Transport In Porous Materials Research Articles

Understanding the diffusional tortuosity of porous materials: An effective medium theory perspective

The interpretation of experimental data on transport in porous materials is often based on the use of a single representative pore size, overlooking effects of the pore size distribution (PSD) and pore network connectivity, and fitting a tortuosity into which all such uncertainties are consigned. Using literature data on the diffusion of N2, Xe and i-C4H10 in mesoporous Shell silica spheres, we demonstrate that the tortuosity depends on the choice of the representative pore radius as well as gas species. Both the Knudsen model and the Oscillator model considering dispersive fluid–solid interactions, developed in this laboratory, are found to adequately interpret the data in conjunction with effective medium theory (EMT) by fitting a network coordination number instead of tortuosity. This insensitivity to model is due to the large mean mesopore radius of 7.4nm for this silica; however, the Oscillator model is found to yield a value of the coordination number closer to the range of values expected for this material. Using the EMT we demonstrate that the tortuosity is dependent on temperature and diffusing species, because of differences in temperature dependence between the conductance at the representative pore radius and the true conductance which depends on the network connectivity and PSD. In the slip flow regime, which is obtained at large pore size, we show that the superposition of Knudsen and viscous mechanisms leads to temperature and species dependence of tortuosity, because of the different pore size dependence of the two contributions. This leads to different limiting tortuosities and PSD dependence in the Knudsen and viscous flow regimes. These critical aspects are largely unappreciated in the literature, and even systematic variations of tortuosity with temperature or diffusing species usually overlooked, often leading to misrepresentation of the underlying mechanism.

Uniform Model for Moisture Transport in Porous Materials and Its Application to Concrete at Selected Chinese Regions

The present study investigates the mechanisms of moisture transport in porous materials. For partially saturated porous materials, moisture transport relies on both the Darcian flow by capillary pressure gradient and the Fickian flow by gas concentration gradient. Taking into account the capillary curves that are associated intimately with the pore structure and play crucial roles on both drying and wetting processes, a uniform model that only depends on one variable, the saturation degree, is established. The isothermal adsorption/desorption method and the Kelvin equation are used to evaluate the capillary curve that obeys the van Genuchten form equation. The established model is applied to characterize the moisture distribution in four (near) coastal regions of China (Guangzhou, Hangzhou, Jinan, and Shenyan). Wetting time is shown to be a dominant factor influencing the stable saturation degree and the influence depth.

3D Data for Calculation of Capillary Conductivity Coefficient

The moisture in building construction material affects the physical properties of buildings and he may lead to their degradation. With few exceptions, building materials are almost never dry. For the expected negative effect of moisture on building materials of structures is needed accurate method of determining the characteristics of their moisture as possible. The capillary conductivity coefficient characterizes transfer of liquid moisture in porous material. The method for its determination is experimentally arranged in such a way that it is possible to apply diffusion equation derived from the Luikov equation that is a phenomenological description of liquid moisture transport in porous materials as well as from the continuity equation, which expresses the classic conservation of matter principle. To records of the moisture distribution has been developed the methodology for measuring of moisture in the porous material, using microwave radiation. The calculation of the capillary conductivity coefficient and its dependence is based on the moisture curves in 3 D in non-stationary state of wetting, determined by non-destructive method.

Overhauser dynamic nuclear polarization-enhanced NMR relaxometry

We present a new methodological basis for selectively illuminating a dilute population of fluid within a porous medium. Specifically, transport in porous materials can be analyzed by now-standard nuclear magnetic resonance (NMR) relaxometry and NMR pulsed field gradient (PFG) diffusometry methods in combination with the prominent NMR signal amplification tool, dynamic nuclear polarization (DNP). The key components of the approach introduced here are (1) to selectively place intrinsic or extrinsic paramagnetic probes at the site or local volume of interest within the sample, (2) to amplify the signal from the local solvent around the paramagnetic probes with Overhauser DNP, which is performed in situ and under ambient conditions, and (3) to observe the ODNP-enhanced solvent signal with 1D or 2D NMR relaxometry methods, thus selectively amplifying only the relaxation dynamics of the fluid that resides in or percolates through the local porous volume that contains the paramagnetic probe. Here, we demonstrate the proof of principle of this approach by selectively amplifying the NMR signal of only one solvent population, which is in contact with a paramagnetic probe and occluded from a second solvent population. An apparent one-component T2 relaxation decay is shown to actually contain two distinct solvent populations. The approach outlined here should be universally applicable to a wide range of other 1D and 2D relaxometry and PFG diffusometry measurements, including T1–T2 or T1–D correlation maps, where the occluded population containing the paramagnetic probes can be selectively amplified for its enhanced characterization.

