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La lecture que fait Michel de Certeau du livret des Exercices, dans ses articles de la revue Christus, s'inscrit dans le sillage de l'interpretation que venait d'en donner le philosophe Gaston Fess...

We analyze experimentally the behavior of a non-Brownian, iso-dense suspension of spheres submitted to periodic square wave oscillations of the flow in a Hele-Shaw cell of gap H. We do observe an instability of the initially homogeneous concentration in the form of concentration variation stripes transverse to the flow. The wavelength of these regular spatial structures scales roughly as the gap of the cell and is independent of the particle concentration and of the period of oscillation. This instability requires large enough particle volume fractions and a gap large enough compared to the sphere diameter . Mapping the domain of the existence of this instability in the space of the control parameters shows that it occurs only in a limited range of amplitudes of the fluid displacement. The analysis of the concentration distribution across the gap supports a scenario of particle migration towards the wall followed by an instability due to a particle concentration gradient with a larger concentration at the walls. In order to account for the main features of this stripes instability, we use the theory of longitudinal instability due to normal stresses difference and recent observations of a dependence of the first normal stresses difference on the particle concentration. Fil: Roht, Yanina Lucrecia. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Física. Grupo de Medios Porosos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Université Paris Sud; Francia. Centre National de la Recherche Scientifique; Francia Fil: Ippolito, Irene Paula. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Física. Grupo de Medios Porosos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Hulin, J. P.. Centre National de la Recherche Scientifique; Francia. Université Paris Sud; Francia. Université Paris-Saclay; Francia Fil: Salin, D.. Université Paris Sud; Francia. Centre National de la Recherche Scientifique; Francia. Université Paris-Saclay; Francia Fil: Gauthier, G.. Centre National de la Recherche Scientifique; Francia. Université Paris Sud; Francia. Université Paris-Saclay; Francia

We develop a pore network model for the evaporative drying of macroporous media that accounts for the major pore-scale mechanisms experimentally identified to play an important role on the drying rates and phase distribution patterns. The model accounts for viscous flow through liquid films, gravity and mass transfer, both within the dry medium and also through a mass boundary layer over the external surface of the medium. Also accounted are the heterogeneity of the pore size distribution and pore wall microstructure effects expressed through the degree of corner roundness. The latter plays a major role on the extent of the film region. The model is then used to study capillary, gravity and external mass transfer effects through the variation of the appropriate dimensionless numbers. The effect of gravity is particularly analyzed for the two cases, when gravity is opposing and when it is enhancing drying, respectively. In the latter case, strong mass transfer and viscous forces compared to gravity can prevent instability of the receding evaporation front, leading to a two constant-rate-regime drying curve in agreement with the 1-D theory proposed earlier.

Ammonia toxicity in the Siberian sturgeon, Acipenser baerii, a fresh water fish, was studied under controlled conditions of pH, temperature and ammonia concentrations in water.The effects of ammonia during a 72-h exposure to lethal and sublethal doses were examined on the morphology of branchial epithelium. Some hypertrophies and necrosis were observed in proportion with the ammonia doses.Ammonia has no effect on haematological characteristics except for the [K+] plasmatic concentration and the erythrocyte volume for lethal levels of ammonia.Among the numerous hypotheses to explain ammonia toxicity on fish, some refer to oxygen transport and oxygen affinity of the blood. In fact, the partial pressure of oxygen in the blood (PaO2) decreases significantly for a lethal dose only. Moreover, the influence of ammonia on oxyphoric properties of red blood cells of Siberian sturgeon has been investigated in vivo (blood of fish exposed for 72 h to 4.5 mmol L−1 total ammonia, a lethal concentration) and in vitro (ammonia added to blood of control fish). Whatever the experimental conditions, ammonia did not modify the affinity of haemoglobin for oxygen illustrated by P50, Bohr effect, Hill number and percentage of methaemoglobin. Consequently, the toxicity of ammonia on Siberian sturgeon cannot be explained by an alteration of the gill morphology, the ionic exchanges or the oxygen-binding properties of the haemoglobin only.

