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We analyze the displacement of a viscous fluid by a miscible more viscous one in heterogeneous porous media. We performed lattice Bhatnagar–Gross–Krook simulations, which were previously successfully applied to the study of the dispersion of a passive tracer in a stochastic heterogeneous porous medium. In the present situation, the flow is stable (no viscous fingering) and leads to an overall Gaussian dispersion, the coefficient of which decreases as the viscosity ratio increases. The results are in reasonable agreement with the stochastic approach of Welty and Gelhar.

We consider miscible displacement between parallel plates in the absence of diffusion, with a concentration-dependent viscosity. By selecting a piecewise viscosity function, this can also be considered as 'three-fluid' flow in the same geometry. Assuming symmetry across the gap and based on the lubrication ('equilibrium') approximation, a description in terms of two quasi-linear hyperbolic equations is obtained. We find that the system is hyperbolic and can be solved analytically, when the mobility profile is monotonic, or when the mobility of the middle phase is smaller than its neighbours. When the mobility of the middle phase is larger, a change of type is displayed, an elliptic region developing in the composition space. Numerical solutions of Riemann problems of the hyperbolic system spanning the elliptic region, with small diffusion added, show good agreement with the analytical outside, but an unstable behaviour inside the elliptic region. In these problems, the elliptic region arises precisely at the displacement front. Crossing the elliptic region requires the solution of essentially an eigenvalue problem of the full higher-dimensional model, obtained here using lattice BGK simulations

We revisit the Rayleigh–Taylor instability when the two fluids are miscible and in the geometry of a Hele-Shaw cell. We provide analytical dispersion relations for the particular cases of either a sharp front between the two fluids or of a uniform density gradient stratification and for various fluid flow models, including an unbounded geometry, a two-dimensional gap-averaged Navier–Stokes–Darcy equation, and an effective porous medium. The results are compared to three-dimensional lattice BGK simulations, based on which the relevance of the various models in different wavelength regimes is discussed.

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 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. We present a set of complementary experimental and numerical tools for studying miscible fluid displacements in porous media with large scale heterogeneities. Experiments are realized in transparent 2D Hele-Shaw cells allowing optical observations and in 3D packings of glass beads with an acoustical technique for imaging fluid displacements. Permeability heterogeneities are modeled by spatial variations of either the local aperture of the Hele-Shaw cell or the diameter of the grains used in the packing. The Hele-Shaw cell model provides high resolution maps of the invasion front location at regular time intervals and of the flow lines: the velocity field is determined by combining these informations. Acoustical images of relative concentration distributions in the 3D packing are in agreement with Hele-Shaw cell data and can be obtained in a broader range of experimental situations. Such experiments realized with a stabilizing density contrast between invading and displaced fluids demonstrate a strong reduction of the front width at low flow velocities, a similar reduction is obtained at high velocities with a stabilizing viscosity contrast. The technique is also applicable to study fluid displacements in natural opaque media. Numerical simulations by a Boltzmann lattice technique using a Stokes-like diffusive term to smooth out the effect of permeability discontinuities provide complementary informations. They are shown to give similar results as experiments for same flow parameter values and to allow for a fast exploration of a broad range of fluid properties and flow situations.

We study the downward miscible displacement of a fluid by a lighter and less viscous one in the gap of a Hele-Shaw cell. For sufficiently large velocities, a well-defined interface separates the two fluids. As long as the velocity or the viscosity ratio are below a critical value, the interface has the shape of a tongue symmetric across the gap. For viscosity ratios larger than a critical value, estimated at 1.5, there exists a critical velocity, above which the interface becomes unstable, leading to a new 3D pattern involving regularly spaced fingers of wavelength about 5 times the cell thickness. We delineate the stability diagram.

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.

