Fluid-saturated Porous Material Research Articles

A Semi-analytical Solution for Start-Up Flow in an Annulus Partially Filled with Porous Material

This study investigates the start-up flow in a horizontal annulus partially filled with clear fluid and partially with a fluid-saturated porous material (composite channel) as a result of the sudden application of constant pressure gradient in horizontal direction. Momentum transfer in the porous medium is simulated using the Brinkman-extended Darcy model. The fluid and porous regions are linked together by equating their velocities and incorporating the shear stress jump conditions at the interface. With the application of Laplace transform technique, the governing partial differential equations are transformed into ordinary differential equations which are solved in the Laplace domain to obtain exact solutions. Inversion of the exact solution in Laplace domain to time domain is done using the Riemann-sum approximation approach. Validation of the Riemann-sum approximation method is achieved by comparing numerical values obtained with those of exact solution obtained for steady state flow and transient solution obtained by implicit finite difference method. At large values of time, transient solution obtained using Riemann-sum approximation approach and implicit finite difference method coincide with closed form solution obtain exactly for steady state flow showing excellent agreement between these methods. Line graphs are used to discuss the effect of the different flow parameters involved in the flow formation.

Homogenization of coupled flow and deformation in a porous material

In this paper we present a framework for computational homogenization of the fluid–solid interaction that pertains to the coupled deformation and flow of pore fluid in a fluid-saturated porous material. Large deformations are considered and the resulting problem is established in the material setting. In order to ensure a proper FE-mesh in the fluid domain of the RVE, we introduce a fictitious elastic solid in the pores; however, the adopted variational setting ensures that the fictitious material does not obscure the motion of the (physical) solid skeleton. For the subsequent numerical evaluation of the RVE-response, hyperelastic properties are assigned to the solid material, whereas the fluid motion is modeled as incompressible Stokes’ flow. Variationally consistent homogenization of the standard first order is adopted. The homogenization is selective in the sense that the resulting macroscale (upscaled) porous media model reminds about the classical one for a quasi-static problem with displacements and pore pressure as the unknown macroscale fields. Hence, the (relative) fluid velocity, i.e. seepage, “lives” only on the subscale and is part of the set of unknown fields in the RVE-problem. As to boundary conditions on the RVE, a mixture of Dirichlet and weakly periodic conditions is adopted. In the numerical examples, special attention is given to an evaluation of the Biot coefficient that occurs in classical phenomenological models for porous media.

Waves in a Porous Viscoelastic Material Saturated with a Fluid

The problem for a fluid-saturated porous viscoelastic material is a direct analogy of the problem for a saturated elastic material solved earlier. The material is theoretically described using Biot’s classical linear model. The system of coupled integro-differential equations for the displacements of the skeleton and fluid is derived using the Volterra principle and Rabotnov’s operator method. The propagation of linear elastic waves in a half-space subject to a short harmonic pulse of given frequency is studied. The problem is solved using the Laplace transform method. The analytical solution in the frequency domain is obtained taking into account the viscoelastic properties of the skeleton. The inverse transformation procedure is described in detail

Recovery of Biot's transition frequency of air-saturated poroelastic media using vibroacoustic spectroscopy

The transition frequency marks the passage from low-frequency viscosity dominated flow to high-frequency inertia dominated one in porous media. It was one of the principal characteristics predicted by Biot's theory. The transition frequency has been a theoretical concept for which only theoretical expressions have been developed in recent years. A vibroacoustic spectroscopy experimental method to recover the characteristic frequency (fC) and for gaining insight into the frequency response of fluid-saturated porous materials has been developed. Long thin air-saturated porous rods solicited mechanically are employed for the experiment. Changes in the fluid flow profile with excitation frequency results in relative motion between the skeleton and the saturating-fluid. This enhances the frictional viscous forces, which, in turn, increases damping of the skeletal motion. These transitions are signaled by observable cues in the acquired laser-vibrometry spectrum of the rods' longitudinal vibration mode patterns. The resonance peaks exhibit sudden attenuation (increase in damping) and are interrupted at the transition frequencies evoking a change of propagation medium. These patterns are compared with those of two plains, single phase material (viscoelastic) rods whose modes stand out as regularly spaced moderately damped peaks.

Shear wave attenuation and micro-fluidics in water-saturated sand and glass beads.