Numerical studies of interfacial phenomena in liquid water transport in polymer electrolyte membrane fuel cells using the lattice Boltzmann method

Water management is an important issue in the polymer electrolyte membrane (PEM) fuel cell, which is considered as a promising alternative power source for future automotive applications. In this article, lattice Boltzmann simulations are conducted to examine the interfacial phenomena in liquid water transport in porous materials of a PEM fuel cell. Numerical results clearly indicate that large perforated pores through the porous diffusion layers can serve as a convenient liquid water transport pathway and thus assist in liquid water removal. An interconnected horizontal and vertical pore combination is especially beneficial to liquid water transport through the porous layers in flooding conditions. Therefore, liquid water transport in a PEM fuel cell may be effectively managed through well engineered interfacial structures in porous materials.

Hydrodynamic drag coefficient for soft core–shell nanoparticles in hydrogels

Nanoparticle transport in porous materials, including nanoparticle gel electrophoresis, hinges on knowledge of the hydrodynamic drag coefficient. Here, we compute the drag force on a soft core–shell sphere translating in a porous medium from a continuum hydrodynamic model in which slow viscous flow in the soft shell and embedding porous medium are modelled using Brinkman's equations. This model unifies the Brinkman force for bare spheres in porous media and the drag force of Masliyah et al. (1987) for soft core–shell spheres in pure viscous fluids. We compare the drag force with the Brinkman force evaluated using the composite sphere hydrodynamic radius, showing that this convenient approximation is reasonable when the Brinkman screening length of the embedding porous medium is large compared to the core radius; otherwise, the Brinkman force can significantly underestimate the force.

Influence of uncertainty in heat–moisture transport properties on convective drying of porous materials by numerical modelling

The influence of uncertainties in heat–moisture transport properties, due to measurement errors and material heterogeneity, on the numerical simulation results of convective drying of two capillary-saturated porous materials is investigated by a transport-property parameter analysis (TP-PA), based on the Monte Carlo method. Here, the heat–air–moisture transfer model is evaluated many times, each time using a random set of one or multiple input parameters (i.e. transport properties), by which a stochastic model output is generated. The propagation of these transport-property uncertainties to the hygrothermal behaviour of the drying system is evaluated by statistical analysis of the model simulation output. The spread on the hygrothermal response is found to be strongly material dependent and is related to the dominant mode of moisture transport in the material, i.e. liquid or vapour transport. The TP-PA results clearly indicate that uncertainties in the heat–moisture transport properties can lead to significant differences in drying behaviour predictions, where differences of the total drying time with respect to its mean value up to 200% are found for the materials considered. Therefore, numerical modelling of heat and moisture transport in porous materials should preferably include a quantification of the propagation of these uncertainties, for example by means of the proposed transport-property parameter analysis. Such analysis, however, additionally requires detailed (a priori) experimental material characterisation to determine realistic uncertainty ranges.

Inhibition of electrokinetic ion transport in porous materials due to potential drops induced by electrolysis

