Log-normal Pore Size Distribution Research Articles

Numerical simulation of pore structure and heat transfer behavior in aerated concrete

The pore structure of porous concrete is randomly formed, which brings thorny obstacle to accurately predict its thermal performance. In this study, a numerical approach was proposed for the simulation of pore structure and heat transfer behavior in aerated concrete. According to the porosity (ε) and log-normal pore size distribution parameters (μ, σ), an idea of “random distribution” was developed to reconstruct the pore structure via computer modeling, and also an overlap ratio (δ) was defined and adopted to generate a structure closer to reality. In parallel with this, a Finite Volume Model (FVM) was established to solve the energy control equation, and thus the effective thermal conductivities (ETCs) were numerically calculated. The calibrated and validated FVM model was also used to systematically study the effects of air-void content, air-void distribution and structural parameters, including pore size and porosity on the heat transfer behavior of aerated concrete. The numerical results show that the ETCs tend to slightly decrease with the increase of overlap ratio (δ), pore size (μ) and distribution (σ) due to an increased degree of consolidation between pores, which leads to the solid phase easily blocked by the connected pores so that the optimal heat transfer path through the solid phase conduction is blocked. Further, the comparisons of predictions of ETCs with the experimental data and other existing models indicate that the numerical predictions agree well with the experimental data, and the experimental and simulated values of the ETCs are intermediate between the Maxwell-Eucken 1 and Effective Medium Percolation Theory (EMPT) models.

Ultrasonic-Assisted Rapid Preparation of Sulfonated Polyether Ether Ketone (PEEK) and Its Testing in Adsorption of Cationic Species from Aqueous Solutions.

Herein, we report a new approach for the sulfonation of polyether ether ketone (PEEK) following a shorter path of reaction undertaken at 60 °C under ultrasonication. The application of this method enabled the reduction of the reaction time from several hours to less than one hour, achieving a relevant sulfonation degree. The sulfonated-PEEK (SPEEK) was characterized by advanced chemical and physical instrumental methods. According to 1H-NMR analysis, the degree of sulfonation of the polymer was equal to 70.3%. Advanced microscopy (SEM) showed that the fabricated SPEEK beads (2-4 mm) were porous inside with a log-normal distribution of pore sizes within the range 1.13-151.44 μm. As an application, the SPEEK polymer was tested for the adsorption of a cationic organic pollutant (Methylene blue, MB) from aqueous solutions. The equilibrium studies (isotherms) disclosed maximum adsorption capacities of 217 mg/g, 119 mg/g, and 68 mg/g at temperatures of 323 K, 313 K, and 300 K, respectively. The thermodynamic calculations indicated an endothermic effect (ΔHad = +11.81 kJ/mol) of the investigated adsorption process. The maximum removal efficiency of 99.14% was established by process optimization using the design of experiments strategy and data-driven modeling. Additionally, molecular docking simulations were performed to disclose the mechanism of interaction at the molecular level between the adsorbent (SPEEK) and pollutant.

Antibody retention by virus filtration membranes: Polarization and sieving effects

Virus filtration is a key component of the overall virus clearance strategy in the production of monoclonal antibodies. These virus filtration membranes also provide one of the most selective membrane separations ever demonstrated, with more than 95% recovery of the antibody product in the filtrate with more than 99.99% retention of even small parvovirus, despite the less than 2-fold difference in size between the virus and antibody. However, there is currently no quantitative data on the intrinsic sieving characteristics of commercially available virus filters. Experiments were performed with the Viresolve® Pro and Pegasus™ SV4 virus filters both with and without stirring to control the effects of concentration polarization. The actual sieving coefficient of a highly purified monoclonal antibody was less than 0.05 for both membranes, demonstrating that the high antibody recovery during typical virus filtration processes is a direct result of the high degree of concentration polarization in these systems. The intrinsic selectivity of the virus filter was in good agreement with predictions of available hydrodynamic models accounting for a log-normal pore size distribution. The actual sieving coefficient also decreased with increasing antibody concentration, consistent with available models for proteins with attractive interactions (negative values of the interaction parameter). These results provide important insights into the transport characteristics of virus filters and their effect on the performance of these virus filters in bioprocessing.

A three-parameter analytical model for the acoustical properties of porous media.