Neurological disorders appear extremely rapidly for elevated doses of ammonia in Siberian sturgeon baerii. To explain this phenomenon, the effects of ammonia during a 72-h exposure in control conditions and for a lethal and a sublethal doses were examined on the concentration of free amino-acids and adenyl nucleotides in the Siberian sturgeon plasma, muscle and brain.

The ammonia concentration was studied in the blood of the Siberian sturgeon, Acipenser baerii, with and without high concentration in water. In control conditions, the ammonia excretion was mainly due to NH3 diffusion according to the partial pressure gradient. So the distribution of the total ammonia followed the pH gradient between water and blood. After exposure to high concentration of ammonia, the blood concentration increased quickly during the early hours and a metabolic alkalosis appeared. PNH3 was stabilized after less than 24-h exposure, while the total ammonia concentration increased continuously as blood pH returned to initial values. If we take into account the real pH in the branchial boundary layer and not in the water of the circuit to calculate PNH3, we could conclude that the evolution of the blood ammonia concentration could be explained by NH3 diffusion along its partial pressure and that the ammonia exchanges by simple diffusion were dominant. However, whatever the ammonia concentration in water, the fish quickly reached a PNH3 equilibrium with the water and seemed incapable of preventing the invasion of the blood by ammonia. That also explained the initial metabolic alkalosis. But these results did not allow to attribute the ammonia toxicity to NH3.

The initial aim of this work was to situate the sensitivity of the Siberian sturgeon (Acipenser baerii B.) to ammonia compared with other species. Ammonia toxicity in the Siberian sturgeon was analysed, and the 24 h LC50 was performed for different weight groups. This sensitivity is currently determined by normalized tests of short duration, even if their practical application is difficult. During exposure to high levels of ammonia, we also observed alterations of the branchial tissue and modifications in haematological characteristics, in the behaviour of the fishes and tetany. Thus, the interpretation of these observations remains difficult, and we propose an experimental protocol under controlled conditions of pH, oxygen partial pressure PO2, carbon dioxide partial pressure PCO2, temperature and ammonia concentrations in water for 72 h duration to perform additional experiments in physiology and biochemistry.

The instability of an iso-dense non-Brownian suspension of polystyrene beads of diameter 40 μm dispersed in a water-glycerol mixture submitted to a periodic square wave oscillating flow in a Hele-Shaw cell is studied experimentally. The instability gives rise to stationary bead concentration waves transverse to the flow. It has been observed for average particle volume fractions between 0.25 and 0.4, for periods of the square wave flow variation between 0.4 and 10 s and in finite intervals of the amplitude of the fluid displacement. The study shows that the wavelength λ increases roughly linearly with the amplitude of the oscillatory flow; on the other hand, λ is independent of the particle concentration and of the period of oscillation of the flow although the minimum threshold amplitude for observing the instability increases with the period. Fil: Roht, Yanina Lucrecia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Física. Grupo de Medios Porosos; Argentina. Universite de Paris Xi. Laboratoire Automatiques et Systeme Thermiques; Francia Fil: Gauthier, Catherine. Universite de Paris Xi. Laboratoire Automatiques et Systeme Thermiques; Francia Fil: Hulin, J. P.. Universite de Paris Xi. Laboratoire Automatiques et Systeme Thermiques; Francia Fil: Salin, D.. Universite de Paris Xi. Laboratoire Automatiques et Systeme Thermiques; Francia Fil: Chertcoff, Ricardo Héctor. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Física. Grupo de Medios Porosos; Argentina Fil: Auradou, H.. Universite de Paris Xi. Laboratoire Automatiques et Systeme Thermiques; Francia Fil: Ippolito, Irene Paula. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Física. Grupo de Medios Porosos; Argentina

We report on numerical studies of avalanches of an autocatalytic reaction front in a porous medium. The front propagation is controlled by an adverse flow resulting in upstream, static, or downstream regimes. In an earlier study focusing on front shape, we identified three different universality classes associated with this system by following the front dynamics experimentally and numerically. Here, using numerical simulations in the vicinity of the second-order transition, we identify an avalanche dynamics characterized by power-law distributions of avalanche sizes, durations, and lateral extensions. The related exponents agree well with the quenched-Kardar-Parisi-Zhang theory, which describes the front dynamics. However, the geometry of the propagating front differs slightly from that of the theoretical one. We show that this discrepancy can be understood in terms of the nonquasistatic correction induced by the finite front velocity.

