Transport In Porous Materials Research Articles

A network model to predict ionic transport in porous materials

Understanding the dynamics of electric-double-layer (EDL) charging in porous media is essential for advancements in next-generation energy storage devices. Due to the high computational demands of direct numerical simulations and a lack of interfacial boundary conditions for reduced-order models, the current understanding of EDL charging is limited to simple geometries. Here, we present a network model to predict EDL charging in arbitrary networks of long pores in the Debye-Hückel limit without restrictions on EDL thickness and pore radii. We demonstrate that electrolyte transport is described by Kirchhoff's laws in terms of the electrochemical potential of charge (the valence-weighted average of the ion electrochemical potentials) instead of the electric potential. By employing the equivalent circuit representation suggested by these modified Kirchhoff's laws, our methodology accurately captures the spatial and temporal dependencies of charge density and electric potential, matching results obtained from computationally intensive direct numerical simulations. Our network model provides results up to six orders of magnitude faster, enabling the efficient simulation of a triangular lattice of five thousand pores in 6 min. We employ the framework to study the impact of pore connectivity and polydispersity on electrode charging dynamics for pore networks and discuss how these factors affect the time scale, energy density, and power density of capacitive charging. The scalability and versatility of our methodology make it a rational tool for designing 3D-printed electrodes and for interpreting geometric effects on electrode impedance spectroscopy measurements.

A review of Microstructural Characterization and Liquid Transport in Porous Materials Through Image Processing Techniques

A review of Microstructural Characterization and Liquid Transport in Porous Materials Through Image Processing Techniques

Pore-structure control of porous carbon electrode materials and energy-storage performance in water-in-salt electrolytes

The pore structure of carbon-based materials and the voltage window of the electrolyte are two key factors affecting the energy density of carbon-based supercapacitors (SCs). In this paper, activated carbon materials of different pore sizes is successfully synthesized by chemical activation method by adjusting the mass ratio of ZnCl2 to sucrose, and successfully applied to construct SCs based on different electrolyte systems. As the specific surface area of the prepared porous carbon materials shows a tendency to increase and then decrease, reaching a maximum in the presence of micropores. Further summarizing the constitutive relationship between pore structure-electrochemical performance in the high-concentration electrolyte system, it is found that the normalized specific capacity is larger at smaller pore sizes, and with the increase of mesoporous proportion, the normalized specific capacity decreases and tends to be stable. In addition, the different strengths of solvation of anions and cations in the electrolyte, with the cations contributing more to the contrast, and the presence of mesopores providing ion transport channels to improve the efficiency of ion transport in porous materials, which provide directions for designing a suitable pore structure for highly concentrated salt electrolytes, as well as another way of optimizing the properties of carbon-based materials for SCs.

4D microvelocimetry reveals multiphase flow field perturbations in porous media

Many environmental and industrial processes depend on how fluids displace each other in porous materials. However, the flow dynamics that govern this process are still poorly understood, hampered by the lack of methods to measure flows in optically opaque, microscopic geometries. We introduce a 4D microvelocimetry method based on high-resolution X-ray computed tomography with fast imaging rates (up to 4 Hz). We use this to measure flow fields during unsteady-state drainage, injecting a viscous fluid into rock and filter samples. This provides experimental insight into the nonequilibrium energy dynamics of this process. We show that fluid displacements convert surface energy into kinetic energy. The latter corresponds to velocity perturbations in the pore-scale flow field behind the invading fluid front, reaching local velocities more than 40 times faster than the constant pump rate. The characteristic length scale of these perturbations exceeds the characteristic pore size by more than an order of magnitude. These flow field observations suggest that nonlocal dynamic effects may be long-ranged even at low capillary numbers, impacting the local viscous-capillary force balance and the representative elementary volume. Furthermore, the velocity perturbations can enhance unsaturated dispersive mixing and colloid transport and yet, are not accounted for in current models. Overall, this work shows that 4D X-ray velocimetry opens the way to solve long-standing fundamental questions regarding flow and transport in porous materials, underlying models of, e.g., groundwater pollution remediation and subsurface storage of CO2 and hydrogen.