In this work we present non-destructive measurements of sodium ion concentration profiles during the electrokinetic removal of sodium chloride from porous materials using Nuclear Magnetic Resonance (NMR). The effect of both protons and hydroxyl ions, generated due to the electrolysis of water, on the transport of the salt ions is studied by tracking the acidic and alkaline fronts using pH-indicator paper. In addition, the electrical potential distribution within the specimen is monitored to assess its influence on the process. To support the observations we compare the experimental results with a theoretical model based on the Poisson–Nernst–Plank equations. In this model we use the chemical equilibrium condition for the self-electrolysis of water in the description of the transport of protons and hydroxyl ions. In addition we use the electro-neutrality condition to compute the transport of salt ions through the material. At the edges of the system the electrical current is distributed over the chemical active species, i.e. protons, hydroxyl and chloride ions, according to the Butler–Volmer description for charge transfer at electrodes. Both the experimental and model results show in the final stage of the electrokinetic remediation process a sharp transition from the acidic to alkaline region at one third of the length of the specimen away from the positively biased electrode, i.e. the anode. From the model results we found that the formation of chlorine gas at the anode does not influence the position of this transition area. In this transition region we also observe a large gradient in electrical potential and a corresponding local deficit of ions. As a result of the large potential gradient in this small transition zone the electrical field in the acidic and alkaline region diminishes. Consequently, electrokinetic ion transport though the material will stagnate.

Outgassing of icy bodies in the Solar System – II: Heat transport in dry, porous surface dust layers

In this work, we present a new model for the heat conductivity of porous dust layers in vacuum, based on an existing solution of the heat transfer equation of single spheres in contact. This model is capable of distinguishing between two different types of dust layers: dust layers composed of single particles (simple model) and dust layers consisting of individual aggregates (complex model). Additionally, we describe laboratory experiments, which were used to measure the heat conductivity of porous dust layers, in order to test the model. We found that the model predictions are in an excellent agreement with the experimental results, if we include radiative heat transport in the model. This implies that radiation plays an important role for the heat transport in porous materials. Furthermore, the influence of this new model on the Hertz factor are demonstrated and the implications of this new model on the modeling of cometary activity are discussed. Finally, the limitations of this new model are critically reviewed.

Diffusion and electromigration in clay bricks influenced by differences in the pore system resulting from firing

Ion transport in porous materials has been subject of study for several decades. However, the interaction between the pores and the overall pore system make it complicated to obtain a clear picture and predict diffusion and electromigration (transport induced by an applied electric field). Specific bricks were examined with respect to shape, size and interconnection of the pores. The pores were studied at a microscopic level, the interconnected pore system at a macroscopic level and the results obtained were compared with the measurement of the corresponding ion transport of Cl − and Na + through the pore system to contribute to an overall understanding of ion transport in porous materials. The pore system in bricks are influenced by the firing degree, clay mixture composition and ion content. The present paper focuses on the pore system and effects from clay mixture composition and ion content were neglected by using the same brick type from the same brickwork (delivered at the same pallet). The used bricks were fired in a circular kiln were uneven heating during firing occurs. Significant color differences were visible between the bricks in the pallet and for the investigation purpose they were subdivided into three groups: bright, medium and dark colored bricks. The increasing color intensity is most probably caused by increasing firing temperatures. These three groups of bricks were investigated for saturation coefficient, open porosity, dry density and water absorption coefficient which revealed significant differences were encountered. The pore system was studied by using thin sections which demonstrated a change from relatively many fine pores to fewer wide pores with increasing brick firing temperatures. An additional significant difference in the pore system of each brick was found to be related to the distance to the surface. The influence of the pore system on ion transport through the water saturated pore system of the bricks was supported by measurements for calculation of the electrical resistance and an increasing resistance was found for increasing brick firing temperatures. The effective diffusion coefficient was empirically determined for chloride and sodium through the application of an electric DC field across the bricks. The lowest effective diffusion coefficient was found for the dark colored brick, increasing for the medium and bright colored respectively. This finding suggests that in clay bricks the presence of many fine pores improves ion transport compared to fewer wider pores.

Homogenisation of a locally periodic medium with areas of low and high diffusivity

We aim at understanding transport in porous materials consisting of regions with both high and low diffusivities. We apply a formal homogenisation procedure to the case wherethe heterogeneities are not arranged in a strictly periodic manner. The result is a two-scale model formulated inx-dependent Bochner spaces. We prove the weak solvability of the limit two-scale model for a prototypical advection–diffusion system of minimal size. A special feature of our analysis is that most of the basic estimates (positivity,L∞-bounds, uniqueness, energy inequality) are obtained in thex-dependent Bochner spaces.

