Thin Porous Media Research Articles

A numerical model for the transport and drying of solutions in thin porous media — Coffee-stain effect and solute ring formation

We have developed a comprehensive numerical model for the transport and drying of solutions in thin porous media that consist of permeable fibers such as paper. We explicitly account for the gas-phase transport dynamics. Moreover, we introduce an empirical relation for the concentration- and molecular-weight dependence of the pore-fiber transport rate of the solutes. These two key elements enable us for the first time to realistically model two important phenomena relevant to inkjet printing technology. The first is the equivalent of the coffee-stain effect for dilute solutions in porous media. The second is the formation of solute rings for concentrated aqueous mixtures of compounds with a molecular weight significantly above that of water. Whereas the first is governed by spatially non-uniform solvent evaporation, the second case is dominated by solvent-mediated pore-fiber transport. We achieved a good qualitative agreement with the available experimental data.

Pore network simulations of thin porous medium characterization by evapoporometry

Evapoporometry is a technique aiming at characterizing the pore size distribution of a porous medium from evaporated mass measurements. In this work, evapoporometry is studied from numerical simulations on model pore networks allowing a detailed analysis of the underlying physics at play in the technique. Simulations indicate that both the pore body size and throat size distributions can be characterized and pinpoint the need of a very accurate determination of the evaporation rate. This is notably illustrated by varying the evaporated mass acquisition time step. Evapoporometry and liquid-liquid displacement porometry techniques are discussed comparatively in relation with experimental works reporting differences between the pore size distributions identified through both techniques.

Evaporative wicking in thin porous media

Evaporation cooling as an environment-friendly and energy-saving cooling option is usually realized by using porous medium to enhance the transport process, where the evaporation and wicking emerge simultaneously. Thin porous media are commonly applied in the evaporative wicking process. However, the evaporation on thin porous medium imposes significant impact on flow and heat transfer performance of evaporative wicking, which makes the prediction of evaporative wicking behavior more difficult. In this work, experimental studies of evaporative wicking of ethanol in Dutch Twill Weave (DTW) screens are carried out, where the evolution of wicking front and temperature distribution are captured by infrared thermography. Moreover, the numerical model that describes capillary rise, evaporation and heat transfer during evaporative wicking is built, which agrees well with the experimental results. Further investigation suggests that considering the evaporative cooling effect is indispensable for accurately predicting the evaporative wicking behavior in DTW screens. In addition, it is found that there is a rapid increase in temperature difference between the liquid and metal wires around the wicking front based on the local non-thermal equilibrium model.

Ultra Fast Imaging NMR method for measuring fast transport processes in thin porous media

Measuring moisture distributions during fast transport processes in thin porous media is a challenging task. In this paper, Ultra Fast Imaging (UFI) NMR is proposed as a valuable measurement technique for investigating moisture uptake in porous media by achieving a temporal resolution of 10 ms and spatial resolution between 14.5 and 18 μm. This paper gives a detailed explanation about the methodology and the interpretation of the signal intensity. It is shown that there exist specific T1- and T2− relaxation time conditions for performing UFI experiments with signal-to-noise ratios that are sufficiently high. In most cases, a contrast agent is required to optimize these relaxation times and achieve the optimal measurement conditions. In the first part of this paper, both CuSO4 and Clariscan are discussed as possible contrast agents. Furthermore, it is shown that the signal intensity can be linked to the moisture content for water based liquids. The second part of this paper covers penetration experiments on porous PVDF membranes. These measurements show that the technique is able to measure moisture profiles during fast capillary penetration and allows to extract moisture front positions. Those front positions follow a linear time behavior in PVDF membranes. Lastly the NMR-measurements showed similar results when compared to scanning absorptometry (ASA).

Experimental determination of in-plane permeability of nonwoven thin fibrous materials

Knowledge of hydraulic properties is crucial for understanding and modeling fluid flow in thin porous media. In this work, we have developed a new simple custom-built apparatus to measure the intrinsic permeability of a single thin fibrous sheet in the in-plane direction. The permeability was measured for two types of nonwoven thin fibrous porous materials using either the water or gas phase. For each layer, the measurements have been done for different combinations of flow direction and fiber orientation. The permeability values measured using gas and water were approximately close to each other. The permeability of the two samples was found to be anisotropic and the principal permeabilities were determined based on the measurements.