Editorial to the Special Issue: Reactive Transport in Porous Materials: Current Trends and Challenges

Editorial to the Special Issue: Reactive Transport in Porous Materials: Current Trends and Challenges

Introduction of Asymmetry to Enhance Thermal Transport in Porous Metamaterials at Low Temperature

Introducing porosity with different degrees of disorder has been widely used to regulate thermal properties of materials, which generally results in decrease of thermal conductivity. We investigate the thermal conductivity of porous metamaterials in the ballistic transport region by using the Lorentz gas model. It is found that the introduction of asymmetry and Gaussian disorder into porous metamaterials can lead to a strong enhancement of thermal conductivity. By dividing the transport process into ballistic transport, non-ballistic transport, and unsuccessful transport processes, we find that the enhancement of thermal conductivity originates from the significant increase ballistic transport ratio. The findings enhance the understanding of ballistic thermal transport in porous materials and may facilitate designs of high-performance porous thermal metamaterials.

Imaging of unsaturated moisture flow inside cracked porous brick using electrical capacitance volume tomography

Concrete structures unavoidably suffer physical and chemical damage during service and hence easily crack. It is well-known that cracks in cement-based materials are preferential paths for the ingress of moisture and corrosive ions. Electrical capacitance volume tomography (ECVT) has previously been shown to be a powerful tool for imaging the spatial moisture distribution within cement-based materials. This paper investigated whether ECVT can be used for monitoring three-dimensional (3D) water penetration into porous materials containing different cracks. ECVT sensor with top electrodes and reconstruction algorithms were developed and evaluated respectively to improve the spatial resolution. The process of moisture ingress into bricks with different cracks was successfully visualized by ECVT, and the reconstructed results are in good agreement with the known properties of unsaturated water transport in porous materials. The ECVT reconstructions were also compared with moisture flow simulations, showing good agreement. Results suggest that ECVT is a viable tool for imaging 3D water penetration around cracks in porous materials, even for quantifying spatial water distribution.

Experimental Study on Capillary Microflows in High Porosity Open-Cell Metal Foams.

Metal foams have been widely used in heat pipes as wicking materials. The main issue with metal foams is the surface property capillary limit. In this paper, a chemical blackening process for creating a superhydrophilic surface on copper foams is studied with seven different NaOH and NaClO2 solution concentrations (1.5~4.5 mol/L), in which the microscopic morphology of the treated copper foam surface is analyzed by scanning electron microscopy. The capillary experiments are carried out to quantify the wicking characteristics of the treated copper foams and the results are compared with theoretical models. A the microscope is used to detect the flow stratification characteristics of the capillary rise process. The results show that the best wicking ability is obtained for the oxidation of copper foam using 3.5 mol/L of NaOH and NaClO2 solution. Gravity plays a major role in defining the permeability and effective pore radius, while the effect of evaporation can be ignored. The formation of a fluid stratified interface between the unsaturated and saturated zone results in capillary performance degradation. The current study is important for understanding the flow transport in porous materials.

Impact of asymmetries in valences and diffusivities on the transport of a binary electrolyte in a charged cylindrical pore

Ion transport in porous media is present in a wealth of technologies, e.g., energy storage devices such as batteries and supercapacitors, and environmental technologies such as electrochemical carbon capture and capacitive deionization. Recent studies on flat plate electrodes have demonstrated that asymmetries in ions properties, such as valences and diffusivities, lead to intriguing and counter-intuitive physical phenomena. Yet, the consequences of such asymmetries to ion transport have seldom been explored in porous geometries. To bridge this knowledge gap, we employ direct numerical simulations to solve Poisson-Nernst-Planck equations inside a cylindrical pore for a binary electrolyte with arbitrary valences and diffusivities. Next, we conduct a perturbation expansion in the limit of small potential and derive equations for charge and salt transport under confinement. We obtain good agreement between the perturbation analysis and the direct numerical simulations. Our analysis reveals that the charge and the salt transport are coupled with each other. Further, the coupling between the charge and salt transport processes is enhanced by an increase in valence and diffusivity asymmetries of ions. We observe that the mismatch of the ionic diffusivities induces a non-trivial salt dynamics, producing either transient depletion or enhancement of salt in the pore. In the regime of high static-diffusion-layer conductance, we obtain an analytical solution to our perturbation model. The solution elucidates how electrolyte asymmetry induces two charging timescales that are set by the relative pore size. In the overlapping-double-layer regime, these timescales reduce to the diffusion times of each ion such that the transport of the two ions appears to be decoupled. Overall, our work underscores that the asymmetry in cation and anion diffusivities fundamentally alters the behavior of ionic transport inside a charged cylindrical pore and opens up new avenues of research on electrolyte transport in porous materials.