Many models for the prediction of the acoustical properties of porous media require non-acoustical parameters few of which are directly measurable. One popular prediction model by Johnson, Champoux, Allard, and Lafarge [J. Appl. Phys. 70(4), 1975-1979 (1991)] (459 citations, Scopus, April 2019) requires six non-acoustical parameters. This paper proves that the use of more than three parameters in the Johnson-Champoux-Allard-Lafarge model is not necessary at all. Here the authors present theoretical and experimental evidence that the acoustical impedance of a range of porous media with pore size distribution close to log-normal (granular, fibrous, and foams) can be predicted through the knowledge of the porosity, median pore size, and standard deviation in the pore size only. A unique feature of this paper is that it effectively halves the number of parameters required to predict the acoustical properties of porous media very accurately. The significance of this paper is that it proposes an unambiguous relationship between the pore microstructure and key acoustical properties of porous media with log-normal pore size distribution. This unique model is well suited for using acoustical data for measuring and inverting key non-acoustical properties of a wider range of porous media used in a range of applications which are not necessarily acoustic.

A High‐Resolution Global Map of Soil Hydraulic Properties Produced by a Hierarchical Parameterization of a Physically Based Water Retention Model

AbstractA correct quantification of mass and energy exchange processes among Earth's land surface, groundwater, and atmosphere requires an accurate parameterization of soil hydraulic properties. Pedotransfer functions (PTFs) are useful in this regard because they estimate these otherwise difficult to obtain characteristics using texture and other ubiquitous soil data. Most PTFs estimate parameters of empirical hydraulic functions with modest accuracy. In a continued pursuit of improving global‐scale PTF estimates, we evaluated whether improvements can be obtained when estimating parameters of hydraulic functions that make physically based assumptions. To this end, we developed a PTF that estimates the parameters of the Kosugi retention and hydraulic conductivity functions (Kosugi, 1994, https://doi.org/10.1029/93WR02931, 1996, https://doi.org/10.1029/96WR01776), which explicitly assume a lognormal pore size distribution and apply the Young‐Laplace equation to derive a corresponding pressure head distribution. Using a previously developed combination of machine learning and bootstrapping, the developed five hierarchical PTFs allow for estimates under practical data‐poor to data‐rich conditions. Using an independent global data set containing nearly 50,000 samples (118,000 retention points), we demonstrated that the new Kosugi‐based PTFs outperformed two van Genuchten‐based PTFs calibrated on the same data. The new PTFs were applied to a 1 × 1 km2 global map of texture and bulk density, thus producing maps of the parameters, field capacity, wilting point, plant available water, and associated uncertainties. Soil hydraulic parameters exhibit a much larger variability in the Northern Hemisphere than in the Southern Hemisphere, which is likely due to the geographical distribution of climate zones that affect weathering and sedimentation processes.

Apparent permeability and representative size of shale: a numerical study on the effects of organic matter

The impact of organic matter on the flow capacity of shale oil rocks is presumably significant, and the knowledge about the representative size is fundamental for the upscaling studies. The error of the experimentally determined permeability values is comparable with the contribution of kerogen to shale permeability, instead a 2D numerical model is employed to explore the normalised equivalent permeability and the representative elementary area (REA) of shale oil rocks in detail incorporating the effects of kerogen. The discussions on the normalised equivalent permeability and the REA are based on the statistical average and standard deviation from 1000 different runs, respectively. The inorganic permeability heterogeneity is introduced based on the assumption of a lognormal pore size distribution and the Monte Carlo sampling method. The effects of kerogen geometric characteristics are incorporated by putting forward several representative cases for comparison. The effects of the organic permeability contrast (ratio of permeability to the inorganic permeability with no heterogeneity), total organic carbon (TOC, volume fraction), inorganic permeability heterogeneity and kerogen geometric characteristics on the normalised equivalent permeability (ratio of the intrinsic equivalent permeability to inorganic permeability with no heterogeneity) and the REA are discussed comprehensively. This work can provide a better understanding of shale oil rocks at the micrometer scale.

A Method of Calculation of Apparent Gas Permeability for Tight Porous Media

Tight and shale gas reservoirs are characterized by pores in the range of micro- and nanometer. The description of the gas flow in such tight porous media is complicated by the coexistence of various flow regimes. Generally, porous media is represented by a bundle of tortuous capillaries and contributions of various flow regimes are incorporated by numerical integration of the flow rate of individual capillary, which causes inconvenience for practical application. In this paper, approximate expressions for apparent gas permeability of tight porous media with a relative error less than 0.1 based on the lognormal pore size distribution and the fractal pore size distribution have been separately derived. With the proposed expressions, apparent gas permeability of tight porous media can be calculated without numerical integration. The proposed method has been validated by published data.