We address the issue of the convective or absolute nature of the instability of core-annular pipe flows, in experiments using two miscible fluids of equal density but different viscosities, the core fluid being much less viscous than the wall one. We use a concentric co-current injection of the two fluids. An axisymmetric parallel base state is obtained downstream the injector. The core radiusRIand the Reynolds numberReof the so-obtained base state are varied independently due to the control of the flow rate of each fluid. However, a downstream destabilization of this base state was observed within the explored range of the two control parametersRIandRe. Moreover, the fixed location of this destabilization, observed for some particular parameters, suggests an absolute nature of the instability. We present a tentative delineation of the nature (convective or absolute) of the instability and discuss the accessible measurements to experimentally address this issue.

International audience; Self-sustained reaction fronts in a disordered medium subject to an external flow display self-affine roughening, pinning and depinning transitions. We measure spatial and temporal fluctuations of the front in $1+1$ dimensions, controlled by a single parameter, the mean flow velocity. Three distinct universality classes are observed, consistent with the Kardar-Parisi-Zhang (KPZ) class for fast advancing or receding fronts, the quenched KPZ class (positive-qKPZ) when the mean flow approximately cancels the reaction rate, and the negative-qKPZ class for slowly receding fronts. Both quenched KPZ classes exhibit distinct depinning transitions, in agreement with the theory.

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.

Buoyant mixing of two fluids in tubes is studied experimentally as a function of the tilt angle θ from vertical, the density contrast and the common viscosity μ. At high contrasts and low θ, longitudinal mixing is macroscopically diffusive, with a diffusivity D increasing strongly with θ and μ. At lower contrasts and higher θ, a counterflow of the two fluids with little transverse mixing sets in. The transition occurs at an angle increasing with density contrast and decreasing with μ. These results are discussed in terms of the dependence of transerse mixing on θ and an analogy with the Boycott effect.

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 study the Brinkman correction to Darcy’s equation for unidirectional flows in a Hele-Shaw cell. Three examples, describing gravity-driven flow with variable density, pressure-driven flow with variable viscosity, and pressure-driven flow in a cell with a specific variation in aperture are discussed. In general, the Brinkman correction involves nonlocal terms, and it is not simply equal to an effective viscous shear stress involving the gap-averaged velocity. The latter is applicable at long wavelengths, however, provided that the viscosity is augmented by a prefactor equal to 12/π2.

Apres s’etre cherchee dans les apories du pur amour, c’est dans « l’abandon a la Providence » que s’est reconnue la mystique moderne a la fin du XIXe siecle – a l’epoque precisement ou la main de Dieu devenait de moins en moins lisible dans l’histoire. Le traite de L’Abandon et la litterature qu’il ne cesse d’inspirer depuis, invitent a passer de la consideration de l’histoire comme lieu de manifestation d’une volonte (celle de Dieu Providence), a la concentration sur l’instant present comme exercice d’union a Dieu dans « l’indifference », gage de paix et de joie indicibles. L’abandon mystique au « sacrement du moment present » deplace ainsi le terrain de la theodicee. Face a l’apparente inertie divine devant le triomphe des « ennemis de Dieu », la charge de la preuve d’innocence ne revient plus a Dieu mais au sujet mystique. C’est la qualite de son abandon qui devrait valoir, aux yeux des autres, theodicee, justification de la bonte de Dieu, de sa bienveillance, de sa providence. Le Dieu des mystiques n’a decidement rien a voir avec le Destin, meme sous sa forme christianisee, la Providence : il est liberte, libre volonte, evenement, naissance, aventure.

We study two asymptotic regimes of unstable miscible displacements in porous media, in the two limits, where a permeability-modified aspect ratio, RL=L/H(kv/kh)1/2, becomes large or small, respectively. The first limit is known as transverse (or vertical) equilibrium, the second leads to the problem of non-communicating layers (the Dykstra–Parsons problem). In either case, the problem reduces to the solution of a single integro-differential equation. Although at opposite limits of the parameter RL, the two regimes coincide in the case of equal viscosities, M=1. By comparison with high-resolution simulation we investigate the validity of these two approximations. The evolution of transverse averages, particularly under viscous fingering conditions, depends on RL. We investigate the development of a model to describe viscous fingering in weakly heterogeneous porous media under transverse equilibrium conditions, and compare with the various existing empirical models (such as the Koval, Todd–Longstaff and Fayers models).

