Dispersion of imbibition fronts

We have studied the dispersive behaviour of imbibition fronts in a porous medium by X-ray tomography. Injection velocities were varied and the porous medium was initially prewetted or not. At low velocity in the prewetted medium, the imbibition profiles are found to be distinctly hyperdispersive. The profiles are anomalously extended when compared to tracer fronts exhibiting conventional (Gaussian) dispersion. We observe a strong velocity dependence of the exponent characterizing the divergence of the dispersion coefficient for low wetting-fluid saturation. Hyperdispersion is absent at high imbibition velocities or when the medium is not prewetted.Comment: 8 pages, 5 figures; submitted to Europhysics Letter

Advective-diffusive gaseous transport in porous media: the molecular diffusion regime

1993 Spring.Includes bibliographical references.Traditional mathematical models for advective-diffusive transport in porous media fail to represent important physical processes when fluid density depends on composition. Such is the case for gas mixtures comprised of species with differing molecular masses, such as found in the vadose zone near chlorinated hydrocarbon sources. To address problems of this nature, a more general advection-diffusion (A-D) model is presented, which is valid for porous media with permeabilities exceeding 10-10 cm2 (where Klinkenberg and Knudsen effects are negligible). The new mathematical model is derived by thermodynamic means, based on identifying the meaning of Darcy's advective reference velocity in terms of a weighted average of species drift velocities~ The resulting model has no additional parameters, and introduces no additional complexity or nonlinearity when compared to the traditional A-D model most commonly used in hydrology and environmental science. Because the form of traditional A-D models is retained, the new formulations fit readily into existing numerical simulators for the solution of subsurface transport problems. The new model is equivalent to the Dusty-Gas Model of Mason et al. (1967) for cases where the molecular diffusion regime prevails and pressure, temperature, and forced diffusion are negligible. Further support of the model is provided by hydrodynamic analysis, accounting for the diffusive-slip flux identified by Kramers and Kistemaker (1943). The new model is analytically compared to two existing A-D models, one from the hydrology literature, where Darcy's law is assumed to yield a mass-average velocity, and one from the chemical engineering literature, where Darcy's law is assumed to yield a mole-average velocity. Significant differences are shown to exist between the three transport models. The new model is shown to match closely with the experimental data of Evans et al. (1961a), while the existing A-D models are shown to fail in this regard

Separator plugs for liquid helium

Work performed during Summer 1984 (from June to Sept. 30) in the area of porous media for use in low temperature applications is discussed. Recent applications are in the area of vapor - liquid phase separation, pumping based on the fountain effect and related subsystems. Areas of potential applications of the latter are outlined in supplementary work. Experimental data have been developed. The linear equations of the two-fluid model are inspected critically in the light of forced convection evidence reported recently. It is emphasized that the Darcy permeability is a unique throughput quantity in the porous media application areas whose use will permit meaningful comparisons of data not only in one lab but also within a group of labs doing porous plug studies

Geometric gradient-flow dynamics with singular solutions

The gradient-flow dynamics of an arbitrary geometric quantity is derived using a generalization of Darcy's Law. We consider flows in both Lagrangian and Eulerian formulations. The Lagrangian formulation includes a dissipative modification of fluid mechanics. Eulerian equations for self-organization of scalars, 1-forms and 2-forms are shown to reduce to nonlocal characteristic equations. We identify singular solutions of these equations corresponding to collapsed (clumped) states and discuss their evolution.Comment: 28 pages, 1 figure, to appear on Physica

Models for the two-phase flow of concentrated suspensions

A new two-phase model for concentrated suspensions is derived that incorporates a constitutive law combining the rheology for non-Brownian suspension and granular flow. The resulting model exhibits a yield-stress behavior for the solid phase depending on the collision pressure. This property is investigated for the simple geometry of plane Poiseuille flow, where an unyielded or jammed zone of finite width arises in the center of the channel. For the steady states of this problem, the governing equations are reduced to a boundary value problem for a system of ordinary differential equations and the conditions for existence of solutions with jammed regions are investigated using phase-space methods. For the general time-dependent case a new drift-flux model is derived using matched asymptotic expansions that takes into account the boundary layers at the walls and the interface between the yielded and unyielded region. The drift-flux model is used to numerically study the dynamic behavior of the suspension flow including the appearance and evolution of an unyielded or jammed region

Modélisation de la compaction dynamique avec dérive des vitesses

Dans ce rapport, on présente un modèle hyperbolique d'écoulement multiphasique incluant la compaction dynamique irréversible de poudres. Ce modèle doit être capable de remplir quatre principaux objectifs. Le premier objectif concerne le caractère irréversible de la compaction des poudres. Quand un lit de poudres est soumis à un cycle de charge-décharge, le volume final est plus petit que le volume initial. Afin de traiter ce problème d'hystérésie, on construit un modèle avec relaxation. Durant la phase de charge, on suppose que l'équilibre mécanique a lieu, ce qui correspond à une relaxation instantanée des pressions. Dans la phase de décharge, on suppose au contraire qu'une transformation mécanique a lieu, conduisant à un état mécanique hors équilibre. Par conséquent, durant chacun de ces cycles, les vitesses du son des modèles limites sont très différentes. Ces différences dans les propriétes acoustiques sont la cause justement du caractère irréversible du processus de compaction. Le second objectif est relié aux effets dynamiques, là où la pression et les ondes de chocs jouent un rôle important. La dynamique des ondes est assurée par l'hyperbolicité du modèle et l'on tient compte aussi bien de la compressibilité des phases que des énergies de configuration. Le troisième objectif concerne les effets multidimensionnels aux interfaces matérielles. En effet, la plupart des processus de com- paction font intervenir des surfaces libres. Par conséquent, le modèle doit être capable de traiter de problèmes d'interfaces entre des fluides purs et des mélanges granulaires. Enfin, le quatrième objectif concerne la perméa- tion des gaz qui peut jouer un rôle important dans certains cas spécifiques de compaction de poudres. Se pose alors la question délicate de description de ces vitesses multiples. Ces quatre points sont considérés dans un modèle unique appartenant à la classe des modèles des interfaces diffuses. La capacité du modèle a traiter ces phénomènes est validée dans des situations où chaque effet est considéré séparément. En particulier, le caractère irréversible de la compaction est considéré et validé sur plu- sieurs exemples : expérience sur un matériel énergétique (HMX granulaire), compaction granulaire de NaCl. À part les équations d'état des matériaux (pressions granulaires et hydrodynamiques, et les énergies associées), le modèle est de plus exempt de paramètre ajustable. On reproduit enfin les effets de perméation des gaz à l'aide d'un modèle de dérive des vitesses, et une analyse sur la production d'entropie. Le modèle résultant est validé sur un cas test de tube à choc où une onde de choc traverse un lit granulaire de forte densité et montre un accord parfait avec l'expérience