Gas-liquid absorption in industrial cross-flow membrane contactors: Experimental and numerical investigation of the influence of transmembrane pressure on partial wetting

Membrane wetting is a limitation to mass transfer in industrial Hollow-Fiber Membrane Modules (HFMM). The influence of transmembrane pressure on wetting is investigated through both experimental and numerical works. On the one hand, experiments for CO2 absorption in softened water are carried out at pilot scale with Liqui-Cel® Extra-Flow modules operating in a cross-flow mode. After several hours of operation (50–300min), the membrane partially wetted mode is established at steady state and decreases the absorbed CO2 flowrates up to 10.5% compared to membrane dry mode. Interestingly, CO2 absorption is found to be independent on different transmembrane pressure (0.5 and 2.5bar), both in the dry and partially wetted mode. On the other hand, a 2D predictive tool is developed to help in the design of HFMM gas absorption systems. The model depicts the complex hydrodynamics in commercial cross-flow modules. The liquid in the shellside is flowing through the fiber bundle considered as a porous medium. The liquid mass-transfer coefficient is non-uniform over the membrane module and is estimated at a local scale. The parameters from the empirical Chilton-Colburn correlation are optimized with experimental results in the dry mode through a Particle Swarm Optimization (PSO) algorithm. The simulation results are in good agreement with the experiments (−13/+17%). In the partially wetted mode at steady state, wetting is then described by considering a log-normal pore size distribution and the Laplace-Young equation. The transmembrane pressure decreases the simulated absorbed CO2 flowrate. By comparing to experimental data, the numerical relative error is increasing with transmembrane pressure. Therefore, a suggestion is made to adapt the description of wetting in HFMM gas-liquid models.

Acoustic media with pore size distribution and assignment of the pore characteristic lengths and permeabilities

The model by Champoux and Allard [J. Appl. Phys. 70(4), 1975-1979 (1991)] is used extensively for research and development of new porous media solutions and for predicting sound propagation in the presence of porous media. Four key non-acoustical parameters in this model which are rarely measured non-acoustically are: the viscous and thermal characteristic lengths, thermal permeability and Pride parameter Pride et al [Phys. Rev. B 47, 4964-4978 (1993)]. In this work we show how these parameters unambiguously relate to the pore size distribution which is a characteristic measured nonacoustically and more routinely. We compare the predictions by this model against the log-normal pore size distribution model by Horoshenkov et al. [J. Acoust. Soc. Am. 104, 1198-1209 (1998)] and show that these two models provide very close predictions when the four non-acoustic parameters are expressed through the mean pore size and its standard deviation. We also confirm these results through a 4-microphone impedance tube experiment in which we determine the dynamic density and complex bulk modulus of a range of porous media. We also study the values of the viscous and thermal characteristic lengths and viscous and thermal permeabilities which fit our acoustic data.

Vapor intrusion in soils with multimodal pore-size distribution

The Johnson and Ettinger [1] model and its extensions are at this time the most widely used algorithms for estimating subsurface vapor intrusion into buildings (API [2]). The functions which describe capillary pressure curves are utilized in quantitative analyses, although these are applicable for porous media with a unimodal or lognormal pore-size distribution. However, unaltered soils may have a heterogeneous pore distribution and consequently a multimodal pore-size distribution [3], which may be the result of specific granulometry or the formation of secondary porosity related to genetic processes. The present paper was designed to present the application of the Vapor Intrusion Model (SVI_Model) to unsaturated soils with multimodal pore-size distribution. Simulations with data from the literature show that the use of a multimodal model in soils with such pore distribution characteristics could provide more reliable results for indoor air concentration, rather than conventional models.

Strength reliability and in vitro degradation of three-dimensional powder printed strontium-substituted magnesium phosphate scaffolds