Multiscale modeling of ion transport in porous electrodes

AbstractIon transport through nanoporous materials is of fundamental importance for the design and development of filtration membranes, electrocatalysts, and electrochemical devices. Recent experiments have shown that ion transport across porous materials is substantially different from that in individual pores. Here, we report a new theoretical framework for ion transport in porous materials by combining molecular dynamics (MD) simulations at nanopore levels with the effective medium approximation to include pore network properties. The ion transport is enhanced with the combination of strong confinement and dominating surface properties at the nanoscale. We find that the overlap of electric double layers and ion–water interaction have significant effects on the ionic distribution, flux, and conductance of electrolytes. We further evaluate the gap between individual nanopores and complex pore networks, focusing on pore size distribution and pore connectivity. This article highlights unique mechanisms of ion transport in porous materials important for practical applications.

Investigation of the transport properties for saline water in porous materials - Modeling of the permeability coefficient for saline water-

Salt weathering is a major concern for cultural heritages such as ruins and tombs, and desalination by poulticing is an interesting potential method to efficiently remove contaminating salt. Predicting the degree of achievable desalination is very important. However, many existing models used to consider saline water transport in porous materials have been developed based on the theory of pure water. To understand saline water flow in porous materials, we determined the saline water permeability of a tuff stone by the falling-head method. We found that the permeability of the tuff stone was affected by factors other than the density and dynamic viscosity of the saline water.

Confinement effects on the solvation structure of solvated alkali [correction] metal cations in a single-digit 1T-MoS2 nanochannel: A first-principles study.

Confinement plays an important role in determining ion transport in porous materials, which, in turn, may influence the performance of many energy storage and desalination devices. In this work, we combined density functional theory (DFT) with an implicit solvation model and ab initio molecular dynamics (AIMD) to investigate the effects of nanoconfinement on several solvated alkaline metal cations in a single-digit 1T-MoS2 nanochannel. Our DFT calculations with a solvation model indicated that cations with stronger hydration energy introduce a higher number of co-intercalated water molecules into the channel, consistent with early experimental observation obtained for MXene (2D transition metal carbide) channels. The predicted optimal water numbers for the cations were then used for AIMD simulations that explicitly include the effects of the solvent. When compared with the cations in bulk solution, our simulations showed that the hydration structure and coordination number (CN) of the solvated cations confined in the MoS2 channel can be significantly altered. We found that larger cations with weaker hydration energy (K+, Rb+, and Cs+) exhibited a distinctive CN decrease under confinement, while smaller cations (Li+ and Na+) retained a similar hydration shell as in the bulk solution. More specifically, the hydration shell of large cations (K+, Rb+, and Cs+) in MoS2 showed similar features of the coordination angle to the bulk, which suggests the partially broken hydration shell with no geometry change under confinement. Our simulations provided insights into the change of the hydration structure of alkaline metal cations under confinement, which may have important implications on their transport in the 1T-MoS2 channel.

Advancement in Urban Climate Modelling at Local Scale: Urban Heat Island Mitigation and Building Cooling Demand

As cities and their population are subjected to climate change and urban heat islands, it is paramount to have the means to understand the local urban climate and propose mitigation measures, especially at neighbourhood, local and building scales. A framework is presented, where the urban climate is studied by coupling a meteorological model to a building-resolved local urban climate model, and where an urban climate model is coupled to a building energy simulation model. The urban climate model allows for studies at local scale, combining modelling of wind and buoyancy with computational fluid dynamics, radiative exchange and heat and mass transport in porous materials including evaporative cooling at street canyon and neighbourhood scale. This coupled model takes into account the hygrothermal behaviour of porous materials and vegetation subjected to variations of wetting, sun, wind, humidity and temperature. The model is driven by climate predictions from a mesoscale meteorological model including urban parametrisation. Building energy demand, such as cooling demand during heat waves, can be evaluated. This integrated approach not only allows for the design of adapted buildings, but also urban environments that can mitigate the negative effects of future climate change and increased urban heat islands. Mitigation solutions for urban heat island effect and heat waves, including vegetation, evaporative cooling pavements and neighbourhood morphology, are assessed in terms of pedestrian comfort and building (cooling) energy consumption.