Nous avons etudie, theoriquement et a l'aide de simulations numeriques, les correlations spatiales des profils de saturation obtenus au cours de l'invasion d'un milieu poreux par une phase non mouillante (drainage). La saturation (concentration volumique) de la phase envahissante est moyennee dans la direction perpendiculaire a l'ecoulement ; cette saturation est ensuite etudiee dans des conditions ou les effets capillaires sont dominants. Ce processus est bien decrit par la Percolation d'Invasion. Pour un milieu sans correlation, on montre que la structure des correlations approche un mouvement Brownien fractionnaire (fractional Brownian motion (fBm)) d' exposant de Hurst H = (D-1)/2, ou D est la dimension fractale de l' amas de percolation. Suffisamment loin du seuil de percolation, la structure des correlations du profil de saturation est decrite par un bruit blanc. Des mesures de bruits au cours d'experiences de deplacement a l'aide d'une technique acoustique ont ete effectuees. A 2-D, la theorie est confirmee par des simulations. A 3-D, la difference entre theorie d'une part et simulations et experience d'autre part est attribuee a des effets de taille finie. Les resultats sont ensuite generalises au cas de la percolation correlee.

We study the stability of the downdip displacement in a porous medium of a dense and viscous fluid by a lighter and less viscous fluid, and vice versa. Conventional predictions based on a Long-Wave (LW) theory lead to identical instability thresholds for the two flows. A Short-Wave (SW) analysis suggests that instability sets in earlier than the LW predictions and that the two thresholds are different in the two flows. Using an acoustic technique in 3D displacements, we have determined these thresholds and the instability diagram. Our data support the SW approach.

We study theoretically and by simulation the spatial correlation of the fluctuations of the transversely averaged fraction of the invading phase in [ital invasion] [ital percolation]. For an uncorrelated lattice, the profile has the correlation structure of the trace of [ital fractional] [ital Brownian] [ital motion] (FBM) with [ital Hurst] exponent [ital H]=[ital D][minus]2 for 3D percolation and [ital H]=[ital D][minus]1.5 for 2D percolation, where [ital D] is the fractal dimension of the percolation cluster. Extension to correlated percolation shows similar results, with the FBM signal displaying [ital persistent] correlations ([ital H][gt]0.5) in 3D and [ital antipersistent] correlations ([ital H][lt]0.5) in 2D percolation. Experiments of nonwetting fluid invasion in porous media confirm the theory in 3D.

Autocatalytic reaction fronts between two reacting species in the absence of fluid flow, propagate as solitary waves. The coupling between autocatalytic reaction front and forced simple hydrodynamic flows leads to stationary fronts whose velocity and shape depend on the underlying flow field. We address the issue of the chemico-hydrodynamic coupling between forced advection in porous media and self-sustained chemical waves. Towards that purpose, we perform experiments over a wide range of flow velocities with the well characterized iodate arsenious acid and chlorite-tetrathionate autocatalytic reactions in transparent packed beads porous media. The characteristics of these porous media such as their porosity, tortuosity, and hydrodynamics dispersion are determined. In a pack of beads, the characteristic pore size and the velocity field correlation length are of the order of the bead size. In order to address these two length scales separately, we perform lattice Boltzmann numerical simulations in a stochastic porous medium, which takes into account the log-normal permeability distribution and the spatial correlation of the permeability field. In both experiments and numerical simulations, we observe stationary fronts propagating at a constant velocity with an almost constant front width. Experiments without flow in packed bead porous media with different bead sizes show that the front propagation depends on the tortuous nature of diffusion in the pore space. We observe microscopic effects when the pores are of the size of the chemical front width. We address both supportive co-current and adverse flows with respect to the direction of propagation of the chemical reaction. For supportive flows, experiments and simulations allow observation of two flow regimes. For adverse flow, we observe upstream and downstream front motion as well as static front behaviors over a wide range of flow rates. In order to understand better these observed static state fronts, flow experiments around a single obstacle were used to delineate the range of steady state behavior. A model using the "eikonal thin front limit" explains the observed steady states.