Computational modelling of coupled water and salt transport in porous materials using diffusion–advection model

The diffusion–advection model taking into account not only the influence of water flow on salt transport but also the effect of bonded salt on pore walls is used for the description of coupled moisture and chloride transport in lime plaster. Moisture and chloride concentration profiles are determined experimentally and subjected to inverse analysis making possible to identify the moisture diffusivity as a function of moisture content and salt diffusion coefficient as a function of salt concentration. The results of experimental and computational investigations show that the moisture diffusivity of lime mortar increases fast with increase in moisture content, its maximum value being about 10 −6 m 2/s, which indicates very fast moisture transport in that material. The chloride diffusion coefficient of lime mortar is found very high, in the range 10 −6–10 −5 m 2/s. This can be explained by the action of additional driving forces, namely the surface diffusion and osmosis, which accelerate the chloride transport. The obtained results should find use in computational modelling of the damage of lime plasters in historical buildings caused by combined action of water and salts.

The measurement of water transport in porous materials using impedance spectroscopy

This paper describes the application of electrical measurements to monitor the extraction (movement of water from the mortar) of water from calcium lime, natural hydraulic lime and Portland cement mortars placed on an adsorbent brick substrate. Impedance measurements were used to identify the changes in bulk resistance of the mortar. A model has been developed combining sharp front theory and Boltzmann's distribution law of statistical thermodynamics to identify the point at which no further absorption of water into the brick occurs. A linear relationship was found between the exponential of bulk resistance and the square root of time during dewatering. A change in gradient was attributed to the end of dewatering.

A Numerical Approach for Non-Linear Moisture Flow in Porous Materials with Account to Sorption Hysteresis

A numerical approach for moisture transport in porous materials like concrete is presented. The model considers mass balance equations for the vapour phase and the water phase in the material together with constitutive equations for the mass flows and for the exchange of mass between the two phases. History-dependent sorption behaviour is introduced by considering scanning curves between the bounding desorption and absorption curves. The method, therefore, makes it possible to calculate equilibrium water contents for arbitrary relative humidity variations at every material point considered. The scanning curves for different wetting and drying conditions are constructed by using third degree polynomial expressions. The three coefficients describing the scanning curves is determined for each wetting and drying case by assuming a relation between the slope of boundary sorption curve and the scanning curve at the point where the moisture response enters the scanning domain. Furthermore, assuming that the slope of the scanning curve is the same as the boundary curve at the junction point, that is, at the point where the scanning curve hits the boundary curve once leaving the scanning domain, a complete cyclic behaviour can be considered. A finite element approach is described, which is capable of solving the non-linear coupled equation system. The numerical calculation is based on a Taylor expansion of the residual of the stated problem together with the establishment of a Newton-Raphson equilibrium iteration scheme within the time steps. Examples are presented illustrating the performance and potential of the model. Two different types of measurements on moisture content profiles in concrete are used to verify the relevance of the novel proposed model for moisture transport and sorption. It is shown that a good match between experimental results and model predictions can be obtained by fitting the included material constants and parameters.

Coupled simulation of heat and moisture transport in air and porous materials for the assessment of moisture related damage

This paper describes the coupling of a model for heat and moisture transport in porous materials to a commercial Computational Fluid Dynamics (CFD) package. The combination of CFD and the material model makes it possible to assess the risk of moisture related damage in valuable objects for cases with large temperature or humidity gradients in the air. To couple both models the choice was made to integrate the porous material model into the CFD package. This requires the heat and moisture transport equations in the air and the porous material to be written down in function of the same transported variables. Validation with benchmark experiments proved the good functionality of the coupled model. A simulation study of a microclimate vitrine for paintings shows that phenomena observed in these vitrines are well predicted by the model and that data generated by the model provides additional insights in the physical mechanisms behind these phenomena.

Combined Heat, Air and Moisture (HAM) Transfer Model for Porous Building Materials

In the building science area, mathematical models are developed to provide better indoor thermal comfort with lower energy consumption. Although the fact moisture and air transfer can strongly affect the temperature distribution within constructions, whole-building simulation codes do not take into account the convective air transport in porous materials. In this way, this article presents a heat, air, and moisture (HAM) transfer model based on driving potentials of temperature, air pressure, and water vapor pressure gradients for consolidated porous material in both pendular and funicular states. The solution of the set of governing equations has been simultaneously obtained using the MTDMA (MultiTriDiagonal-Matrix Algorithm) for the three potentials. To conclude, results are presented showing the impact of convective terms on the HAM transfer through a two-layer porous building envelope.