A new method to estimate the resistance coefficients of net panels modeled as porous media

Modeling net panels as thin porous media is an effective approach to carry out computational fluid dynamics (CFD) simulations of fishing nets and aquaculture cages. Existing methods to estimate the resistance coefficients for these porous media are based on simplified analytical models that relate these coefficients to the drag and lift coefficients of the panel. We propose a new method that uses a CFD model of the flow through a layer of porous media to estimate the resistance coefficients from regression analysis with experimental data. To increase the computational performance, the CFD model response is pre-calculated and interpolated in the regression analysis. The proposed method is applied to different net panels compared with existing methods. Results show that it provides better results than previous methods. Estimating both the inertial and the viscous resistance coefficients always provides better results than estimating just the inertial coefficients and it does not complicate the regression analysis with the proposed method. The method is easy to implement, fast and it could be used to estimate the resistance coefficients of materials other than net panels, since it does not make any assumption about the geometric characteristics of the actual material.

Spontaneous imbibition dynamics in two-dimensional porous media: A generalized interacting multi-capillary model

The capillary bundle model, wherein the flow dynamics of a porous medium is predicted from that of a bundle of independent cylindrical tubes/capillaries whose radii are distributed according to the medium's pore size distribution, has been used extensively. However, as it lacks an interaction between the flow channels, this model fails at predicting a complex flow configuration, including those involving a two-phase flow. We propose here to predict spontaneous imbibition in quasi-two-dimensional porous media from a model based on a planar bundle of interacting capillaries. The imbibition flow dynamics, and in particular, the breakthrough time, the global wetting fluid saturation at breakthrough, and which capillary carries the leading meniscus are governed by the distribution of the capillaries' radii and their spatial arrangement. For an interacting capillary system consisting of 20 capillaries, the breakthrough time can be 39% smaller than that predicted by the classic, non-interacting, capillary bundle model of identical capillary radii distribution, depending on the spatial arrangement of the capillaries. We propose a stochastic approach to use this model of interacting capillaries for quantitative predictions. Comparing bundles of interacting capillaries with the same capillary diameter distribution as that of the pore sizes in the target porous medium, and computing the average behavior of a randomly chosen samples of such interacting capillary bundles with different spatial arrangements, we obtain predictions of the position in time of the bulk saturating front and of that of the leading visible leading front, which agree well with measurements taken from the literature. This semi-analytical model is very quick to run and could be useful to provide fast predictions on one-dimensional spontaneous imbibition in porous media whose porosity structure can reasonably be considered two-dimensional, e.g., paper, thin porous media in general, or layered aquifers.

Transport and evaporation of aqueous co-solvent solutions in thin porous media

We have studied the imbibition and drying of water/co-solvent mixtures in paper and glass microfiber filters. The experiments reveal a rich interplay of solution imbibition, solvent evaporation and solvent-mediated pore-fiber transport. After deposition, liquids occupy the micron-scale inter-fiber pores of a paper sheet. In thermodynamic equilibrium, polar liquids such as water and co-solvents reside in the nm-scale intra-fiber pores of the cellulose fibers. The timescales for attaining equilibrium prove to depend sensitively on the water content, such that co-solvents can be temporarily trapped in a non-equilibrium configuration. The combination of two experimental methods allows the determination of both the overall co-solvent content and an estimation of what fractions reside in the pores and in the fibers of a paper sheet. The results are relevant to understanding the behavior of solutions in paper and provide insight into the dynamics of aqueous inkjet printing inks.