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.

The injection of reactive mineral suspensions is a possible process to either reinforce or seal wells in geologic carbon sequestration sites. Among others, olivine slurries could be used as CO2-triggered cements, as they carbonate under the thermodynamic conditions of deep storage. However, injection of such slurries requires to control their initial fluidity and its evolution during the displacement. For this purpose, we have characterized the rheological evolution of olivine suspensions, of particle sizes 1−10 μm, sheared at 100 s−1, in the ranges of 10−40% for the volume fractions, 20−50 bars for the CO2 pressure, and 60–110°C for the temperature. The apparent viscosity, measured at 100 s−1, increases exponentially, with a characteristic time ranging from less than 1 h to more than 10 h, and decreasing with olivine concentration, CO2 pressure, and temperature. Moreover, a careful characterization of the slurry rheology carried out in the initial stages of slow evolution, shows that the slurry obeys a Bingham plastic law, with a yield stress ΣB, and a Bingham viscosity µB increasing from 1 to 20 Pa and from 4 to 110 mPa s, respectively, when the olivine volume fraction φ is increased from 10 to 30%. Such variations can be accounted by classical models (Wildemuth and Williams [1984]: Rheologica Acta, 23,627–635, Krieger [1972]: Advances in Colloid and Interface Science, 3, 111–136). © 2013 American Institute of Chemical Engineers Environ Prog, 33: 572–580, 2014

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.

Despite significant progress made in recent years, a fundamental understanding of immiscible displacements at the macroscale is lacking. In this paper we use a version of percolation theory, based on invasion percolation in a gradient, to connect drainage processes at the pore-network scale with the displacement at the macroscale. When the mobility ratio M is sufficiently small, the displacement is stabilized and can be described by invasion percolation in a stabilizing gradient. In the opposite case, it has common features with invasion percolation in a destabilizing gradient. A diagram delineating the regimes of fully developed drainage is developed. The transition between stabilized displacement and fingering is controlled by the change of the sign of the gradient of the percolation probability, and the transition boundary is described by a scaling law involving the capillary number and the viscosity ratio. We review recent work for random networks and extend the method to correlated pore networks. As the regimes of stabilized displacement are also those for which conventional theories (such as the Buckley–Leverett equation) are expected to apply, the phase diagram helps to delineate their validity.

Non-Brownian sedimenting suspensions exhibit density and velocity fluctuations. We have performed experiments on a quasi-two-dimensional counter-flow stabilized suspension of 2000 spherical particles, namely a liquid–solid fluidized bed in a Hele–Shaw cell. This two-dimensional suspension displays a uniform concentration but the particle radial distribution function and the fluctuations of the particle number in a subvolume of the suspension suggest that the microstructure is far from being random. We have also measured the velocity fluctuations of a test particle and the fluctuations of the mean particle velocity in a subvolume. It happens that the relation between velocity and concentration fluctuations in a subvolume can be deduced from a balance between buoyancy and parietal friction forces.

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.

We study experimentally the hydrodynamic-interaction-controlled random walk (RW) of noncolloidal spheres in a quasi-2D fluidized suspension. This macroscopic ``molecular'' system is anisotropic. Particle trajectories are Brownian-like and, from time to time, fast upward correlated. The vertical RW is hyperdiffusive, but the horizontal one is Gaussian. Velocity fluctuation distributions vary from Gaussian to exponential as particle concentration $C$ increases. The dynamics varies from liquidlike to gaslike as $C$ decreases. These features are attributed to the formation of ``transient channels'' at higher $C$.

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.

