Function Of Pore Size Research Articles

Diffusive nature of different gases in graphite: Implications for gas separation membrane technology

Graphite membranes have gained attention in membrane technology for gas separation due to their high stiffness, strength, and stability in corrosive and high-temperature environments. Graphite exists naturally in geologic media and can also be prepared by synthetic processes. In- situ hydrogen (H2) production in petroleum reservoirs or H2 storage in depleted gas reservoirs results in contamination with CH4 and CO2. To address the separation challenge at the surface, a sustainable downhole wellbore membrane must be available to separate H2, leaving behind CO2 and other gases to improve operational economics. Currently, there are no studies in the literature on the self-diffusivity of gases (CO2, H2, and CH4) in graphite as a function of pore size. To overcome time constraints in diffusivity experiments, this work utilized mathematical models and molecular simulations to delineate the self-diffusivity of gases in graphite of different pore sizes.To acknowledge subsurface operational conditions during in situ hydrogen production, we considered a temperature of 360 K and a wide pressure spectrum from 2 MPa to 20 MPa. In this study, we explored the diffusive nature of H2, CH4, and CO2 gases in different nanopore-sized graphite using analytical and molecular simulation approaches. We validated the results by presenting unrestricted case density calculations. First, effective diffusivity was calculated using the mean free pore path, followed by gas adsorption at high pressures (10–20 MPa) and a temperature of 350 K. The study utilized theoretical models and molecular dynamics (MD) simulations to determine the self-diffusivity of gases in graphite systems with various structures.

Impact of aminopropyl units on physisorption in mesostructured silica is larger for CH4 than CO2 and depends on pore curvature

Mesoporous silica-based materials attract great interest for diverse applications, including capture, storage, and catalysis due to their large surface area, uniform pore size distribution, and customizable surface. The regular 2D hexagonal pore symmetry of MCM-41 makes it an ideal model. Amine groups are introduced to enhance CO2 adsorption, but the interplay of factors influencing overall performance, including pore size, remains unclear. This computational study explores the physisorption of CO2 and CH4, shedding light on the microscopic details underlying adsorption capacity and selectivity. Three aminopropyl-functionalized MCM-41 models with different pore size are compared through Grand Canonical Monte Carlo and Molecular Dynamics simulations. Aminopropyl chains affect CO2 adsorption, but its affinity for the preserved silanol groups is larger. In addition, the competitive interaction between amine and silanol groups emerged, and it is pore curvature dependent. Surprisingly, CH4 physisorption is influenced even more by surface functionalization. Results show a non-monotonic trend as a function of pore size. Local density of the alkyl chains plays the major role. Overall, the intermediate pore size demonstrates the best performance, thanks to the balance among the various effects. The study emphasizes the importance of understanding the interplay between material texture and gas interactions to optimize adsorption performance.

Microstructural and transport characteristics of triply periodic bicontinuous materials

Three-dimensional (3D) bicontinuous two-phase materials are increasingly gaining interest because of their unique multifunctional characteristics and advancements in techniques to fabricate them. Because of their complex topological and structural properties, it still has been nontrivial to develop explicit microstructure-dependent formulas to predict accurately their physical properties. A primary goal of the present paper is to ascertain various microstructural and transport characteristics of five different models of triply periodic bicontinuous porous materials at a porosity ϕ1=1/2: those in which the two-phase interfaces are the Schwarz P, Schwarz D and Schoen G minimal surfaces as well as two different pore-channel structures. We ascertain their spectral densities, pore-size distribution functions, local volume-fraction variances, and hyperuniformity order metrics and then use this information to estimate certain effective steady-state as well as time-dependent transport properties via closed-form microstructure–property formulas. Specifically, the recently introduced time-dependent diffusion spreadability is determined exactly from the spectral density. Moreover, we accurately estimate the fluid permeability of such porous materials from a closed-form formula that depends on the second moment of the pore-size function and the formation factor, a measure of the tortuosity of the pore space, which is exactly obtained for the three minimal-surface structures. We also rigorously bound the permeability from above using the spectral density. For the five models with identical cubic unit cells, we find that the permeability, inverse of the specific surface, hyperuniformity order metric, pore-size second moment and long-time spreadability behavior are all positively correlated and rank order the structures in exactly the same way. We also conjecture what structures maximize the fluid permeability for arbitrary porosities and show that this conjecture must be true in the extreme porosity limits by identifying the corresponding optimal structures.