Carreau law for non-newtonian fluid flow through a thin porous media

Summary We consider the flow of generalized Newtonian fluid through a thin porous media. The media under consideration is a bounded perforated three dimensional domain confined between two parallel plates, where the distance between the plates is described by a small parameter $\varepsilon$. The perforation consists in an array of solid cylinders, which connect the plates in perpendicular direction, with diameter of size $\varepsilon$ and distributed periodically with period $\varepsilon$. The flow is described by the three dimensional incompressible stationary Stokes system with a nonlinear viscosity following the Carreau law. We study the limit when the thickness tends to zero and prove that the averaged velocity satisfies a nonlinear two-dimensional homogenized law of Carreau type. We illustrate our homogenization result by numerical simulations showing the influence of the Carreau law on the behavior of the limit system, in the case where the flow is driven by a constant pressure gradient and for different geometries of perforations.

Theoretical derivation of Darcy's law for fluid flow in thin porous media

AbstractIn this paper we study stationary incompressible Newtonian fluid flow in a thin porous media. The media under consideration is a bounded perforated 3D domain confined between two parallel plates. The description of the domain includes two small parameters: ε representing the distance between plates and connected to the microstructure of the domain such that . We consider the classical setting of perforated media, i.e. ‐periodically distributed solid (not connected) obstacles of size . The goal of this paper is to introduce a version of the unfolding method, depending on both parameters ε and , and then to derive the corresponding 2D Darcy law.

A Three-Dimensional Homogenization Approach for Effective Heat Transport in Thin Porous Media

Heat transport through a porous medium depends on the local pore geometry and on the heat conductivities of the solid and the saturating fluid. Through upscaling using formal homogenization, the local pore geometry can be accounted for to derive effective heat conductivities to be used at the Darcy scale. We here consider thin porous media, where not only the local pore geometry plays a role for determining the effective heat conductivity, but also the boundary conditions applied at the top and the bottom of the porous medium. Assuming scale separation and using two-scale asymptotic expansions, we derive cell problems determining the effective heat conductivity, which incorporates also the effect of the boundary conditions. Through solving the cell problems, we show how the local grain shape, and in particular its surface area at the top and bottom boundary, affects the effective heat conductivity through the thin porous medium.

Numerical study of the hydraulic tortuosity for fluid flow through elliptical particle packings

In this work, the hydraulic tortuosity (Th) specific for the binary-sized elliptical particle packings is studied using the Lattice Boltzmann method (LBM) and discrete element method (DEM). The model is validated by comparing with experimental and simulation data with an average deviation of 6% (Max 10%). Then the model is used to develop a reliable Th correlation to describe the fluid streamlines in elliptical particle packings. Firstly, a generalized Th correlation format is proposed, containing porosity (ε) and two empirical coefficients (a, b). Then the effects of ε and size ratio (r) on the Th are studied, and by curve-fitting the simulation results, the empirical coefficients (a, b) are formulated as a function of r. Meanwhile, the generalized Th correlation format is applicable for predicting the Th in porous media with different microstructures. The Th correlations provide a theoretical basis for macroscopic modelling of fluid flow through porous media of elliptical particles.

Inkjet printing of surfactant solutions onto thin moving porous media

We have studied the combined imbibition and evaporation of surfactant solutions into thin porous media by means of experiments and numerical simulations. Solutions of anionic and non-ionic surfactants were deposited onto moving sheets of paper by a droplet-on-demand inkjet system. Optical transmission imaging and infrared thermography were used to monitor their lateral transport and evaporation. Moreover, we propose a theoretical model based on a dual-porosity approach that accounts for moisture and surfactant transport in both the pores and the fibers of the paper sheets as well as for surfactant adsorption. The numerical simulations reproduce the experimental data qualitatively well.