A viscous lock-exchange gravity current corresponds to the reciprocal exchange of two fluids of different densities in a horizontal channel. The resulting front between the two fluids spreads as the square root of time, with a diffusion coefficient reflecting the buoyancy, viscosity, and geometrical configuration of the current. On the other hand, an autocatalytic reaction front between a reactant and a product may propagate as a solitary wave, namely, at a constant velocity and with a stationary concentration profile, resulting from the balance between molecular diffusion and chemical reaction. In most systems, the fluid left behind the front has a different density leading to a lock-exchange configuration. We revisit, with a chemical reaction, the classical situation of lock-exchange. We present an experimental analysis of buoyancy effects on the shape and the velocity of the iodate arsenous acid autocatalytic reaction fronts, propagating in horizontal rectangular channels and for a wide range of aspect ratios (1/3 to 20) and cylindrical tubes. We do observe stationary-shaped fronts, spanning the height of the cell and propagating along the cell axis. Our data support the contention that the front velocity and its extension are linked to each other and that their variations scale with a single variable involving the diffusion coefficient of the lock-exchange in the absence of chemical reaction. This analysis is supported by results obtained with lattice Bathnagar-Gross-Krook (BGK) simulations Jarrige et al. [Phys. Rev. E 81, 06631 (2010)], in other geometries (like in 2D simulations by Rongy et al. [J. Chem. Phys. 127, 114710 (2007)] and experiments in cylindrical tubes by Pojman et al. [J. Phys. Chem. 95, 1299 (1991)]), and for another chemical reaction Schuszter et al. [Phys. Rev. E 79, 016216 (2009)].

Stable and unstable displacement experiments were performed in millstone and limestone cores. Concentration histories at ten locations along the core samples were obtained by acoustic measurements. Particle‐tracking simulations of the displacements were also made utilizing permeability distributions measured with a permeameter. The combination of experimental observations and simulations indicate that superstable (M

For sufficiently large viscosity ratios and injection rates, miscible displacements in a vertical Hele–Shaw cell at high rates become unstable, leading to three-dimensional (3D) fingering patterns. Below the instability threshold, the base state is 2D in the form of a “tongue” of constant thickness. We apply the long wave Saffman–Taylor stability analysis to find an expression for the threshold of instability as a function of the viscosity ratio and the injection rate. The results are in agreement with the experimental data.

We present a numerical analysis of solutal buoyancy effects on the shape and the velocity of autocatalytic reaction fronts, propagating in thin tilted rectangular channels. We use two-dimensional (2D) lattice Bathnagar-Gross-Krook (BGK) numerical simulations of gap-averaged equations for the flow and the concentration, namely a Stokes-Darcy equation coupled with an advection-diffusion-reaction equation. We do observe stationary-shaped fronts, spanning the width of the cell and propagating along the cell axis. We show that the model accounts rather well for experiments we performed using an Iodate Arsenous Acid reaction propagating in tilted Hele-Shaw cells, hence validating our 2D modelization of a three-dimensional problem. This modelization is also able to account for results found for another chemical reaction (chlorite tetrathionate) in a horizontal cell. In particular, we show that the shape and the traveling velocity of such fronts are linked with an eikonal equation. Moreover, we show that the front velocity varies nonmonotonically with the tilt of the cell, and nonlinearly with the width of the cell.

The growth of viscous fingers inside three‐dimensional (3‐D) porous media is studied using an acoustic technique to determine the concentration profile. Three different porous media and a wide range of viscosity ratios and flow rates have been considered. The experimental data support the definition of an instability parameter that characterizes the essential features of the viscous fingering phenomenon. The dependence of this parameter on viscosity ratio, flow rate, and the nature of the medium is compared to theoretical predictions made using a continuum approach. The data demonstrate the predicted crossover between diffusive and linear growth, and the increase of the instability with heterogeneity. The enhancement of the growth rate due to the coupling between large viscosity ratio and velocity‐dependent hydrodynamic dispersion is also observed.

We have studied experimentally the electrical fluctuations which result when colloidal particles suspended in an electrolyte flow through a current carrying pore. A pressure difference across the pore sets up a Poiseuille flow that transports particles through the pore at low Reynolds numbers. The shape of the power spectrum depends on the particle transit time distribution, and the amplitude is proportional to the particle concentration, the particle size, and the average transit time. We cover the size range from large particle sizes, where distinct electrical particle pulses can be observed, to small particles, where individual particles can no longer be characterized. The aim of this work is to explore the particle flow noise in the transition from macroscopic to microscopic particle sizes, allowing the determination of particle size and concentration, and with applications to flow properties on the pore level, relevant to, for instance, flow in natural porous media.