Strontium ions (Sr2+) are known to prevent osteoporosis and also encourage bone formation. Such twin requirements have motivated researchers to develop Sr-substituted biomaterials for orthopaedic applications. The present study demonstrates a new concept of developing Sr-substituted Mg3(PO4)2 – based biodegradable scaffolds. In particular, this work reports the fabrication, mechanical properties with an emphasis on strength reliability as well as in vitro degradation of highly biodegradable strontium-incorporated magnesium phosphate cements. These implantable scaffolds were fabricated using three-dimensional powder printing, followed by high temperature sintering and/or chemical conversion, a technique adaptable to develop patient-specific implants. A moderate combination of strength properties of 36.7MPa (compression), 24.2MPa (bending) and 10.7MPa (tension) were measured. A reasonably modest Weibull modulus of up to 8.8 was recorded after uniaxial compression or diametral tensile tests on 3D printed scaffolds. A comparison among scaffolds with varying compositions or among sintered or chemically hardened scaffolds reveals that the strength reliability is not compromised in Sr-substituted scaffolds compared to baseline Mg3(PO4)2. The micro-computed tomography analysis reveals the presence of highly interconnected porous architecture in three-dimension with lognormal pore size distribution having median in the range of 17.74–26.29μm for the investigated scaffolds. The results of extensive in vitro ion release study revealed passive degradation with a reduced Mg2+ release and slow but sustained release of Sr2+ from strontium-substituted magnesium phosphate scaffolds. Taken together, the present study unequivocally illustrates that the newly designed Sr-substituted magnesium phosphate scaffolds with good strength reliability could be used for biomedical applications requiring consistent Sr2+- release, while the scaffold degrades in physiological medium. Statement of significanceThe study investigates the additive manufacturing of scaffolds based on different strontium-substituted magnesium phosphate bone cements by means of three-dimensional powder printing technique (3DPP). Magnesium phosphates were chosen due to their higher biodegradability compared to calcium phosphates, which is due to both a higher solubility as well as the absence of phase changes (to low soluble hydroxyapatite) in vivo. Since strontium ions are known to promote bone formation by stimulating osteoblast growth, we aimed to establish such a highly degradable magnesium phosphate ceramic with an enhanced bioactivity for new bone ingrowth. After post-processing, mechanical strengths of up to 36.7MPa (compression), 24.2MPa (bending) and 10.7MPa (tension) could be achieved. Simultaneously, the failure reliability of those bioceramic implant materials, measured by Weibull modulus calculations, were in the range of 4.3–8.8. Passive dissolution studies in vitro proved an ion release of Mg2+ and PO43- as well as Sr2+, which is fundamental for in vivo degradation and a bone growth promoting effect.In our opinion, this work broadens the range of bioceramic bone replacement materials suitable for additive manufacturing processing. The high biodegradability of MPC ceramics together with the anticipated promoting effect on osseointegration opens up the way for a patient-specific treatment with the prospect of a fast and complete healing of bone fractures.

Impact of long‐term mineral and organic fertilizer application on the water stability, wettability and porosity of aggregates obtained from two loamy soils

SummaryThe impact of fertilizer application on soil aggregate stability is of increasing interest to soil scientists. Aggregate water stability depends primarily on soil organic matter. We studied silty loam and loamy sand aggregates from three long‐term fertilizer treatments (control, pig manure and NPK) which significantly altered the quantity of organic matter. A new approach to examining aggregate stability was used: soil aggregates were immersed in methanol‐water solutions with methanol at 0, 20, 40 and 60% concentration (C), and non‐disrupted aggregates were separated after 30 minutes. The aggregate resistance R(C) against each solution was taken as the percentage of stable aggregates. Overall resistance of the aggregates was taken as the Rtot parameter given by the product of four R(C) values. The R(C) values of all aggregates were positively correlated with C. The R(60) values were independent of the applied fertilizer. The R(0) value for silty loam aggregates ranged from 28% (pig manure) to 7% (NPK), while that for loamy sand equalled 7–9% in all cases. The R(20) values were most effective at differentiating the soils and the fertilizer treatments. However, the Rtot value was a better indicator of aggregate stability. Greater differences in stabilities of aggregates were noted in loamy sand. Mineral fertilizer application seemed to decrease aggregate resistance in both soils. Total organic carbon and nitrogen content in all non‐disrupted aggregates were negatively correlated with methanol concentration (C) of the solution applied for aggregate separation. The largest decrease was for the pig manure treatment, and the smallest was for the control. Porosity and pore size distributions of the aggregates were derived from micro‐tomography and approximated to lognormal pore size distributions. Larger porosities and pores were found in water‐stable aggregates than in methanol‐stable aggregates. It seems that the dominant mechanisms for aggregate instability during fast wetting were not related only to the pore air compression, but to weakening of attractive forces between aggregate particles by water.

An AFM study of ultrafiltration membranes: Peculiarities of pore size distribution

The Mifil ultrafiltration membrane made from aromatic polyamide PA-100 has been studied using a SmartSPM-1000 atomic force microscope (AIST-NT, Zelenograd, Russia). Pores on the AFM images have been identified using the Gwyddion software in two ways, by threshold and watershed methods. The pore size data have been subjected to statistical processing and interpretation. Along with the log-normal pore-size distribution law, a bimodal curve of a special kind has been considered. The accuracy of the approximation has been assessed using Pearson’s goodness of fit test, in which the bimodal distribution has demonstrated better agreement with the experimental data. It has been shown that the watershed method provides more detailed information about the pore size distribution of the investigated membrane.