Nanoparticle Tracking to Probe Transport in Porous Media.

From the granular and fractured subsurface environment to highly engineered polymer membranes used in pharmaceutical purification, porous materials are ubiquitous in nature and industrial applications. In particular, porous media are used extensively in processes including water treatment, pharmaceutical sterilization, food/beverage processing, and heterogeneous catalysis, where hindered mass transport is either essential to the process or a necessary but undesirable limitation. Unfortunately, there are currently no universal models capable of predicting mass transport based on a description of the porous material because real porous materials are complex and because many coupled dynamic mechanisms (e.g., adsorption, steric effects, hydrodynamic effects, electrostatic interactions, etc.) give rise to the observed macroscopic transport phenomena.While classical techniques, like nuclear magnetic resonance and dynamic light scattering, provide useful information about mass transport in porous media at the ensemble level, they provide limited insight into the microscopic mechanisms that give rise to complex phenomena such as anomalous diffusion, hindered pore-space accessibility, and unexpected retention under flow, among many others. To address this issue, we have developed refractive index matching imaging systems, combined with single-particle tracking methods, allowing the direct visualization of single-particle motion within a variety of porous materials.In this Account, we summarize our recent efforts to advance the understanding of nanoparticle transport in porous media using single-particle tracking methods in both fundamental and applied scenarios. First, we describe the basic principles for two-dimensional and three-dimensional single-particle tracking in porous materials. Then, we provide concrete examples of nanoparticle transport in porous materials from two perspectives: (1) understanding fundamental elementary particle transport processes in porous media, including pore accessibility and cavity escape, which limit transport in porous media, and (2) facilitating applications in industrial processes, e.g., by understanding the mechanisms of particle fouling and remobilization in filtration membranes. Finally, we provide an outlook of opportunities associated with investigating other types of mass transport in confined environments using single-particle tracking methods, including electrophoretic and self-propelled motion.

A greyscale volumetric lattice Boltzmann method for upscaling pore-scale two-phase flow

Solving image-based pore-scale flow and transport in porous materials is a mainstream of fundamental and industrial research to reveal the pertinent physics in the field of hydrogeology, reservoir engineering, paper and filter engineering. This research discipline requires tremendous integration of multidisciplinary research areas of image processing, computational fluid modelling, and high-performance computing. The key challenge in pore-scale multi-phase flow simulation is the overwhelming computational expense. In this paper, we develop a new computational method that integrates GPU-accelerated volumetric lattice Boltzmann method (VLBM) with an upscaling scheme to solve the pore-scale two-phase flow at the centimetre-level length scales. The lattice Boltzmann concept is employed to solve both the level-set equation for image segmentation and governing equations for multi-phase flow dynamics. The signed distance field solved from the level set equation is used to calculate the void volume ratio of each lattice cell, resulting in a seamless connection between image segmentation and computational fluid dynamics. The pore-scale porous materials upscaling is carried out through the average void volume ratio of the neighbouring cells. The algorithm is rigorously tested in three cases: contact angle test for droplets between two plates, co-current flow in a cylindrical tube, and the two-phase flow in a sandstone sample. For the sandstone sample, the porosity, void space topology, relative permeability and preferential flow channels are well retained after 8-times upscaling, while the computational time is dramatically decreased.

Determination of the diffusion coefficient and the hydraulic conductivity of porous media based on embedded humidity sensors

Reinforced concrete and several other building materials deteriorate during their service life. Almost all deterioration processes are related to moisture. For understanding those processes, knowing the exact amount of the moisture content and the moisture transport characteristics is crucial. In fact, the moisture transport in porous materials is a two-phase flow; consisting of the vapour and the liquid phase. The two corresponding parameters are the diffusion coefficient and the hydraulic conductivity. By means of an inverse approach, these two coefficients are experimentally determined. The moisture transport of eight different screed types during hydration and evaporation is monitored based on embedded humidity sensors. The measured humidity profiles are converted into a pore saturation by adapting the approach of Hillerborg to the measured pore volume distribution. The summation of all pore saturations yields the total moisture content including the ink-bottle effect during desorption. The pore volume distribution was determined by mercury intrusion porosimetry as well as by gas adsorption. The measurement of the humidity and the pore saturation in the entire sample enables to invert the mass balance in order to extract the diffusion coefficient and the hydraulic conductivity. The determined diffusion coefficients of the eight investigated screeds are between 2.98·10^-8m2s-1 and 3.08·10^-7m2s-1.