Tamoxifen is widely used to treat oestrogen-dependent carcinoma of the breast. Previous long-term studies have shown that oral administration of tamoxifen induces hepatoproliferative lesions and hepatocellular tumours in rats. 4-hydroxytamoxifen is an active metabolite of tamoxifen undergoing clinical evaluation for the treatment of various non-malignant breast diseases by topical application. In the present study, 4-hydroxytamoxifen was administered daily by cutaneous application for 101 weeks to groups of 50 female Sprague-Dawley rats at 20, 140 or 1000 microg/kg/day. The product was applied with no occlusive bandage and oral ingestion was avoided by application of an Elizabethan collar for 6 h after administration. Treatment with 4-hydroxytamoxifen was clinically well tolerated and induced changes such as decreased food consumption and body weight gain, uterine and ovarian atrophy, mucification of vaginal epithelium and reduced mammary development, all of which were attributed to its pharmacological action. Mortality was significantly lower in the treated animals. The number of animals with palpable masses was similarly reduced. The incidence of mammary tumours and hypophyseal tumours was markedly lower in 4-hydroxytamoxifen-treated animals. The incidence of chronic tubulo-interstitial nephropathies, a common cause of mortality, was also lowered. There was no evidence of a carcinogenic action of 4-hydroxytamoxifen on the liver, genital organs or skin. Plasma levels of 4-hydroxytamoxifen were stable over the duration of the study and were proportional to the administered dose, exceeding clinical plasma levels by 60-fold at the high dose-level. In conclusion, 4-hydroxytamoxifen is not carcinogenic in the rat and reduces the incidence of spontaneous mammary and hypophyseal tumours.

We study invasion percolation in the presence of viscous forces, as a model of the drainage of a wetting fluid from a porous medium. Using concepts from gradient percolation, we consider two different cases, depending on the magnitude of the mobility ratio $M.$ When $M$ is sufficiently small, the displacement can be modeled by a form of gradient percolation in a stabilizing gradient, involving a particular percolation probability profile. We develop the scaling of the front width and the saturation profile, in terms of the capillary number. In the opposite case, the displacement is described by gradient percolation in a destabilizing gradient and leads to capillary-viscous fingering. This regime is identified in the context of viscous displacements and in general differs from diffusion-limited aggregation, which also describes displacements at large $M.$ Constraints for the validity of the two regimes are developed. Limited experimental and numerical results support the theory of stabilized displacement. The effect of heterogeneity is also discussed.

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.

Using concepts of invasion percolation in a gradient, we develop a phase diagram of fully developed drainage in porous media. The transition between stabilized displacement (where the conventional continuum applies) and fingering is controlled by the change of the sign of the gradient of the percolation probability (from stabilizing to destabilizing). The transition boundary is described by scaling laws. {copyright} {ital 1997} {ital The American Physical Society}

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.

We analyze experimentally chemical waves propagation in the disordered flow field of a porous medium. The reaction fronts travel at a constant velocity which drastically depends on the mean flow direction and rate. The fronts may propagate either downstream and upstream but, surprisingly, they remain static over a range of flow rate values. Resulting from the competition between the chemical reaction and the disordered flow field, these frozen fronts display a particular sawtooth shape. The frozen regime is likely to be associated with front pinning in low velocity zones, the number of which varies with the ratio of the mean flow and the chemical front velocities. PACS numbers

We study the dynamics of nonwetting liquid blobs during immiscible two-phase flows in stochastically reconstructed porous domains predominantly saturated by a wetting fluid. The flow problem is solved explicitly using a Lattice-Boltzmann model that captures both the bulk phase and interfacial dynamics of the process. We show that the nonwetting blobs undergo a continuous life cycle of dynamic breaking up and coalescence producing two populations of blobs, a mobile and a stranded one, that exchange continuously mass between them. The process reaches a “steady state” when the rates of coalescence and breaking up become equal, and the macroscopic flow variables remain practically constant with time. At steady state, mass partitioning between mobile and immobile populations depends strongly on the applied Bond number Bo and the initial nonwetting phase distributions. Three flow regimes are identified: a single-phase flow Darcy-type regime at low Bo numbers, a non-Darcy two-phaseflow regime at intermediate values of Bo, where the capillary number scales as Ca ∝ Bo 2 , and a Darcy-type two-phase flow regime at higher values of Bo. Our numerical results are found to be in good agreement with recent experimental and theoretical works.

