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Autocatalytic reaction fronts are able to propagate as a solitary wave, that is at a constant velocity and with a stationary concentration profile which result from a balance between diffusion and chemical reaction. Experiments in thin cells have shown a buoyant instability due to the slightly smaller density of the reacted fluid. We provide an extension of our recent analysis of the Rayleigh-Taylor instability of the interface between two miscible fluids by including the chemical process by a reaction-convection-diffusion approach. The computed dispersion relation as well as our lattice BGK simulations compare reasonably well with the growth rates obtained experimentally.

We study the displacement of miscible fluids of different viscosities (viscosity ratio M) between two parallel plates, using the BGK lattice gas method. At high Peclet numbers, a symmetric interface develops in the gap between the plates. Above M ∼10, the interface becomes a well–defined finger, the reduced width of which tends to λ∞= 0.56 at large M. Assuming that a miscible displacement at high Peclet numbers is equivalent to an immiscible displacement at high capillary numbers, we extend the calculations of Reinelt & Saffman for immiscible fluids, and find the analytical shape of the finger. The result is compared to the celebrated Saffman–Taylor finger.

An apparatus has been constructed to characterize transient fluid displacements in porous media, and probe sedimenting suspensions. The technique used is to propagate an ultrasonic wave in the sample. Both ultrasonic attenuation and velocity are related to the static and hydrodynamic properties of the medium. The system was built so as to perform array imaging (mapping) and tested with different fluids and suspensions. It is suggested that the ultrasonic technique can be suitable whenever transient, low cost and safe saturation and concentration measurements are to be performed.

We study the spatial correlation of one-dimensional (1-D) saturation profiles obtained during slow drainage in porous media, where capillary effects predominate. Using properties of Invasion Percolationin an uncorrelated medium, we compute the correlation structure of the profile. At small values of the lag (but for sufficiently large systems) the profile approaches the structure of the record of a fractional Brownian motion(fBm) with Hurstexponent H=(D-1)/2, where D is the fractal dimension of the percolation cluster. Sufficiently far from percolation, the profile is a white noise. Noise measurements in displacement experiments using an acoustic technique are reported for the 3-D case. The theory is confirmed with 2-D simulations. An apparent mismatch in the 3-D case is attributed to finite-size effects. The approach is generalized to correlated percolation.

We study experimentally and theoretically the downward vertical displacement of one miscible fluid by another lighter one in the gap of a Hele-Shaw cell at sufficiently high velocities for diffusive effects to be negligible. Under certain conditions on the viscosity ratio, M, and the normalized flow rate, U, this results in the formation of a two-dimensional tongue of the injected fluid, which is symmetric with respect to the midplane. Thresholds in flow rate and viscosity ratio exist above which the two- dimensional flow destabilizes, giving rise to a three-dimensional pattern. We describe in detail the two-dimensional regime using a kinematic wave theory similar to Yang & Yortsos (1997) and we delineate in the (M, U)-plane three different domains, characterized respectively by the absence of a shock, the presence of an internal shock and the presence of a frontal shock. Theoretical and experimental results are compared and found to be in good agreement for the first two domains, but not for the third domain, where the frontal shock is not of the contact type. An analogous treatment is also applied to the case of axisymmetric displacement in a cylindrical tube.

Due to technical errors, the figures have been badly printed. We publish entirely the article herein, sincerely apologizing to the authors for the unpleasant inconvenience.

Discusses the increase in the percentage of French students who go on for secondary education. Increased government interest in education; Questioning the quality of education; Private Catholic education.

We study the effect of fluid contact area on viscous coupling in the parallel flow of immiscible fluids in a porous media geometry. We consider flow on opposite sides of a planar interface, consisting of alternating solid and open (slit) segments. We use the analytical solution of Tio and Sadhal [15] to derive explicit expressions for viscous coupling in terms of the fractional area of contact between the fluids and the viscosity ratio,M. ForM=1, the coefficient matrix obtained is symmetric showing that Onsager's relations are satisfied. In this case, the resulting viscous coupling is typically very small, in agreement with recent experimental results. Lattice gas simulations forM=1 using theBGK model support the theoretical results and show that viscous coupling further diminishes as the wall thickness increases. Assuming the same configuration, analytical results are next derived forM?1. The results confirm an existing reciprocity relation between the off-diagonal terms. Viscous coupling remains small.