An improvement in the modeling of shear wave attenuation and speed in water-saturated sand and glass beads is introduced. Some dry and water-saturated materials are known to follow a constant-Q model in which the attenuation, expressed as Q(-1), is independent of frequency. The associated loss mechanism is thought to lie within the solid frame. A second loss mechanism in fluid-saturated porous materials is the viscous loss due to relative motion between pore fluid and solid frame predicted by the Biot-Stoll model. It contains a relaxation process that makes the Q(-1) change with frequency, reaching a peak at a characteristic frequency. Examination of the published measurements above 1 kHz, particularly those of Brunson (Ph.D. thesis, Oregon State University, Corvalis, 1983), shows another peak, which is explained in terms of a relaxation process associated with the squirt flow process at the grain-grain contact. In the process of deriving a model for this phenomenon, it is necessary to consider the micro-fluidic effects associated with the flow within a thin film of water confined in the gap at the grain-grain contact and the resulting increase in the effective viscosity of water. The result is an extended Biot model that is applicable over a broad band of frequencies.

The dynamic response of fluid-saturated porous materials with application to seismically induced soil liquefaction

The numerical simulation of liquefaction phenomena in fluid-saturated porous materials within a continuum-mechanical framework is the aim of this contribution. This is achieved by exploiting the Theory of Porous Media (TPM) together with thermodynamically consistent elasto-viscoplastic constitutive laws. Additionally, the Finite Element Method (FEM) besides monolithic time-stepping schemes is used for the numerical treatment of the arising coupled multi-field problem. Within an isothermal and geometrically linear framework, the focus is on fully saturated biphasic materials with incompressible and immiscible phases. Thus, one is concerned with the class of volumetrically coupled problems involving a potentially strong coupling of the solid and fluid momentum balance equations and the algebraic incompressibility constraint. Applying the suggested material model, two important liquefaction-related incidents in porous media dynamics, namely the flow liquefaction and the cyclic mobility, are addressed, and a seismic soil–structure interaction problem to reveal the aforementioned two behaviors in saturated soils is introduced.

Modeling and Experimental Identification of Cracks in Porous Materials During Drying

The main aim of this paper is to mathematically describe and experimentally determine the self-fracturing of fluid-saturated porous materials during drying processes. The thermo-hydro-mechanical model of drying that is suitable for a mathematical description of these phenomena as well as the acoustic emission (AE) technique for their experimental detection are presented. Numerical solutions based on the thermo-hydro-mechanical drying model are used to analyze stress development and to formulate the crack criterion in dried material. The studies concern the convective drying of kaolin-clay material. Bar-shaped samples with a rectangular cross-section were used for the mechanical tests and cylindrically shaped samples of kaolin-clay were used for the drying tests. Good agreement of the theoretical predictions to the experimental data is shown.

Thermal Convection in a Cattaneo–Fox Porous Material with Guyer–Krumhansl Effects

The Guyer–Krumhansl equation is coupled with the Cattaneo–Fox law for the temperature and heat flux fields to study thermal convection in a fluid-saturated Darcy porous material. In particular the effects of the Guyer–Krumhansl terms on oscillatory convection are studied. It is found that for a certain range of the Guyer–Krumhansl coefficient stationary convection occurs while changing the range results in oscillatory convection. Numerical results quantify this effect.

Nonlocal Maxwellian theory of sound propagation in fluid-saturated rigid-framed porous media

Following a deep electromagnetic–acoustic analogy and making use of an overlooked thermodynamic concept of acoustic part of the energy current density, which respectively shed light on the limitations of the near-equilibrium fluid-mechanics equations and the still elusive thermodynamics of electromagnetic fields in matter, we develop a new nonperturbative theory of longitudinal macroscopic acoustic wave propagation allowing for both temporal and spatial dispersion. In this manner, a definitive answer is supplied to the long-standing theoretical question of how the microgeometries of fluid-saturated rigid-framed porous materials determine the macroscopic acoustic properties of the latters, within Navier–Stokes–Fourier linear physics.