The onset of viscous instability and the subsequent fingering have been mostly studied under conditions of a sharp mobility contrast. In stable miscible flows in porous media, however, mobility gradients of variable extent can develop due to hydrodynamic dispersion. Graded mobility and density profiles will affect instabilities, either by mitigating (in the case of a monotonic variation) or by enhancing (nonmonotonic variation) the rates of growth. The mitigating effect was exploited by Claridge and Gorrel and Homsy for the optimal design of graded mobility banks. Hickernell and Yortsos showed that in the linear stability limit, the growth rate is controlled by the maximum of the logarithmic derivative of the mobility profile. We present an experimental study of miscible displacements in porous media to study effects of mobility gradients in viscous instability. We take advantage of molecular diffusion in miscible displacements to create a mobility gradient zone and subsequently initiate the instability b...

Anomalous dispersion refers to concentration profiles that exhibit long‐time tails as opposed to normal or Gaussian dispersion, which does not exhibit such tails. An original acoustic technique has enabled experimentally the demonstration that, in an unsaturated porous medium, the observed non‐Gaussian dispersion is due only to finite‐size effects: the sample length is set too small to achieve a statistical Gaussian random walk. An accurate fit to the data with a semiphenomenological model is suitable for comparison with a nonlocal theory concerning this transient effect. Thus the mechanism involved in the dispersion process, and also, the characteristic length of this dispersion, can be determined.

We address the question of using a lattice gas method to study flows of complex fluids, such as non‐Newtonian or miscible fluids. A Bhatnagar, Gross, and Krook lattice technique provides a tool to simulate the flow of one fluid and the diffusion of a tracer in that fluid. We extend the technique to flows in which the viscosity is space and time dependent. This approach is suitable for non‐Newtonian fluids (shear dependent viscosity) and miscible fluids (concentration dependent viscosity). The modified scheme is tested on physical flow situations, analytically tractable for the sake of comparison.

Autocatalytic reaction fronts between unreacted and reacted mixtures in the absence of fluid flow propagate as solitary waves. In the presence of imposed flow, the interplay between diffusion and advection enhances the mixing, leading to Taylor hydrodynamic dispersion. We present asymptotic theories in the two limits of small and large Thiele modulus (slow and fast reaction kinetics, respectively) that incorporate flow, diffusion, and reaction. For the first case, we show that the problem can be handled to leading order by the introduction of the Taylor dispersion replacing the molecular diffusion coefficient by its Taylor counterpart. In the second case, the leading-order behavior satisfies the eikonal equation. Numerical simulations using a lattice gas model show good agreement with the theory. The Taylor model is relevant to microfluidics applications, whereas the eikonal model applies at larger length scales.

Change-of-type behavior from hyperbolic to elliptic is common to quasilinear hyperbolic systems. This issue is addressed here for the particular case of miscible flow of three fluids between two parallel plates. Change of type occurs at the leading edge of the displacement front and reflects the failing of the equilibrium assumption, necessary for the quasilinear hyperbolic formalism, at the front. To cross the elliptic region requires the solution of the full, higher-dimensionality problem, obtained here using lattice gas simulations. For the specific example, it is found that the system self-selects a front structure independent of injection conditions.

[1] We use the extended Darcy's law, which also accounts for the Brinkman correction, to study macrodispersion in a two-dimensional (2-D) porous medium. The former is necessary when permeability changes fast at a relatively small scale, and in general, it is a more complete description of flow in a heterogeneous medium. Lattice-gas methods are ideally suited to simulate such flows. Simulations using a lattice BGK method and a small-fluctuation approach are described for an isotropic, exponentially decaying correlation function of the permeability field. The analytical results contain the additional parameter Kl/λ2 (where Kl and λ are the typical permeability and velocity variation length, respectively), the sensitivity to which was studied. As expected, the contribution of the Brinkman effect is insignificant for typical field values of this parameter, in which case, the classical results are recovered. At larger values, for example, for heterogeneous media of a small correlation length, and possibly in laboratory applications, the Brinkman correction leads to a decrease in macrodispersivity, reflecting the smoothing effect of the Brinkman correction on the velocity field. Nonetheless, for practical values of the parameters, this reduction is no larger than 50% of the classical expression. The small fluctuation theory was found to be in good agreement with the simulations, provided that it was consistently applied (namely, by not mixing first-order with second-order expansions). The results also show that lattice-gas simulations can be usefully employed to study macrodispersion in heterogeneous porous media.