Applications of critical path analysis to uniform grain packings with narrow conductance distributions: I. Single-phase permeability

Accurate estimation of single-phase permeability (k) has broad application in numerous areas, particularly modeling flow and transport in porous materials. Various techniques have been proposed in the literature to estimate k from other medium's properties, such as porosity, grain and/or pore size distribution, and pore connectivity. Among them critical path analysis (CPA) from statistical physics − first developed to model fluid flow in media with broad conductance distributions − has been successfully applied to heterogeneous soils and rocks. However, its application to uniform sphere and/or glass bead packs that represent homogeneous porous media with narrow conductance distributions needs to be investigated. In this study, we invoke concepts from CPA and estimate k from average grain diameter and formation factor in uniform sand and glass bead packings. By comparing theory with eight datasets including 105 packs from the literature, we demonstrate that CPA estimates permeability in homogeneous media accurately. We also compare our CPA-based model estimations with those from the Kozeny–Carman, Revil and Cathles, and RGPZ models. Results indicate that the CPA approach estimates k more precisely than other three models studied here.

Pore scale modelling of moisture transfer in building materials with the phase field method

This study explores the applicability of the phase field method for modelling moisture storage and transport in porous materials. Accordingly, the system is treated as a continuum where the phases (liquid and humid air) are separated through a diffuse interface, which evolves in the pores until the equilibrium state is reached. The interface thickness is related to the surface tension, while the contact angle is defined as a boundary condition. The mass transfer in the porous matrix is driven by the Cahn-Hilliard equation and the phase transition is controlled by an equation of state. The above method is tested for a simple geometry (infinitely extended parallel plates), by comparing the numerical outcomes against available measured data and analytical solutions. The challenges arising for a further application to complex pore structures and real building materials are discussed.

Multilayered Microfluidic Paper-Based Devices: Characterization, Modeling, and Perspectives.

Microfluidic paper-based analytical devices (μPADs) are simple but powerful analytical tools that are gaining significant recent attention due to their many advantages over more traditional monitoring tools. These include being inexpensive, portable, pump-free, and having the ability to store reagents. One major limitation of these devices is slow flow rates, which are controlled by capillary action in the hydrophilic pores of cellulosic paper. Recent investigations have advanced the flow rates in μPADs through the generation of a gap or channel between two closely spaced paper sheets. This multilayered format has opened up μPADs to new applications and detection schemes, where large gap sizes (>300 μm) provide at least 169× faster flow rates than single-layer μPADs, but do not conform to established mathematical models for fluid transport in porous materials, such as the classic Lucas-Washburn equation. In the present study, experimental investigations and analytical modeling are applied to elucidate the driving forces behind the rapid flow rates in these devices. We investigate a range of hypotheses for the systems fluid dynamics and establish a theoretical model to predict the flow rate in multilayered μPADs that takes into account viscous dissipation within the paper. Device orientation, sample addition method, and the gap height are found to be critical concerns when modeling the imbibition in multilayered devices.

Macroscopic description of quasi-static and quasi-stationary processes in unsaturated porous materials

The main aim of this work is to derive equations describing quasi-static and quasi-stationary processes of capillary transport of liquid and gas in unsaturated porous materials. Considerations are based on the new macroscopic model of the capillary transport in porous media, proposed in the paper (Cieszko, 2016). This model has been formulated in the spirit of the theory of interacting continua and shows that the capillary processes of transport in porous materials take place in five-dimensional pressure-time-space. This means that the equations for quasi-static and quasi-stationary processes are not a simple consequence of reduction of the general system of equations. An extended definition of quasi-static processes is proposed, allowing such processes to be analysed as a special case of the general description. A nonlinear first-order evolution equation is obtained for pore saturation with mobile liquid in quasi-static processes; it simultaneously describes the non-stationary processes of saturation evolution taking place in the pressure-space continuum. A new class of processes of capillary transport in unsaturated porous materials is proposed, called quasi-stationary, and a system of strongly coupled nonlinear equations describing these processes is derived. It is shown that even the geometrically very simple boundary value problem of non-wetting liquid flow through an unsaturated porous layer is described by a system of three nonlinear coupled equations for the saturation, pressure and velocity of the liquid.