Liquid dynamics in a self-oscillating poroelastic model of the vocal fold

The vocal fold tissue is considered as the composite of a porous elastic frame (composed of specialized proteins, carbohydrates, lipids, collagen fibers, and elastin fibers) filled with liquid. The properties of tissue are codetermined by the porous solid, the fluid, and their interaction. The poroelastic description of the vocal fold tissue could improve our knowledge about the mechanical properties and microstructures of these biological tissues. In this study, a self-oscillating poroelastic model is proposed to study the liquid dynamics in the vibrating vocal folds, where the vocal-fold tissue is treated as a transversally isotropic fluid-saturated porous material. Rich liquid dynamics have been found in this model. In the vertical direction, the liquid is transported from the inferior side to the superior side due to the propagation of the mucosal wave. In the longitudinal direction, the liquid is accumulated at the anterior-posterior midpoint. However, the strong collision between two vocal folds forces the accumulated liquid out there in a very short duration. These findings of the liquid dynamics could be helpful for exploring etiology of some laryngeal pathology, optimizing laryngeal disease treatment, understanding hemodynamics in the vocal folds, etc.

Porous convection and thermal oscillations

A theory is developed for thermal convection in a fluid saturated porous material when the temperature may propagate as a thermal wave. In particular, we are interested in the mechanism of thermal oscillation and so allow for Guyer–Krumhansl effects but employ a heat flux equation developed by Christov and Morro. The instability mechanism is investigated in complete detail and it is shown that stationary convection is likely to prevail under normal terrestrial conditions, but if the thermal relaxation time is sufficiently large there is a possible parameter range which allows for oscillatory convection. However, the presence of the Guyer–Krumhansl terms has the effect of damping the oscillatory convection and returning the instability mechanism to one of stationary convection.

Multiscale FE simulation of diffusion-deformation processes in homogenized dual-porous media

AbstractThe paper deals with a model of the homogenized fluid saturated porous material which recently was obtained by the authors using the asymptotic analysis of the Biot type medium characterized by the double porosity. The homogenized macroscopic model is featured by the fading memory effects arising from the microflow in the dual porosity. We derive the steady state formulations and discuss several topics related to the numerical implementation of the model, namely the solution procedure of the discretized microscopic problems, evaluation of the homogenized coefficients and an approximation of the convolution integrals of the macroscopic model, so that the fading memory effects are computationally tractable. Numerical examples are presented to illustrate the approximation schemes discussed in the paper. All computations were performed using the in-house developed finite element code SfePy allowing the multiscale simulations. Besides various potential engineering applications, the present model is intended for simulations of compact bone poroelasticity.

Effects of poroelastic coefficients on normal vibration modes in vocal-fold tissues

The vocal-fold tissue is treated as a transversally isotropic fluid-saturated porous material. Effects of poroelastic coefficients on eigenfrequencies and eigenmodes of the vocal-fold vibration are investigated using the Ritz method. The study demonstrates that the often-used elastic model is only a particular case of the poroelastic model with an infinite fluid-solid mass coupling parameter. The elastic model may be considered appropriate for the vocal-fold tissue when the absolute value of the fluid-solid mass coupling parameter is larger than 10(5) kg/m(3). Otherwise, the poroelastic model may be more accurate. The degree of compressibility of the vocal tissue can also been described by the poroelastic coefficients. Finally, it is revealed that the liquid and solid components in a poroelastic model could have different modal shapes when the coupling between them is weak. The mode decoupling could cause desynchronization and irregular vibration of the folds.

Axial conduction effect in flow through circular porous passages with prescribed wall heat flux

This study presents a series solution for computation of the steady state temperature field in circular ducts with prescribed wall heat flux. The ducts are filled with fluid saturated porous materials. The developed methodology includes a simple transformation that improves the convergence of this series solution. The acquired solution includes the contribution of axial conduction that leads to a modified Graetz-type solution for these fluid passages. Finally, this solution is augmented by the contribution of frictional heating.

A two-scale approach for propagating cracks in a fluid-saturated porous material

An extension to a finite strain framework of a two-scale numerical model for propagating crack in porous material is proposed to model the fracture in intervertebral discs. In the model, a crack is described as a propagating cohesive zone by exploiting the partition-of-unity property of finite element shape functions. At the micro-scale, the flow in the cohesive crack is modelled as viscous fluid using Stokes' equations which are averaged over the cross section of the cavity. At the macro-scale, identities are derived to couple the local momentum and the mass balance to the governing equations for a saturated porous material. The resulting discrete equations are nonlinear due to the cohesive constitutive equations and the geometrically nonlinear kinematic relations. A Newton-Raphson iterative procedure is used to consistently linearise the derived system while a Crank-Nicholson scheme takes care of the time integration of the system. The derived model is used to analyse a quasi-static crack growth in confined compression under tensile loading.