Hydrodynamic dispersion is responsible for the spreading of the sedimentation front even in a noncolloidal monodisperse suspension. Measurements of the broadening of the top front observed during sedimentation have been used in determining the hydrodynamic dispersion coefficient. Hindered settling has an opposed effect and leads to the self‐sharpening of the front. Both effects have to be taken into account simultaneously. This Letter provides a simple, but complete determination of the space and time concentration profile and shows that the final front should consist of a steady‐shape profile propagating at constant velocity. With such a solution, the data of Davis et al. [AIChE J. 34, 123 (1988); J. Fluid Mech. 196, 107 (1988)] give hydrodynamic dispersion coefficient five times larger than their former analysis, in agreement with Lee et al. [Phys. Fluids A 4, 2601 (1992)].

Autocatalytic reaction between reacted and unreacted species may propagate as solitary waves, namely at a constant front velocity and with a stationary concentration profile, resulting from a balance between molecular diffusion and chemical reaction. The effect of advective flow on the autocatalytic reaction between iodate and arsenous acid in cylindrical tubes and Hele-Shaw cells is analyzed experimentally and numerically using lattice BGK simulations. We do observe the existence of solitary waves with concentration profiles exhibiting a cusp and we delineate the eikonal and mixing regimes recently predicted., 4 pages, 3 figures. This paper report on experiments and simulations in different geometries which test the theory of Boyd Edwards on flow advection of chemical reaction front which just appears in PRL (PRL Vol 89,104501, sept2002)

An autocatalytic reaction-diffusion front between two reacting species may propagate as a solitary wave, namely, at constant velocity and with a stationary concentration profile. Recent experiments on such reactions have been reported to be buoyancy unstable, under certain conditions. We calculate the linear dispersion relation of the resulting instability, by applying our recent analysis of the Rayleigh-Taylor instability of two miscible fluids in a Hele-Shaw cell. The computed dispersion relation as well as our three-dimensional lattice Bhatnagar-Gross-Krook (BGK) simulations fit reasonably well experimental growth rates reported previously.

The parallel flow of one or two fluids of contrasted viscosities through a rectangular channel of large aspect ratio is studied. The usual result for an infinite aspect ratio is that the velocity profile is parabolic throughout the gap and flat in the other direction. For a finite aspect ratio a deviation from this usual profile is found in boundary layers along the edges of the channel or close to the interface. The extension of these boundary layers is of the order of the small dimension of the channel. In the two-fluid case we find, however, that the velocity profile at the interface is strictly a parabola. The velocity profiles obtained by a 3-D lattice BGK simulation are successfully compared to the analytical results in the one- and two-fluid cases.

Abstract We investigate effects of capillary heterogeneity induced by variations in permeability in the direction of displacement in heterogeneous porous media. The investigation is three-pronged and uses macroscopic simulation, based on the standard continuum equations, experiments with the use of an acoustic technique and pore network numerical models. It is found that heterogeneity affects significantly the saturation profiles, the effect being stronger at lower rates. For drainage, a good agreement is found between continuum model predictions, experimental results and the pore network numerical models based on which it can be concluded that capillary heterogeneity effects in the direction of displacement act much like a body force (e.g. gravity). The results are interpreted with the use of invasion percolation concepts. For secondary imbibition, a poorer agreement exists between continuum model and experimental results at low capillary numbers, which requires the use of a pore network simulator involving film flow. Numerical simulation results are discussed for 2-D geometries. INTRODUCTION In displacement processes in porous media, such as oil reservoirs, of particular significance is the inherent heterogeneity of medium properties. While recognized in early studies, a systematic investigation of the effects of heterogeneity has been undertaken mostly during the last decade [1]. In immiscible displacement, pore-scale studies led to statistical tools such as Invasion Percolation (IP) and Diffusion-Limited-Aggregation (DLA) [2]. In miscible displacement, large-scale investigations led to classifications of flow regimes in terms of correlation length, degree of heterogeneity and mobility ratio [3], [4]. The emphasis on miscible displacement (for an exception, see [5]) reflects the premise that on a large scale, differences between immiscible and miscible displacements are minimal. However, this depends on geometric and flow properties. In immiscible displacement at sufficiently low capillary numbers, for example, permeability gradients have effects similar to gravity, leading to gradient percolation patterns (both stable and unstable) [6]; sharp changes in permeability in the direction of flow significantly change steady-state saturation profiles [7]; random distribution of permeabilities attributes large-scale percolation features (such as large-scale trapping) to displacements [8]; while correlated fields drastically alter the percolation aspects of the displacement [9]. All these capillary effects are driven by permeability heterogeneity and they are absent in miscible displacement.

