precursors were incorporated into oligonucleotides, and subsequent coupling reactions through Click-O and Click-H (or vice versa) were successfully achieved. In particular, we exhaustively investigated the full compatibility of each required step for both tethering strategies. The results demonstrate that click Huisgen and click oxime reactions are fully compatible. However, whilst both approaches can deliver the targeted doubly conjugated oligonucleotide, the route involving click oxime ligation prior to click Huisgen is significantly more successful. Thus the reactions investigated here can be considered to be key elements of the chemical toolbox for the synthesis of highly sophisticated bioconjugates.     

Double-diffusive parallel flow induced in a horizontal Brinkman porous layer subjected to constant heat and mass fluxes: analytical and numerical studies

Fluid flow and heat and mass transfer induced by double-diffusive natural convection in a horizontal porous layer subjected to vertical gradients of temperature and concentration are studied analytically and numerically using the Brinkman-extended Darcy model. Both cases of rigid and free horizontal boundaries are examined in the present study. The parameters governing the problem are the Rayleigh number R_T, the Lewis number Le, the buoyancy ratio N, the Darcy number Da and the aspect ratio Ar. The analytical solution is based on the parallel flow approximation. The critical Rayleigh number corresponding to the onset of the parallel flow in this system is determined analytically as a function of Le, N and Da. For sufficiently small Da, both free and rigid boundaries yield results which are identical to those predicted by the Darcy model. The present investigation shows that there exists a region in the plane (N, Le) where the convective flow is not possible in the layer regardless of the Rayleigh and Darcy numbers considered. Received on 21 December 1998     

Phase-controlling phononic crystals: realization of acoustic Boolean logic gates

A phononic crystal (PC) consisting of a square array of cylindrical polyvinylchloride inclusions in air is used to construct a variety of acoustic logic gates. In a certain range of operating frequencies, the PC band structure shows square-like equi-frequency contours centered off the gamma point. This attribute allows for the realization of non-collinear wave and group velocity vectors in the PC wave vector space. This feature can be utilized to control with great precision, the relative phase between propagating acoustic waves in the PC. By altering the incidence angle of the impinging acoustic beams or varying the PC thickness, interferences occur between acoustic wave pairs. It is recognized that information can be encoded with this mechanism (e.g., wave amplitudes/interference patterns) and accordingly to construct a series of logic gates emulating Boolean functions. The NAND, XOR, and NOT gates are demonstrated with finite-difference time-domain simulations of acoustic waves impinging upon the PC.     

Natural convection in inclined rectangular enclosures with perfectly conducting fins attached on the heated wall

The natural convection heat transfer in inclined rectangular enclosures with perfectly conducting fins attached to the heated wall is numerically studied. The parameters governing this problem are the Rayleigh number (10²≤Ra≤2×10⁵), the aspect ratio of the enclosures (2.5≤A=H′/L′≤∞), the dimensionless lengths of the partitions (0≤B=?′/L′≤1), the aspect ratio of micro-cavities (A≤C=h′/L′≤0.33), the inclination angle (0≤φ≤60^°) and the Prandtl number (Pr=0.72). The results indicate that the heat transfer through the cover is considerably affected by the presence of the fins. At low Rayleigh numbers, the heat transfer regime is dominated by conduction. When B≈0.75 and C≈0.33, the heat transfer through the cold wall decreases considerably. This trend is enhanced when the enclosure is inclined. Useful engineering correlations are derived for practical applications.