We study miscible fluid displacement in heterogeneous porous media, in the presence of gravity, where the heterogeneity consists of multiple layers. Miscible fluids of different density and viscosity contrasts are used, such that the displacement is hydrodynamically stable. Depending on the values of the control parameters, the overall fluid displacement exhibits either an enhancement of the effect of heterogeneity or a damping. For a sufficiently large viscosity and/or density contrast, the effect of heterogeneity is overcome and the multi-layer system behaves as a single homogeneous layer. We determine experimentally an associated phase diagram and compare our data to a theoretical model valid for systems of large aspect ratio.

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.

The extension of a gravity current in a lock-exchange problem, proceeds as square root of time in the viscous-buoyancy phase, where there is a balance between gravitational and viscous forces. In the presence of particles however, this scenario is drastically altered, because sedimentation reduces the motive gravitational force and introduces a finite distance and time at which the gravity current halts. We investigate the spreading of low Reynolds number suspension gravity currents using a novel approach based on the Lattice-Boltzmann (LB) method. The suspension is modeled as a continuous medium with a concentration-dependent viscosity. The settling of particles is simulated using a drift flux function approach that enables us to capture sudden discontinuities in particle concentration that travel as kinematic shock waves. Thereafter a numerical investigation of lock-exchange flows between pure fluids of unequal viscosity, reveals the existence of wall layers which reduce the spreading rate substantially compared to the lubrication theory prediction. In suspension gravity currents, we observe that the settling of particles leads to the formation of two additional fronts: a horizontal front near the top that descends vertically and a sediment layer at the bottom which aggrandises due to deposition of particles. Three phases are identified in the spreading process: the final corresponding to the mutual approach of the two horizontal fronts while the laterally advancing front halts indicating that the suspension current stops even before all the particles have settled. The first two regimes represent a constant and a decreasing spreading rate respectively. Finally we conduct experiments to substantiate the conclusions of our numerical and theoretical investigation.

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.

A nonlinear, Galilean invariant 2-color Boltzmann cellular automaton is used to study spinodal decomposition in 2-dimensional systems. The initial conditions for the process correspond to a well mixed state of two fluids, present in equal proportions. We specify two types of such initial conditions—corresponding to a correlated quench and to a deep quench. In the former case, a specific color is assigned randomly to each site. In the latter, individual states on each site are populated by the two colors about evenly, with small fluctuations. In the correlated quench situation, the domain growth exponent is initially equal to 0.33 ± 0.06 and for the late time stage it is equal to 0.66 ± 0.06. In the deep quench situation, on the other hand, the effective exponent from initial value of 0.33 takes on the value of 0.82 ± 0.05 for intermediate time scales and only at later times it crosses over to the exponent corresponding to the correlated quench. Spinodal decomposition taking place in a porous medium is slower and the effective exponents are nonuniversal. Inadequacies in the existing models of the surface tension in cellular automata are pointed out.

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.

Following Einsteins's argument for the diffusion coefficient of colloidal dispersions, we postulate that the steady state concentration profile in a suspension of noncolloidal monodisperse particles reflects the dynamic equilibrium resulting from a balance between gravity-driven convection and hydrodynamic dispersion. Using an acoustic technique, the steady state concentration profile of a counterflow-stabilized suspension (a fluidized bed) as well as stationary propagating sedimentation fronts inside the bed were determined. From these profiles we can derive the concentration dependence of the hydrodynamic dispersion coefficient.

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.