Viscous fingering resulting from unstable fluid displacements in porous media has been studied extensively over the last forty years since the pioneering experiments of Hill1. Recent reviews on this subject by Homsy2 and Yortsos3 are available as well as on the special issue of the Saffman-Taylor4 finger in a Hele-Shaw cell by Bensimon et al.5. Most of the papers on viscous fingering deal with immiscible fluids, but indeed the problem involving miscible fluids deserves at least as much attention as the immiscible case: as in the immiscible case, the unfavorable viscosity ratio (displacing fluid less viscous than the displaced one) generates the instability but here the stabilizing effect is due to the hydrodynamic dispersion which tends to spread out growing fingers. Dispersion is more subtle than interfacial tension. Further, it is anisotropic and flow dependent which leads to new predictions6–12 such as a cross-over between diffusive and linear growth regimes7, 12 and an enhancement of the instability due to the interplay between the large viscosity ratio and the velocity dependent hydrodynamic dispersion9. Experiments are scarce1, 13–18 and deal generally with a pseudo 2D geometry involving qualitative visualization. In this paper, we use a newly developed acoustic technique19–21 to carry out the first study of the profiles of viscous fingers in 3D porous media. Our experiments have been performed out on three different porous media with a wide range of viscosity ratios and flow rates. Both the diffusive and the linear growth are observed including the cross-over from one to the other. Taken together, our data are best understood in terms of a new instability parameter, that characterizes the main features of viscous fingering. Our determination of the dependence of this parameter on the viscosity ratio, the flow rate and on the porous medium when placed in the context of existing theory leads to new physical insights on this rich and varied problem.

Autocatalytic reaction fronts between reacted and unreacted species may propagate as solitary waves, that is, at a constant front velocity and with a stationary concentration profile, which result from a balance between molecular diffusion and chemical reaction. A velocity field in the supporting medium may affect the propagation of such fronts through different phenomena: advection, diffusion enhancement, front shape changes, etc. Here, we report on an experimental study and lattice Bhatnagar–Gross–Krook numerical simulations of the effect of an oscillating flow on the autocatalytic reaction between iodate and arsenous acid in a Hele–Shaw cell. In the low frequency range covered by the experiments, the front behavior is controlled by the flow across the gap and is reproduced with two-dimensional numerical simulations. It is shown that the front velocity oscillates at the frequency of the flow, whereas the front width oscillates at twice that frequency. Moreover, the Taylor regime in the presence of a Poi...

We report on experiments with two miscible fluids of equal density but different viscosities. The fluids were injected co-currently and concentrically into a cylindrical pipe. The resulting base state is an axisymmetric parallel flow. The ratio of the two fluid flow rates determines the relative amount of the fluids, thus the radius of the inner core fluid. Depending on this radius and the total flow rate, two different and unstable axisymmetric patterns, denoted by mushrooms and pearls, were observed. We delineate the diagram of occurrence of the two patterns as a function of the various parameters.

By means of an acoustic technique, we follow the time and space dependence of the concentration of a settling suspension composed of spherical glass beads in water. The concentration profile consists of two shock fronts, one at the top, one at the bottom of the sedimentation column. The velocity determination of these two fronts allows a precise analysis of how the settling velocity for suspension concentrations close to the packing vanishes.

Grâce a une technique acoustique, on a mesure la dispersion longitudinale de fluides miscibles dans des milieux poreux desordonnes pour une large gamme de nombres de Peclet. La dispersion hydrodynamique est toujours gaussienne quelque soit le debit, l'echantillon et sa longueur