Microfluidic investigation of pore-size dependency of barite nucleation

The understanding and prediction of mineral precipitation processes in porous media are relevant for various energy-related subsurface applications. While it is well known that thermodynamic effects can inhibit crystallization in pores with sizes <0.1 µm, the retarded observation of mineral precipitation as function of pore size is less explored. Using barite as an example and based on a series of microfluidic experiments with well-defined pore sizes and shapes, we show that retardation of observation of barite crystallite can already start in pores of 1 µm size, with the probability of nucleation scaling with the pore volume. In general, it can be expected that mineralization occurs preferentially in larger pores in rock matrices, but other parameters such as the exchange of the fluids with respect to reaction time, as well as shape, roughness, and surface functional properties of the pores may affect the crystallization process which can reverse this trend.

Molecular insights into nuclear-magnetic-resonance properties of NaCl solution confined within calcite nanopores

Nuclear magnetic resonance (NMR) relaxation time is an important petrophysical property probing fluid dynamics within pores and providing valuable information to understand solid–fluid interactions and ion-related effects. In this study, we investigate NMR and diffusion properties of confined sodium chloride (NaCl) solutions within calcite nanopores via molecular dynamics (MD) simulations. Density profiles, self-diffusion coefficients, and NMR relaxation times were analyzed as a function of pore size, pore geometry, and NaCl concentration. MD results indicate that the presence of NaCl hinders water movement, resulting in reduced self-diffusion coefficients and relaxation times of water. Nevertheless, the influence of NaCl on water mobility is less than the effects caused by confinement and geometry. Strength of oscillations in water and ion density profiles increases when the slit pore size is reduced to 1 nm, suggesting that water-calcite interactions near pore surfaces are stronger in smaller pore sizes. Analysis of dipole–dipole correlation functions and probability distribution of correlation times shows that ions in aqueous solution have an impact on both intra- and intermolecular interactions. A comprehensive comparison of NMR relaxation times of water in both slit and spherical nanopores reveals that spherical models provide a more accurate representation of the confinement effect induced by pore networks within tight rocks. These findings provide a novel quantitative understanding of the impact of confinement, pore geometry, and ion concentration on the translational and rotational dynamics of confined fluids in calcite nanopores.

Modeling Dynamic Rate Dependent Pore Closure with A Range of Pore Sizes

Previously we presented a model (which we call PORT) with rate dependent pore closing/opening, for which we assumed that all pores close/open with the same dynamics [1]. Here we upgrade PORT to take into account different dynamics as function of pore size. We represent different pore sizes by their volume (v), and we have k discrete pore sizes. We therefore call this model VK. For the ith pore size we have ni, i=1,k pores per unit mass. We’re not aware of information on pore size distributions of porous materials, and we assume arbitrarily that pore sizes are initially distributed with a log-normal distribution. Similar to PORT, we define quasistatic pore closure curves that depend on pore volume v, and we compute the rate of pore closure with a linear overstress equation relative to these curves. From the values of v and vdot (rate of change of v) we then compute (for each cell and for each time) the overall porosity j and its rate of change jdot. Finally, we compute Pdot and Tdot (P=pressure and T=temperature) in the same way as in PORT, using the equation of state of the porous material. To show how our VK model works, we apply it to a simple 1D problem: a 20GPa sustained pressure pulse enters a porous aluminum target. We show histories of pressure, temperature and porosity at several locations into the target. We compare these curves to the ones obtained for k=1 (which are as in PORT).

Numerical analysis of the fluid-solid interactions during steady and oscillatory flows of non-Newtonian fluids through deformable porous media

The flow of non-Newtonian fluids through evolving porous media is involved in important processes including blood flow and remediation of deformable aquifers. However, the effects of a moving solid boundary and the coupling between fluid rheology and solid deformation are still unclear. This study considers the steady and oscillatory flows of a yield stress fluid through a bundle of deformable channels. Simple semi-empirical expressions to predict the relationships between Darcy velocity and pressure gradient as a function of pore sizes, shear-rheology parameters and inlet pressure are developped, based on the results of innovative numerical simulations. The results show that channel deformation reduces the minimum pressure gradient required to induce the flow of a yield stress fluid through a porous medium, which results in lower values of Darcy-scale viscosity. For the considered conditions, macroscopic flow can be accurately predicted without a detailed knowledge of the hydraulic conductances of the deformed pores.

Non-equilibrium Effects of Polymer Dynamics under Nanometer Confinement: Effects of Architecture and Molar Mass.