In a recent paper [Yiotis et al., Phys. Rev. E 85, 046308 (2012)] we developed a model for the drying of porous media in the presence of gravity. It incorporated effects of corner film flow, internal and external mass transfer, and the effect of gravity. Analytical results were derived when gravity opposes drying and hence leads to a stable percolation drying front. In this paper, we test the theory using laboratory experiments. A series of isothermal drying experiments in glass bead packings saturated with volatile hydrocarbons is conducted. The transparent glass cells containing the packing allow for the visual monitoring of the phase distribution patterns below the surface, including the formation of liquid films, as the gaseous phase invades the pore space, and for the control of the thickness of the diffusive mass boundary layer over the packing. The experimental results agree very well with theory, provided that the latter is generalized to account for the effects of corner roundness in the film region (which was neglected in the theoretical part). We demonstrate the existence of an early constant rate period (CRP), which lasts as long as the films saturate the surface of the packing, and of a subsequent falling rate period (FRP), which begins practically after the detachment of the film tips from the external surface. During the CRP, the process is controlled by diffusion within the stagnant gaseous phase in the upper part of the cells, yielding a Stefan tube problem solution. During the FRP, the process is controlled by diffusion within the packing, with a drying rate inversely proportional to the observed position of the film tips in the cell. Theoretical and experimental results compare favorably for a specific value of the roundness of the films, which is found to be constant and equal to 0.2 for various conditions, and verify the theoretical dependence on the capillary Ca(f), Bond Bo, and Sherwood Sh numbers.

We develop a mathematical model for the drying of porous media in the presence of gravity. The model incorporates effects of corner flow through macroscopic liquid films that form in the cavities of pore walls, mass transfer by diffusion in the dry regions of the medium, external mass transfer over the surface, and the effect of gravity. We consider two different cases: when gravity opposes liquid flow in the corner films and leads to a stable percolation drying front, and when it acts in the opposite direction. In this part, we develop analytical results when the problem can be cast as an equivalent continuum and described as a one-dimensional (1D) problem. This is always the case when gravity acts against drying by opposing corner flow, or when it enhances drying by increasing corner film flow but it is sufficiently small. We obtain results for all relevant variables, including drying rates, extent of the macroscopic film region, and the demarkation of the two different regimes of constant rate period and falling rate period, respectively. The effects of dimensionless variables, such as the bond number, the capillary number, and the Sherwood number for external mass transfer are investigated. When gravity acts to enhance drying, a 1D solution is still possible if an appropriately defined Rayleigh number is above a critical threshold. We derive a linear stability analysis of a model problem under this condition that verifies front stability. Further analysis of this problem, when the Rayleigh number is below critical, requires a pore-network simulator which will be the focus of future work.

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This paper uses an acoustic technique to determine the concentration profile developing during the sedimentation of noncolloidal bidisperse suspensions of glass beads in a Newtonian fluid. Various bead diameter ratios have been used and a wide range of relative concentrations is covered. From the shock front velocities and the concentrations in different zones, the sedimentation velocities of small and large particles in a homogeneous suspension of respective concentrations cs0 and cl0 have been determined. The semidilute regime (c0=ss0+cl0

A two-dimensional two-colour, nonlinear, Galilean-invariant, Boltzmann cellular automaton is developed and used to study two-fluid hydrodynamics and to model fluid interfaces. The interfacial tension and interface width are flexibly controlled by the parameters defining collision rules for the colored particles. Results of studies of both the static and dynamical relaxation of the surface tension and wetting properties are presented.

We investigate effects of capillary heterogeneity induced by variations in permeability in the direction of displacement in heterogeneous porous media under drainage conditions. 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. A good agreement is found between the continuum model predictions and the experimental results 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). A qualitative agreement is also found between the continuum approach and the pore network numerical models, which is expected to improve when finite size effects in the pore network simulations diminish. The results are interpreted with the use of invasion percolation concepts.

In a viscous lock-exchange gravity current, which describes the reciprocal exchange of two fluids of different densities in a horizontal channel, the front between two Newtonian fluids spreads as the square root of time. The resulting diffusion coefficient reflects the competition between the buoyancy driving effect and the viscous damping, and depends on the geometry of the channel. This lock-exchange diffusion coefficient has already been computed for a porous medium, a 2D Stokes flow between two parallel horizontal boundaries separated by a vertical height, H, and, recently, for a cylindrical tube. In the present paper, we calculate it, analytically, for a rectangular channel (horizontal thickness b, vertical height, H) of any aspect ratio (H/b) and compare our results with experiments in horizontal rectangular channels for a wide range of aspect ratios (1/10-10). We also discuss the 2D Stokes-Darcy model for flows in Hele-Shaw cells and show that it leads to a rather good approximation, when an appropriate Brinkman correction is used., Comment: 16 pages,7 figures

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)].