Cerebral aneurysm flow diverter modeled as a thin inhomogeneous porous medium in hemodynamic simulations

Rapid and accurate simulation of cerebral aneurysm flow modifications by flow diverters (FDs) can help improving patient-specific intervention and predicting treatment outcome. However, when FD devices are explicitly represented in computational fluid dynamics (CFD) simulations, flow around the stent wires must be resolved, leading to high computational cost. Classic porous medium (PM) methods can reduce computational expense but cannot capture the inhomogeneous FD wire distribution once implanted on a cerebral artery and thus cannot accurately model the post-stenting aneurysmal flow. We report a novel approach that models the FD flow modification as a thin inhomogeneous porous medium (iPM). It improves over the classic PM approaches in two ways. First, the FD is more appropriately treated as a thin screen, which is more accurate than the classic 3D-PM-based Darcy–Forchheimer relation. Second, pressure drop is calculated cell-by-cell using the local FD geometric parameters across an inhomogeneous PM. We applied the iPM technique to simulating the post-stenting hemodynamics of three patient-specific aneurysms. To test its accuracy and speed, we compared the results from the iPM technique against CFD simulations with explicit FD devices. The iPM CFD ran 500% faster than the explicit CFD while achieving 94%–99% accuracy; thus, iPM is a promising clinical bedside modeling tool to assist endovascular interventions with FD and stents.

Lower-Dimensional Nonlinear Brinkman’s Law for Non-Newtonian Flows in a Thin Porous Medium

In this paper, we study the stationary incompressible power law fluid flow in a thin porous medium. The media under consideration is a bounded perforated 3D domain confined between two parallel plates, where the distance between the plates is very small. The perforation consists in an array solid cylinders, which connect the plates in perpendicular direction, distributed periodically with diameters of small size compared to the period. For a specific choice of the thickness of the domain, we found that the homogenization of the power law Stokes system results a lower-dimensional nonlinear Brinkman type law.

Inkjet deposition of lines onto thin moving porous media - experiments and simulations

We have studied the deposition of lines of water onto a thin porous medium by means of a droplet-on-demand, single-nozzle inkjet system. We systematically varied the substrate speed and the droplet frequency. Optical transmission imaging was used to measure the dynamic moisture distribution in the substrate in conjunction with infrared thermography to determine the in-plane temperature distribution of the paper. The temperature of the paper becomes non-uniform due to evaporative cooling. Furthermore, we have developed a two-dimensional model coupling the Richards equation for moisture transport in unsaturated porous media with evaporative mass loss and heat transfer. The results of the numerical simulations agree qualitatively well with the measured data.

Modeling Capillary Transport in Thin Porous Media Using a Composite Continuum-Pore Network Formulation: Effect of Water Blockage on Gas Diffusion and Convection

In this work, a composite continuum-pore network formulation is presented to model two-phase transport in thin fibrous porous media [1,2]. The composite model incorporates a control volume (CV) mesh at the layer scale, which embeds a structured cubic pore network. Capillary transport is simulated using the discrete pore network, considering the Purcell toroid model to determine the local entry capillary pressures in the fibrous material [3]. In addition, the pore-network model is used to determine analytically local anisotropic effective transport properties (local effective diffusivity and permeability), which are mapped onto the CV mesh to simulate transport within the porous layer using a continuum formulation. The relative effect of local water blockage on gas diffusion and convection is taken into account using a power-law function of the form (1-s)n, where s is the local liquid saturation. Good agreement is found between the predicted global effective transport properties (global effective diffusivity and permeability) under dry and wet conditions and previous experimental data reported in the literature for Toray TGP-H series carbon paper. Moreover, water saturation distributions are compared with results obtained using X-ray computed tomography [4]. As shown by García-Salaberri et al. [4,5], local water accumulation is found to play an important role on gas diffusion and convection. As a result, the exponent n increases from nearly n=2 at the local, pore scale to nearly n=3 at the global, layer scale. Currently, work is underway to implement the composite model in multiphysics models of a polymer electrolyte fuel cell and a redox flow battery to examine the impact of material heterogeinities on performance and durability.[1] P.A. García-Salaberri, I.V. Zenyuk, J.T. Gostick, A.Z. Weber, Modeling Gas Diffusion Layers in Polymer Electrolyte Fuel Cells Using a Continuum-based Pore-network Formulation, ECS Trans. 97 (7) 615.[2] P.A. García-Salaberri, Modeling diffusion and convection in thin porous transport layers using a composite continuum-network model: Application to gas diffusion layers in polymer electrolyte fuel cells, Int. J. Heat Mass Trans. (2020), accepted.[3] J.T. Gostick, Random Pore Network Modeling of Fibrous PEMFC Gas Diffusion Media Using Voronoi and Delaunay Tessellations, J. Electrochem. Soc 160 (2013) F731–F743.[4] P.A. García-Salaberri, G. Hwang, M. Vera, A.Z. Weber, J.T. Gostick, Effective diffusivity in partially-saturated carbon-fiber gas diffusion layers: Effect of through-plane saturation distribution, Int. J. Heat Mass Trans. 86 (2015) 319–333.[5] P.A. García-Salaberri, J.T. Gostick, G. Hwang, A.Z. Weber, M. Vera, Effective diffusivity in partially-saturated carbon-fiber gas diffusion layers: Effect of local saturation and application to macroscopic continuum models, J. Power Sources 296 (2015) 440–453.. Figure 1. Global relative effective diffusivity in the through-plane direction, gTP=Deff TP,wet/Deff TP,dry, as a function of average saturation, savg, computed with the composite continuum-pore network model. The gas species concentration distributions corresponding to different average saturations are shown on the top.. Figure 1