The non-equilibrium dynamics of linear and star-shaped cis-1,4 polyisoprenes confined within nanoporous alumina is explored as a function of pore size, d, molar mass, and functionality (f = 2, 6, and 64). Two thermal protocols are tested: one resembling a quasi-static process (I) and another involving fast cooling followed by annealing (II). Although both protocols give identical equilibrium times, it is through protocol I that it is easier to extract the equilibrium times, teq, by the linear relationships of the characteristic peak frequencies with time and rate, respectively, as log(fmax) = C1 - k log(t) and log(fmax) = C2 + λ log(β). Both thermal protocols establish the existence of a critical temperature (at Tc, where k → 0 and λ → 0) below which non-equilibrium effects set-in. The critical temperature depends on the degree of confinement, 2Rg/d, and on molecular architecture. Strikingly, establishing equilibrium dynamics at all temperatures above the bulk, Tg, requires 2Rg/d ∼ 0.02, i.e., pore diameters that are much larger than the chain dimensions. This reflects non-equilibrium configurations of the adsorbed layer that extent away from the pore walls. The equilibrium times depend strongly on temperature, pore size, and functionality. In general, star-shaped polymers require longer times to reach equilibrium because of the higher tendency for adsorption. Both thermal protocols produced an increasing dielectric strength for the segmental and chain modes. The increase was beyond any densification, suggesting enhanced orientation correlations of subchain dipoles.

Scaffold Pore Curvature Influences ΜSC Fate through Differential Cellular Organization and YAP/TAZ Activity.

Tissue engineering aims to repair, restore, and/or replace tissues in the human body as an alternative to grafts and prostheses. Biomaterial scaffolds can be utilized to provide a three-dimensional microenvironment to facilitate tissue regeneration. Previously, we reported that scaffold pore size influences vascularization and extracellular matrix composition both in vivo and in vitro, to ultimately influence tissue phenotype for regenerating cranial suture and bone tissues, which have markedly different tissue properties despite similar multipotent stem cell populations. To rationally design biomaterials for specific cell and tissue fate specification, it is critical to understand the molecular processes governed by cell-biomaterial interactions, which guide cell fate specification. Building on our previous work, in this report we investigated the hypothesis that scaffold pore curvature, the direct consequence of pore size, modulates the differentiation trajectory of mesenchymal stem cells (MSCs) through alterations in the cytoskeleton. First, we demonstrated that sufficiently small pores facilitate cell clustering in subcutaneous explants cultured in vivo, which we previously reported to demonstrate stem tissue phenotype both in vivo and in vitro. Based on this observation, we cultured cell-scaffold constructs in vitro to assess early time point interactions between cells and the matrix as a function of pore size. We demonstrate that principle curvature directly influences nuclear aspect and cell aggregation in vitro. Scaffold pores with a sufficiently low degree of principle curvature enables cell differentiation; pharmacologic inhibition of actin cytoskeleton polymerization in these scaffolds decreased differentiation, indicating a critical role of the cytoskeleton in transducing cues from the scaffold pore microenvironment to the cell nucleus. We fabricated a macropore model, which allows for three-dimensional confocal imaging and demonstrates that a higher principle curvature facilitates cell aggregation and the formation of a potentially protective niche within scaffold macropores which prevents MSC differentiation and retains their stemness. Sufficiently high principle curvature upregulates yes-associated protein (YAP) phosphorylation while decreased principle curvature downregulates YAP phosphorylation and increases YAP nuclear translocation with subsequent transcriptional activation towards an osteogenic differentiation fate. Finally, we demonstrate that the inhibition of the YAP/TAZ pathway causes a defect in differentiation, while YAP/TAZ activation causes premature differentiation in a curvature-dependent way when modulated by verteporfin (VP) and 1-oleyl-lysophosphatidic acid (LPA), respectively, confirming the critical role of biomaterials-mediated YAP/TAZ signaling in cell differentiation and fate specification. Our data support that the principle curvature of scaffold macropores is a critical design criterion which guides the differentiation trajectory of mesenchymal stem cells’ scaffolds. Biomaterial-mediated regulation of YAP/TAZ may significantly contribute to influencing the regenerative outcomes of biomaterials-based tissue engineering strategies through their specific pore design.