Modelling non-linear heat conduction via a fast matrix-free implicit unstructured-hybrid algorithm

A matrix-free implicit algorithm is developed for the fast and efficient solution of the non-linear diffusion equation on unstructured-hybrid meshes. The aforementioned captures the physics prevalent in plasticity (structural mechanics), moisture transport in porous materials and non-linear heat conduction. This paper will be restricted to the latter. The boundary condition types supported are prescribed temperature, convection and radiation type Neumann conditions. A compact edge-based vertex-centered finite volume technique is employed for spatial discretisation purposes, while implicit temporal discretisation is effected. The resulting system of equations is Newton-linearized, where approximate analytical expressions for the Jacobian terms are developed. The discrete system is solved via a preconditioned Generalised Minimal Residual (GMRES) algorithm, where Lower–Upper Symmetric Gauss–Seidel (LU-SGS) is used as preconditioner. The computational performance of the developed algorithm is demonstrated by application to the modelling of steady 2D non-linear heat conduction problems. The calculated Jacobian terms are stored in the interest of computational speed, with an associated additional overall memory cost of less than 10%. Even for small problems, the developed solver outperforms Jacobi with local time-stepping in terms of computational time by a factor ranging between 30 and 1000, while having a total memory requirement of 1.9 times the aforementioned. Further, as compared to the LU-SGS and GMRES methods, the proposed solver methodology offers a speed-up in solution time of between one and two orders of magnitude.

Estimation–identification problem for diffusive transport in porous materials based on single reservoir test: Results for silica hydrogel

In this paper the problems of selection of an appropriate model of diffusive transport in silica hydrogel and estimation of model parameters are considered. The analytical solutions and simulations of diffusive transport in a single reservoir test with equilibrium model of sorption are developed. The mathematical models refer to transport of solute from a porous material to water or in reverse direction assuming arbitrary initial concentrations and Dirichlet or mixed type of boundary conditions. In order to quantify the relative importance of the model parameters, logarithmic sensitivity analysis of solute concentration with respect to estimated parameters describing diffusion, sorption, and interfacial effects is performed. The application of the discussed models for estimation of transport parameters is discussed using experimental results for diffusion of sodium chloride in silica hydrogel.

Simulation of Radon Transport through Building Materials: Influence of the Water Content on Radon Exhalation Rate

Radon transport in porous materials is strongly influenced by the presence of water. It is also necessary to be able to numerically control the effects of this parameter. The radon concentration and radon exhalation rate have been determined by simulation in various building materials containing an increasing water content. It has been proved that the presence of water does not involve the same variations in the concentration on the surface of the medium, according to its porosity. For porous media with low porosity like concrete or granite, (e < 0.2), the radon concentration and radon exhalation rate sharply increase with water until the volumetric water content becomes higher than 30%. At this point, radon emanation plays an important role, in relation to the molecular diffusion process. For materials with medium porosities (e.g., limestone, brick, cement: 0.3 < e < 0.45), the concentration was observed to increase up to a volumetric water content of about 10% and then decreased from there. In this case, the molecular diffusion has a greater effect due to a greater quantity of pores in the material. For a small water content, this parameter tends to make the radon concentration decrease at the surface of the medium. These simulations have been compared with experimental analysis and are in strong accordance with the experimental results.

Modelling strategies for liquid spreading in medical absorbents

The use of validated computational models to predict liquid spreading in fibrous materials is an important tool for understanding and optimising the function of absorbent products. The aim of this paper is to review these modelling strategies and their limitations. Experimental methods to find the closure relationships required as an input into Richards' equation (which describes the fluid transport in porous materials) are discussed. The computational models are validated against the detailed laboratory experiments of the flow of fluid from sources on inclined or horizontal homogeneous fibrous sheets, and are extended to inhomogeneous layered structures. Recent progress towards modelling simple incontinence products is described.