Dependence of adsorption/diffusion processes in porous media on bulk and surface permeabilities

The paper contains a brief summary of a macroscopic continuum model for adsorption in porous materials which is an extension of the model for porous bodies by K. Wilmanski on mass exchange processes. We consider the flow of a fluid/adsorbate mixture through channels of a solid component. The fluid serves as carrier for an adsorbate whose mass balance equation contains a source term. Due to low adsorbate concentration we deal with a physical adsorption process which means that particles of the adsorbate stick to the skeleton due to weak van der Waals forces. The model contains two different permeability parameters whose nature is completely different: The first one, the usual bulk permeability coefficient, describes the resistance of the skeleton to the flow of the fluid/adsorbate mixture. The second one describes the surface resistance to the outflow of the mixture from the solid. This work shows within a simple example the range of these parameters and the dependence of adsorption/diffusion on them

Coupling of Adsorption and Diffusion in Porous and Granular Materials. A 1-D Example of the Boundary Value Problem

In the paper we present a macroscopic continuum model of adsorption in porous materials consisting of three components. We consider the flow of a fluid component through channels of the skeleton. It serves as carrier for an adsorbate whose mass balance equation contains a source term. The source consists of two parts: a Langmuir contribution connected with bare sides on internal surfaces which becomes in equilibrium the Langmuir isotherm, and changes of the internal surface driven by the source of porosity. The model for the latter contribution is new. Parameters of this model are analyzed by means of an example of solution of a boundary value problem for the full set of field equations which describes the transport of pollutants in soils

Modelling of surface waves in poroelastic saturated materials by means of a two component continuum -- Lecture notes

These lecture notes are devoted to an overview of the modelling and the numerical analysis of surface waves in two-component saturated poroelastic media. This is an extension to the part of the lecture notes by K. Wilmanski (WIAS-Preprint No. 945) which is primarily concerned with the classical surface waves in single component media. We use the ''simple mixture model'' which is a simplification of the classical Biot's model for poroelastic media. Two interfaces are considered here: firstly the interface between a porous half space and a vacuum and secondly the interface between a porous halfspace and a fluid halfspace. For both problems we show how a solution can be constructed and a numerical solution of the dispersion relation can be found. We discuss the results for phase and group velocities and attenuations, and compare some of them to the high and low frequency approximations. For the interface porous medium/vacuum there exist in the whole range of frequencies two surface waves - a leaky Rayleigh wave and a true Stoneley wave. For the interface porous medium/fluid one more surface wave appears - a leaky Stoneley wave. For this boundary velocities and attenuations of the waves are shown in dependence on the surface permeability. The true Stoneley wave exists only in a limited range of this parameter. At the end we have a look on some results of other authors and a glance on a logical continuation of this work, namely the description of the structure and the acoustic behavior of partially saturated porous media

Monochromatic surface waves at the interface between poroelastic and fluid halfspaces

The topic of a previous work was the study of monochromatic surface waves at the boundary between a porous medium and a vacuum. This article is an extension of this research to the propagation of surface waves on the interface between a porous halfspace and a fluid halfspace. Results for phase and group velocities and attenuations are shown in dependence on both the frequency and the surface permeability. In contrast to classical papers on surface waves where only the limits of the frequency (zero and infinity) and the limits of the surface permeability (fully sealed and fully open boundary) were studied, we investigate the problem in the full range of both parameters. For the analysis we use the ''simple mixture model'' which is a simplification of the classical Biot model for poroelastic media. The construction of a solution is shown and the dispersion relation solved numerically. There exist three surface waves for this boundary: a leaky Rayleigh wave and both a true and a leaky Stoneley wave. The true Stoneley wave exists only in a limited range of the surface permeability

Surface waves on permeable and impermeable boundaries of poroelastic media

This work is devoted to the numerical analysis of surface waves in two-component saturated poroelastic media. We use the "simple mixture model" which is a simplification of the classical Biot's model for poroelastic media. For the interface porous medium/vacuum there exist two surface waves in the whole range of freuencies - a leaky Rayleigh wave and a true Stoneley wave. For the interface porous medium/fluid one more surface wave appears - a leaky Stoneley wave. For this boundary velocities and attenuations of the waves are shown in dependence on the surface permeability. The true Stoneley wave exists only in a limited range of this parameter