Ionophobicity of carbon sub-nanometer pores enables efficient desalination at high salinity

Electrochemical seawater desalination has drawn significant attention as an energy-efficient technique to address the global issue of water remediation. Microporous carbons, that is, carbons with pore sizes smaller than 2 nm, are commonly used for capacitive deionization. However, micropores are ineffective for capacitive deionization at high molar strength because of their inability to permselectively uptake ions. In our work, we combine experimental work with molecular dynamics simulation and reveal the ability of sub-nanometer pores (ultramicropores) to effectively desalinate aqueous media at seawater-like molar strength. This is done without any ion-exchange membrane. The desalination capacity in 600 mM reaches 12 mg/g, with a charge efficiency of 94% and high cycling stability over 200 cycles (97% of charge efficiency retention). Using molecular dynamic simulations and providing experimental data, our work makes it possible both to understand and to calculate desalination capacity and charge efficiency at high molar strength as a function of pore size.

Heat capacity, isothermal compressibility, isosteric heat of adsorption and thermal expansion of water confined in C-S-H

Nanoconfinement is known to affect the property of fluids. The changes in some thermo-mechanical properties of water confined in C-S-H are still to be quantified. Here, we perform molecular simulations to obtain the adsorption isotherms in C-S-H as a function of the pore size (spanning interlayer up to large gel pores). Then, fluctuations formula in the grand canonical ensemble are used to compute the isothermal compressibility (and its reciprocal, the bulk modulus), the heat capacity, the coefficient of thermal expansion and thermal pressure, and the isosteric heat of adsorption of confined water as a function of the (nano)pore size. All these properties exhibit a pore size dependence, retrieving the bulk values for basal spacing above 2 nm. To understand why property changes with confinement, we compute structural descriptors including the radial distribution function, apparent density, hydrogen bonds counting, and excess pair entropy of water as a function of the confinement. These descriptors reveal significant structural changes in confined water. The heat capacity shows a good linear correlation with the apparent density, entropy, and hydrogen bond number. The values of water property as a function of the basal spacing are a valuable input for multiscale modeling of cement-based materials.

Phase Behavior and Composition Distribution of Multiphase Hydrocarbon Binary Mixtures in Heterogeneous Nanopores: A Molecular Dynamics Simulation Study.

In this study, molecular dynamics (MD) simulation is used to investigate the phase behavior and composition distribution of an ethane/heptane binary mixture in heterogeneous oil-wet graphite nanopores with pore size distribution. The pore network system consists of two different setups of connected bulk and a 5-nm pore in the middle; and the bulk connected to 5-nm and 2-nm pores. Our results show that nanopore confinement influences the phase equilibrium of the multicomponent hydrocarbon mixtures and this effect is stronger for smaller pores. We recognized multiple adsorbed layers of hydrocarbon molecules near the pore surface. However, for smaller pores, adsorption is dominant so that, for the 2-nm pore, most of the hydrocarbon molecules are in the adsorbed phase. The MD simulation results revealed that the overall composition of the hydrocarbon mixture is a function of pore size. This has major implications for macro-scale unconventional reservoir simulation, as it suggests that heterogenous shale nanopores would host fluids with different compositions depending on the pore size. The results of this paper suggest that modifications should be made to the calculation of overall composition of reservoir fluids in shale nanopores, as using only one overall composition for the entire heterogenous reservoir can result in significant error in recovery estimations.

Critical pore radius and transport properties of disordered hard- and overlapping-sphere models

Transport properties of porous media are intimately linked to their pore-space microstructures. We quantify geometrical and topological descriptors of the pore space of certain disordered and ordered distributions of spheres, including pore-size functions and the critical pore radius δ_{c}. We focus on models of porous media derived from maximally random jammed sphere packings, overlapping spheres, equilibrium hard spheres, quantizer sphere packings, and crystalline sphere packings. For precise estimates of the percolation thresholds, we use a strict relation of the void percolation around sphere configurations to weighted bond percolation on the corresponding Voronoi networks. We use the Newman-Ziff algorithm to determine the percolation threshold using universal properties of the cluster size distribution. The critical pore radius δ_{c} is often used as the key characteristic length scale that determines the fluid permeability k. A recent study [Torquato, Adv. Wat. Resour. 140, 103565 (2020)10.1016/j.advwatres.2020.103565] suggested for porous media with a well-connected pore space an alternative estimate of k based on the second moment of the pore size 〈δ^{2}〉, which is easier to determine than δ_{c}. Here, we compare δ_{c} to the second moment of the pore size 〈δ^{2}〉, and indeed confirm that, for all porosities and all models considered, δ_{c}^{2} is to a good approximation proportional to 〈δ^{2}〉. However, unlike 〈δ^{2}〉, the permeability estimate based on δ_{c}^{2} does not predict the correct ranking of k for our models. Thus, we confirm 〈δ^{2}〉 to be a promising candidate for convenient and reliable estimates of the fluid permeability for porous media with a well-connected pore space. Moreover, we compare the fluid permeability of our models with varying degrees of order, as measured by the τ order metric. We find that (effectively) hyperuniform models tend to have lower values of k than their nonhyperuniform counterparts. Our findings could facilitate the design of porous media with desirable transport properties via targeted pore statistics.