A drop of ionic ferrofluid, strongly magnetic (μ ∼ 40), exhibits an instability when it is confined between two parallel boundaries perpendicular to the magnetic field direction. Increasing the magnetic field, the drop successively undergoes a deformation, develops pointed feet and splits into two smaller droplets. We present a model of ellipsoidal shapes to account for the magnetic thresholds of deformation and scissions. It is possible to observe eight successive scissions of a single initial drop leading to 256 smaller droplets which arrange themselves in a regular hexagonal array similar to a two dimensional crystal the long-range order of which is optically tested.

Frozen ferrofluids are used as a three-dimensional model system to test experimentally the Néel theory on the magnetic properties of non-interacting fine grains. Subdomain magnetic grains are, chemically synthesized, γ-Fe2O3particles, suspended in an aqueous medium, frozen either at low temperature or using a tight polymeric array. Various magnetic measurements are presented as a function of temperature, T, grain diameter, d, and magnetic field, H. The various regimes corresponding to various orderings of anisotropy, magnetic and thermal motion energies of magnetic moments are investigated. Low field properties, remanence and coercive field variations may all be described with a single reduced parameter θ, the ratio of anisotropy energy to thermal motion energy. A given value, θN, of this parameter limits the range of magnetization reversibility. θNdepends on the time scale of the experiment. Magnetic hysteresis is observed if the relaxation time of the particles is too large to allow magnetic moments to reach a complete equilibrium during the measurement. Onset of magnetic hysteresis is determined by the largest particles in the sample corresponding to a high order moment (≈3) of the size distribution.

Large-scale averaging is important for the description of displacement processes in heterogeneous porous media. For immiscible displacement, a key objective is the determination of effective (pseudo) capillary pressure and phase permeabilities. Present continuum models rely on volume averaging, mixture theories, and homogenization methods, typically under the premise of capillary control. However, such methods are intrinsically unable to provide the local saturation distribution, which is needed for the computation of effective flow properties. In this paper, paralleling pore-level approaches, a percolation method is proposed for the derivation of large-scale properties in a drainage process at low flow rates. Percolation concepts are applied to a macroscopically heterogeneous region with a random and uncorrelated permeability distribution. Appropriate modifications of ordinary and invasion percolation, and percolation with trapping are developed for the determination of the large scale averages. Analytical results are also presented for certain simple cases. We show that for drainage at conditions of local capillary control, when a local description is possible, the large-scale capillary pressure curve is a nontrivial average of the individual curves. Large scale capillary trapping is predicted and a corresponding large-scale trapped saturation is calculated. Large-scale phase premeabilities are also derived. It is found that capillary heterogeneity renders a system more strongly wet in a macroscopic sense. The results are applicable to drainage, but not to imbibition, where a different mode of penetration holds.

We report a study of the inhomogeneities in thin helium films due to the van der Waals potential by a resonant acoustical technique. The van der Waals constant between helium and quartz is estimated to be a=65±5 K (layer)3; the model leads to a solid helium layer on the substrate of the order ofH=2.2a0. A comparison is made with data extracted from interferometric acoustical methods and third-sound type experiments.

Using a technique involving the mechanical resonance of a film at 18 and 9.1 GHz, we have experimentally studied the equation of state of unsaturated helium films nearT?. We show the necessity of modifying the equation and we fit our data with a derivation based on the Ginzburg—Pitaevskii model. Then we deduce the phase diagram of helium films.

We study the displacement of miscible fluids between two parallel plates, for different values of the Péclet number Pe and of the viscosity ratio M. The full Navier–Stokes problem is addressed. As an alternative to the conventional finite difference methods, we use the BGK lattice gas method, which is well suited to miscible fluids and allows us to incorporate molecular diffusion at the microscopic scale of the lattice. This numerical experiment leads to a symmetric concentration profile about the middle of the gap between the plates; its shape is determined as a function of the Péclet number and the viscosity ratio. At Pe of the order of 1, mixing involves diffusion and advection in the flow direction. At large Pe, the fluids do not mix and an interface between them can be defined. Moreover, above M~10, the interface becomes a well-defined finger, the reduced width of which tends to λ∞=0.56 at large values of M. Assuming that miscible fluids at high Pe are similar to immiscible fluids at high capillary numbers, we find the analytical shape of that finger, using an extrapolation of the Reinelt–Saffman calculations for a Stokes immiscible flow. Surprisingly, the result is that our finger can be deduced from the famous Saffman–Taylor one, obtained in a potential flow, by a stretching in the flow direction by a factor of 2.12.