Theory of Porous Media

The Theory of Porous Media (TPM) is a macroscopic continuum theory which is based on the theory of mixtures and the concept of volume fractions. For more details see [1] and citations therein. 

Abstract A simplified quintuple model for the description of freezing and thawing processes in gas and liquid saturated porous materials is investigated by using a continuum mechanical approach based on the Theory of Porous Media (TPM). The porous solid consists of two phases, namely a granular or structured porous matrix and an ice phase. The liquid phase is divided in bulk water in the macro pores and gel water in the micro pores. In contrast to the bulk water the gel water is substantially affected by the surface of the solid. This phenomenon is already apparent by the fact that this water is frozen by homogeneous nucleation. 

Taking into account the aforementioned effects of ice formation in porous materials, a macroscopic quintuple model within the framework of the Theory of Porous Media (TPM) for the numerical simulation of initial and boundary value problems of freezing and thawing processes in saturated porous materials will be investigated. The porous solid is made up of a granular or structured porous matrix (a = S) and ice (a = I), where it will be assumed that both phases have the same motion. Due to the different freezing points of water in the macro and micro pores, the liquid will be distinguished into bulk water ( a = L) in the macro pores and gel water (a = P, pore solution) in the micro pores. With exception of the gas phase (a = G), all constituents will be considered as incompressible. 

Abstract In this contribution, the coupled flow of liquids and gases in capillary thermoelastic porous materials is investigated by using a continuum mechanical model based on the Theory of Porous Media. The movement of the phases is influenced by the capillarity forces, the relative permeability, the temperature and the given boundary conditions. In the examined porous body, the capillary effect is caused by the intermolecular forces of cohesion and adhesion of the constituents involved. The treatment of the capillary problem, based on thermomechanical investigations, yields the result that the capillarity force is a volume interaction force. Moreover, the friction interaction forces caused by the motion of the constituents are included in the mechanical model. The relative permeability depends on the saturation of the porous body which is considered in the mechanical model. In order to describe the thermo-elastic behaviour, the balance equation of energy for the mixture must be taken into account. The aim of this investigation is to provide with a numerical simulation of the behavior of liquid and gas phases in a thermo-elastic porous body. 

Keywords Theory of Porous Media (TPM), ternary model, capillarity, thermo-elasticity... 

In the last 20 years, there has been a growing interest in investigations concerning porous multi phase bodies. Due to the fact of the increasing body of acquired knowledge in the physics of multi body system, connecting with the wide range of applications, this interest is not remarkable. However, all these new perceptions have to be embedded in a thermomechanical concept. This can be afforded by the Theory of Porous Media. 

The Theory of Porous Media is the Mixture Theory, restricted by the concept of the Volume Fractions. Hereby, we have a look at a continuum which consists of several constituents. In this investigation we deal with a solid phase a = S), a Liquid phase (a = L) and a Gas phase (a = G). The components of the real structure will be statistically distributed over the control space, so that we gain to a smeared model of the real structure. 

The reader who is interested in a review of the Theory of Porous Media and the kinematics is referred to de Boer [4]. 

DE Discrete Element EE Finite Element FEM Finite Element Method TPM Theory of Porous Media... 

To gain a more precise insight into the phenomena occurring in gels, the Theory of Porous Media (TPM), or the coupled chemo-electro-mechanical formulation is a good choice. Normally, the TPM is applied for the gel only, while the coupled multi-field formulation incorporates the gel and the surrounding solution. 

The general Theory of Porous Media (TPM) is a macroscopic continuum theory which is based on the theory of mixtures extended by the concept of volume fractions. In this theory neither the local porous micro structure nor the actual geometrical distributions of all the constituents have to be known. The TPM is a homogenized model, i.e. all geometrical and physical quantities can be seen as statistical averages of the real quantities (Bowen 1980 Ehlers 2002). 

Dunn J.E. and Chen T. (1993) Critical evaluation of the diffusion hypothesis in the theory of porous media volatile organic compounds (VOC) sources and sinks. In Nagda N.L.(ed) Proceedings of Modeling of Indoor Air Quality and Exposure, ASTM STP 1205, 64 - 80. 

De Boer, R., 2000. Theory of porous media Highlights in historical development and current state. Dordrecht Springer-Verlag. 

ABSTRACT In the present paper a multiphase model including a hypoplastic formulation of the solid phase is presented and its application to earthquake engineering problems discussed. The macroscopic soil model, which is based on the theory of porous media, comprises three distinct phases namely, solid, fluid and gas phase. For each of these the compressibility of the respective medium is taken into account in the mathematical formulation of the model. The solid phase is modelled using the hypoplastic constitutive equation including intergranular strain to allow for a realistic description of material behaviour of cohesionless soils even under cyclic loading. The model was implemented into the finite element package ANSYS via the user interface and also allows the simulation of soil-structure interaction problems. 

Efforts of polymer scientists and fuel cell developers alike are driven by one question What specific properties of the polymeric host material determine the transport properties of a PEM, especially proton conductivity The answer depends on the evaluated regime of the water content. At water content above kc, relevant structural properties are related to the porous PEM morphology, described by volumetric composition, pore size distribution and pore network connectivity. As seen in previous sections, effective parameters of interest are lEC, pKa, and the tensile modulus of polymer walls. In this regime, approaches familiar from the theory of porous media or composites (Kirkpatrick, 1973 Stauffer and Aharony, 1994), can be applied to relate the water distribution in membranes to its transport properties. Random network models and simpler models of the porous structure were employed in Eikerling et al. (1997, 2001) to study correlations between pore size distributions, pore space connectivity, pore space evolution upon water uptake, and proton conductivity, as will be discussed in the section Random Network Model of Membrane Conductivity. ... 

The Theory of Porous Media (TPM) is a concept based on the fundamentals of classical continuum mechanics and thermodynamics. It is used in numerous fields of research to model the behavior of saturated porous solid materials. The fluid-stracture interaction within the material is incorporated by a statistical homogenization of a representative elementary volume. Hence, no knowledge of the geometry and the stracture of the interfering components is required the investigated domain has to be rather large and it has to comprise a sufficiently homogenous substmcture. 

Brock D, Lee W, Segalman D, Witkowski W (1994) A dynamic model of a linear actuator based on polymer hydrogel. J Int Mater Syst Struct 5 764-771 de Boer R (2000) Theory of porous media. Springer, Berlin... 

---