On the Gibbs-Thomson equation for the crystallization of confined fluids.

The Gibbs-Thomson (GT) equation describes the shift of the crystallization temperature for a confined fluid with respect to the bulk as a function of pore size. While this century old relation is successfully used to analyze experiments, its derivations found in the literature often rely on nucleation theory arguments (i.e., kinetics instead of thermodynamics) or fail to state their assumptions, therefore leading to similar but different expressions. Here, we revisit the derivation of the GT equation to clarify the system definition, corresponding thermodynamic ensemble, and assumptions made along the way. We also discuss the role of the thermodynamic conditions in the external reservoir on the final result. We then turn to numerical simulations of a model system to compute independently the various terms entering in the GT equation and compare the predictions of the latter with the melting temperatures determined under confinement by means of hyper-parallel tempering grand canonical Monte Carlo simulations. We highlight some difficulties related to the sampling of crystallization under confinement in simulations. Overall, despite its limitations, the GT equation may provide an interesting alternative route to predict the melting temperature in large pores using molecular simulations to evaluate the relevant quantities entering in this equation. This approach could, for example, be used to investigate the nanoscale capillary freezing of ionic liquids recently observed experimentally between the tip of an atomic force microscope and a substrate.

A Monte Carlo Model of Gas-Liquid-Hydrate Three-phase Coexistence Constrained by Pore Geometry in Marine Sediments

Gas hydrates form at relatively high pressures in near-surface, organic-rich marine sediments, with the base of the hydrate stability field and the onset of partial gas saturation determined by temperature increases with depth. Because of pore-scale curvature and wetting effects, the transition between gas hydrate and free gas occurrence need not take place at a distinct depth or temperature boundary, but instead can be characterized by a zone of finite thickness in which methane gas bubbles and hydrate crystals coexist with the same aqueous solution. Previous treatments have idealized pores as spheres or cylinders, but real pores between sediment grains have irregular, largely convex walls that enable the highly curved surfaces of gas bubbles and/or hydrate crystals within a given pore to change with varying conditions. In partially hydrate-saturated sediments, for example, the gas–liquid surface energy perturbs the onset of gas–liquid equilibrium by an amount proportional to bubble-surface curvature, causing a commensurate change to the equilibrium methane solubility in the liquid phase. This solubility is also constrained by the curvature of coexisting hydrate crystals and hence the volume occupied by the hydrate phase. As a result, the thickness of the three-phase zone depends not only on the pore space geometry, but also on the saturation levels of the hydrate and gaseous phases. We evaluate local geometrical constraints in a synthetic 3D packing of spherical particles resembling real granular sediments, relate the changes in the relative proportions of the phases to the three-phase equilibrium conditions, and demonstrate how the boundaries of the three-phase zone at the base of the hydrate stability field are displaced as a function of pore size, while varying with saturation level. The predicted thickness of the three-phase zone varies from tens to hundreds of meters, is inversely dependent on host sediment grain size, and increases dramatically when pores near complete saturation with hydrate and gas, requiring that interfacial curvatures become large.

Structure of ice confined in silica nanopores.

Observed anomalous thermodynamic properties of confined water such as deviations in the melting point and freezing point motivate the determination of the structure of confined water as a function of pore size and temperature. In this study, we investigate the dynamic evolution of the structure of confined ice in SBA-15 porous materials with pore diameters of 4 nm, 6 nm, and 8 nm at temperatures ranging from 183 K to 300 K using in operando Wide-Angle X-Ray Scattering (WAXS) measurements, X-Ray Partial Distribution Function (PDF) measurements, and classical Molecular Dynamics (MD) simulations. Formation of hexagonal ice structures is noted in all the three pore sizes. In silica nanopores with diameters of 4 nm, cubic ice formation is noted in addition to hexagonal ice. Longer lasting hydrogen bonds and longer residence times of the water molecules in the first coordination shell contribute to observed crystalline organization of ice in confinement. Self-diffusion coefficients of confined liquid water, predicted from classical MD simulations, are four orders of magnitude higher compared to ice formed in confinement. These experimental and simulation results provide comprehensive insights underlying the organization of confined water and ice in silica nanopores and the underlying physico-chemical interactions that contribute to the observed structures.