Randbedingungen für den zweikomponentigen porösen Körper auf dem Rand des Skeletts

Der Anstoß, diesen Vortrag zu halten, ist das Lastverteilungsmodell von Karl von Terzaghi, das er 1936 veröffentlicht hat. Es geht von der Fragestellung aus, in welcher Weise eine aufgebrachte Last auf die Komponenten eines porösen Mediums verteilt wird. Dazu sollten wir zunächst klarstellen, was ein poröser Körper ist. Böden, Gesteine, Keramik und faserige Stoffe sind Beispiele für poröse Körper. Diese Stoffe haben alle die Gemeinsamkeit, dass es sich um einen "Feststoff mit Löchern" handelt. Nun würde man einen hohlen Metallzylinder aber kaum als porösen Körper bezeichnen. D.h. man muss die Definition dahingehend erweitern, dass es sich um einen Körper mit mindestens einer festen Phase handelt, der zufällig verteilte Hohlräume aufweist, die miteinander verbunden sind und von denen wenigstens einige von der einen Seite des Mediums bis zur anderen verlaufen. Wir wollen hier einen zweikomponentigen porösen Körper betrachten, einen Körper bestehend aus einer festen Phase (Skelett) und einer flüssigen Phase (Fluid). Durch die zweite Phase wird neben der Porosität eine zweite Eigenschaft des porösen Körpers erfasst, die wichtige physikalische Beiträge leistet, nämlich die Diffusion

Surface waves in two-component poroelastic media on impermeable boundaries -- numerical analysis in the whole frequency domain

In this work the dispersion relation for surface waves on an impermeable boundary of a fully saturated poroelastic medium is investigated numerically in the whole range of frequencies. A linear model of a two-component poroelastic medium is used in the form proposed by K. Wilma'nski. Similarly to the classical Biot's model it is a continuum mechanical model but it is much simpler. In the whole range of frequencies there exist two modes of surface waves corresponding to the classical Rayleigh and Stoneley waves. The numerical results for velocities and attenuations of these waves are shown for different values of the bulk permeability coefficient in different ranges of frequencies

Relaxation analysis and linear stability vs. adsorption in porous materials

The paper presents a linear stability analysis of a 1D stationary flow through a poroelastic medium. This base flow is perturbed in four ways: by longitudinal (1D) disturbances without and with mass exchange and by transversal (2D) disturbances without and with mass exchange. The eigenvalue problem for the first step field equations is solved using a finite-difference-scheme. For both disturbances without mass exchange results are confirmed by an analytical solution. We present the stability and relaxation properties in dependence on the two most important model parameters, namely the bulk and surface permeability coefficients

On Adsorption and Diffusion in Porous Media

The paper contains a macroscopic continuum model of adsorption in porous materials consisting of three components. We consider the flow of a fluid/adsorbate mixture through channels of a solid component. The fluid serves as carrier for an adsorbate whose mass balance equation contains a source term. This term consists of two parts: first a Langmuir contribution which is connected with bare sites on internal surfaces and describes the Langmuir isotherm in equilibrium. The second one is due to changes of the internal surface driven by the source of porosity which is a part of the balance equation for porosity. We clearly state the range of applicability of the model. A simple numerical example which describes the transport of pollutants in soils illustrates the coupling of adsorption and diffusion. The results show that after a certain time arises a maximum in the rate of adsorption as a function of fluid/adsorbate velocity

Numerical analysis of monochromatic surface waves in a poroelastic medium

The dispersion relation for surface waves on the boundary between a fully saturated poroelastic medium and a vacuum is investigated numerically in the whole range of frequencies. A linear model of a two-component poroelastic medium similar to but simpler than the classical Biot's model is used. In the whole range of frequencies there exist two modes of surface waves corresponding to the classical Rayleigh and Stoneley waves. The numerical results for phase velocities, group velocities and attenuations of these waves are shown for different values of the bulk permeability coefficient