Investigation of Post-Darcy Flow in Thin Porous Media

We present numerical simulations of post-Darcy flow in thin porous medium: one consisting of staggered arrangements of circular cylinders and one random distribution of cylinders bounded between walls. The simulations span a range of Reynolds numbers, 40 to 4000, where the pressure drop varies nonlinearly with the average velocity, covering nonlinear laminar flow to the fully turbulent regime. The results are compared to those obtained by replacing the bounding walls with symmetric boundaries with the aim to reveal the effect of bounding walls on microscopic characteristics and macroscopic measures, i.e., pressure drop, hydrodynamic dispersion and Reynolds stresses. We use large eddy simulation to directly calculate the Reynolds stresses and turbulent intensity. The simulations show that vortical structures emerge at the boundary between the cylinders and the bounding walls causing a difference between the microscopic flow in the confined and non-confined porous media. This affects the averaged values of pressure drop, the hydrodynamic dispersion and the Reynolds stresses. Finally, the distance between the bounding walls is altered with the particle Reynolds number kept constant. It is observed that the difference between results calculated in confined and non-confined cases increases when the bounding walls are narrower.

Permeability Estimation of Regular Porous Structures: A Benchmark for Comparison of Methods

The intrinsic permeability is a crucial parameter to characterise and quantify fluid flow through porous media. However, this parameter is typically uncertain, even if the geometry of the pore structure is available. In this paper, we perform a comparative study of experimental, semi-analytical and numerical methods to calculate the permeability of a regular porous structure. In particular, we use the Kozeny–Carman relation, different homogenisation approaches (3D, 2D, very thin porous media and pseudo 2D/3D), pore-scale simulations (lattice Boltzmann method, Smoothed Particle Hydrodynamics and finite-element method) and pore-scale experiments (microfluidics). A conceptual design of a periodic porous structure with regularly positioned solid cylinders is set up as a benchmark problem and treated with all considered methods. The results are discussed with regard to the individual strengths and limitations of the used methods. The applicable homogenisation approaches as well as all considered pore-scale models prove their ability to predict the permeability of the benchmark problem. The underestimation obtained by the microfluidic experiments is analysed in detail using the lattice Boltzmann method, which makes it possible to quantify the influence of experimental setup restrictions.

Non-Stokesian flow through ordered thin porous media imaged by tomographic-PIV

The 3D flow-fields in a staggered and cubic arrangement of mono-radii cylinders are investigated using tomographic-PIV. The cylinder Reynolds-number is in the range of approx 10 to approx 800 giving an almost complete overview of the transition region. Two pore-scale effects are discovered. The first, visible in the cubic packing, is a spatially alternating lateral velocity field, which has a significant impact on the pressure drop and transversal dispersion. The second effect, present in the staggered array, is an example of a disturbance propagation effect that takes place in the laminar steady region; this manifests as a peculiar and complex flow-pattern. In accordance with other studies, it is shown that Darcy’s law can, from an engineering point of view be valid far beyond the limit for Stokesian flow.Graphic abstract