Enhanced Spatial Light Confinement of All Inorganic Perovskite Photodetectors Based on Hybrid Plasmonic Nanostructures.

3D incident light confinement by radical electromagnetic fields offers a facile and novel way to break through the performance limit of inorganic perovskite CsPbBr3 quantum dots (QDs). Herein, metallic nanoparticles decorated anodic aluminum oxide (AAO) hybrid plasmonic nanostructures with geometric control are first proposed for cyclic light utilization of perovskite photodetectors, enabled by spatially extended light confinement. The drastic multiple interference induced by plasmonic coupling within AAO matrixes are generated as a function of pore sizes, which can effectively collect the transmitted photons back to the surface. In addition, the self-assembled metallic nanoparticles simultaneously concentrate the incident and reflected light beams into the CsPbBr3 QD layers. The light confinement inherently stems from the metallic nanoparticles due to the variation of the near surface electromagnetic fields. As a result, perovskite photodetectors based on Al nanoparticles/AAO hybrid plasmonic nanostructures with a pore size of 220nm exhibit enhanced photoresponse behavior with remarkably increased photocurrent by ≈43× and maintain low dark current under 490nm light illumination at 1V.

Cyclic γ-Peptides With Transmembrane Water Channel Properties.

Self-assembling peptides can be used to design new materials for medical and biological applications. Here we synthesized and characterized two novel cyclic γ-peptides (γ-CPs) with hydrophobic inner surfaces. The NMR and FT-IR studies confirmed that the CPs could self-assemble into parallel stacking structures via intermolecular H-bonds and π-π interactions. The morphologies of the self-assembly CPs showed bundles of nanotubes via transmission electron microscopy (TEM); these nanotubes form water channels to transport water across the lipid membrane. The properties of blocking the transport of protons like natural water channels showed that the hydrophobic inner surfaces are important in artificial transmembrane water channel designs. These studies also showed that water transport was a function of pore size and length of the assemblies.

Sorption of naphthalene and 2-naphthol onto porous carbonaceous materials as a function of pore size, metals, and oxygen-containing groups.

The important role of oxygen-containing groups of porous carbonaceous materials (PCMs) on sorption of organic compounds has been realized, but whether these groups can generate different joint effects, especially when oxidized PCMs with different pore sizes are complexed with heavy metals (Cu2+), remains ambiguous. The present study aimed to determine how pore sizes, metal ions, and oxygen-containing groups as a function affect the sorption of naphthalene and 2-naphthol to PCMs (e.g., activated carbons/ACs and mesoporous carbon/CMK-3). The H2-reduced oxidized PCMs were used as the control of low oxygen content to avoid changes in the pore structure properties compared with the oxidized PCMs. Oxygen-containing groups considerably decreased the sorption of naphthalene and 2-naphthol to PCMs because of their weaker hydrophobic interaction and fewer sorption sites. Notably, naphthalene sorption on oxidized AC was inhibited with Cu2+ because of the steric constraint of Cu2+ hydration shells of the micropores. However, pore blockage by Cu2+ reduced the mesopore size of oxidized CMK-3, leading to enhanced pore filling effect and cation-π bonding, and therefore increased naphthalene sorption. For 2-naphthol, the sorption to oxidized PCMs initially increased and then decreased with increasing Cu2+ concentration attributed to the fewer Cu2+ acting as a bridging agent and excess Cu2+ competing for sorption sites.

Capillary imbibition in open-cell monodisperse foams

Hypothesis: Although capillary imbibition of solid foams is involved in many industrial applications, general theory for capillary imbibition has never been proved to apply for this specific class of porous materials.Experiments: In order to compare accurately experiment and theory we produce solid foam samples with monodisperse pore size distributions and tunable pore volume fraction, and we measure their permeability (Darcy), their capillary pressure and their imbibition rate.Findings: Our findings reveal that the imbibition velocity is qualitatively compatible with the Washburn theory but it is one order of magnitude smaller than the predicted value. This deviation is attributed to the excess time spent by the liquid-gas interface through connections between pores, for which an empirical expression is provided as a function of pore size and solid volume fraction. Our results provide the first step to understand deeply the imbibition process in foams and to predict imbibition rates for various foamed materials.