Poroelasticity-I: Governing Equations of the Mechanics of Fluid-Saturated Porous Materials

We present here the approach to the theory of fluid-filled poroelastics based on consideration of poroelastics as a continuum of “macropoints” (representative elementary volumes), which “internal” states can be described by as a set of internal parameters, such as local relative velocity of fluid and solid, density of fluid, internal strain tensor, specific area, and position of the center of mass of porous space. We use the generalized Cauchy–Born hypothesis and suggest that there is a system of (structural) relationships between external parameters, describing the deformation of the continuum and internal parameters, characterizing the state of representative elementary volumes. We show that in nonhomogenous (and, particularly, nonlinear) poroelastics, an interaction force between solid and fluid appears. Because this force is proportional to the gradient of porosity, absent in homogeneous poroelastics, and one can neglect with dynamics of internal degrees of freedom, this force is equivalent to the interaction force, introduced earlier by Nikolaevskiy from phenomenological reasons. At last, we show that developed theory naturally incorporates three mechanisms of energy absorption: visco-inertial Darcy mechanism, “squirt flow” attenuation, and skeleton attenuation.

An Enriched Biphasic Model for Solute Driven Degradation

AbstractTransport of solutes in porous materials plays an important role in many kinds of materials such as biological tissues, porous implants or even soils. In most of the cases the liquid phase in the pores acts as a solvent for one or more solutions. The motion of the solutions is driven by both, the advective and convective transport. The former is related to the fluid phase velocity whereas the letter follows the concentration gradient. The interactions between the solutes and the solid and liquid phase may influence the overall material behavior. Although the solutes often carry electrical charges this paper is focused on neutrally charged solutions. In this contribution the model to describe the solute transport in a fluid saturated porous material is based on the well founded Theory of Porous Media. We will present the basic framework and the governing equations. Finally, we will show a three dimensional numerical example of the solute driven degradation of a skull implant. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Heat transfer with upstream thermal penetration in flow through porous plate passages

The objective of this study is to develop a series solution for determination of the temperature field in parallel-plate ducts with prescribed wall heat flux. Consideration is also given to ducts filled with fluid saturated porous materials. A simple transformation is used to improve the convergence of this series solution. Temperature variations and heat transfer coefficients are determined for infinitely long parallel-plate ducts when the walls undergo a step change in the applied wall heat flux. Axial thermal penetration near the applied wall heat flux location is studied. The solutions with the contribution of axial conduction in these fluid passages are acquired using a modified Graetz-type solution. Finally, this technique is augmented by the contribution of frictional heating.

A EVI-space-time Galerkin method for dynamics at finite deformation in porous media

We present an EVI-space-time Galerkin method applied to dynamic analysis in fluid-saturated porous materials. The physical model is based on a materially incompressible solid skeleton saturated by a barotropic fluid. The deformation of the solid matrix is described by a compressible Neo-Hookean material law. The model equations are formulated in the Lagrangian description of the solid skeleton. In respect of the numerical modeling, by use of the Embedded Velocity Integration (EVI) technique, the governing set of second-order time-dependent equations is transformed to a first-order one, which is in turn solved by a time-discontinuous Galerkin method. In addition, a stability factor α, describing the embedded integration scheme of the displacement–velocity relation, is introduced. Depending on the chosen value of the α factor, the stability property of the overall solution can be enforced. Numerical experiments demonstrate the superior performance of the proposed method with respect to accuracy and low numerical damping in comparison with conventional time-stepping schemes.

A Biphasic Continuum Approach for Viscoelastic High-Porosity Foams: Comprehensive Theory, Numerics, and Application

This work aims to present a valuable and predictive model for the description of polymeric soft foams which are widely exploited as packaging, padding, or cushioning materials. Belonging to the class of cellular solids, polymeric foams and synthetic sponges can be regarded as permeable or impermeable fluid-saturated porous materials depending on whether their microstructure is open-celled or closed-celled. The pore space formed by the cellular polymer skeleton is filled with a pore fluid (e.g., liquid or gas) which can significantly affect the transient compressive and impact response making particularly air-filled foamed plastics a light-weight and shock-absorbing material par excellence.