Fitting approach to liquid–liquid displacement porosimetry based on the log-normal pore size distribution

Liquid–liquid displacement porosimetry (LLDP) has been used to characterize several UF membranes in a wide range of molecular weight cut-offs (MWCO). A new method to convert porosimetric data into pore size distributions and related information has been developed based on assuming log-normal pore size distributions. The results of this are in good agreement with those from the customary data conversion algorithm (as derived by Grabar and Nikitine). The proposed method can also be used when a reduced number of experimental data points is available, leading to a significant reduction of data acquisition time needed to complete a reliable analysis.

Unsaturated hydraulic conductivity models based on truncated lognormal pore-size distributions.

We develop a closed-form three-parameter model for unsaturated hydraulic conductivity associated with the Kosugi three-parameter lognormal moisture retention model. The model derivation uses a slight modification to Mualem's theory, which is nearly exact for nonclay soils. Kosugi's three-parameter lognormal moisture retention model uses physically meaningful parameters, but a corresponding closed-form relative hydraulic conductivitymodel has never been developed. The model is further extended to a four-parameter model by truncating the underlying pore-size distribution at physically permissible minimum and maximum pore radii. The proposed closed-form models are fitted to well-known experimental data to illustrate their utility. They have the same physical basis as Kosugi's two-parameter model, but are more general.

Root induced changes of effective 1D hydraulic properties in a soil column.

AimsRoots are essential drivers of soil structure and pore formation. This study aimed at quantifying root induced changes of the pore size distribution (PSD). The focus was on the extent of clogging vs. formation of pores during active root growth.MethodsParameters of Kosugi’s lognormal PSD model were determined by inverse estimation in a column experiment with two cover crops (mustard, rye) and an unplanted control. Pore dynamics were described using a convection–dispersion like pore evolution model.ResultsRooted treatments showed a wider range of pore radii with increasing volumes of large macropores >500 μm and micropores <2.5 μm, while fine macropores, mesopores and larger micropores decreased. The non-rooted control showed narrowing of the PSD and reduced porosity over all radius classes. The pore evolution model accurately described root induced changes, while structure degradation in the non-rooted control was not captured properly. Our study demonstrated significant short term root effects with heterogenization of the pore system as dominant process of root induced structure formation.ConclusionsPore clogging is suggested as a partial cause for reduced pore volume. The important change in micro- and large macropores however indicates that multiple mechanic and biochemical processes are involved in root-pore interactions.

Nuclear Magnetic Resonance Pulsed Field Gradient study of self-diffusion of water in hydrated cement pastes

The results of one- and two-dimensional 1H nuclear magnetic resonance (NMR) pulsed field gradient (PFG) diffusometry studies of water in white cement paste with a water-tocement ratio 0.4 and aged from 1 day to 1 year are reported. The study shows that the NMRPFG method is primarily sensitive to the capillary porosity. Data is fit on the basis of a lognormal pore size distribution with pore size dependent relaxation times. The volume mean capillary pore size is 4.2 μm in mature paste, similar to 1 week suggesting that hydrates and gel porosity do not form in the capillary porosity once the latter has been substantially created. No evidence is found of capillary pore anisotropy in cement paste.

Environmental and management influences on temporal variability of near saturated soil hydraulic properties

Structural porosity is a decisive property for soil productivity and soil environmental functions. Hydraulic properties in the structural range vary over time in response to management and environmental influences. Although this is widely recognized, there are few field studies that determine dominant driving forces underlying hydraulic property dynamics. During a three year field experiment we measured temporal variability of soil hydraulic properties by tension infiltrometry. Soil properties were characterized by hydraulic conductivity, effective macroporosity and Kosugi's lognormal pore size distribution model. Management related influences comprised three soil cover treatment (mustard and rye vs. fallow) and an initial mechanical soil disturbance with a rotary harrow. Environmental driving forces were derived from meteorological and soil moisture data. Soil hydraulic parameters varied over time by around one order of magnitude. The coefficient of variation of soil hydraulic conductivity K(h) decreased from 69.5% at saturation to 42.1% in the more unsaturated range (−10cm pressure head). A slight increase in the Kosugi parameter showing pore heterogeneity was observed under the rye cover crop, reflecting an enhanced structural porosity. The other hydraulic parameters were not significantly influenced by the soil cover treatments. Seedbed preparation with a rotary harrow resulted in a fourfold increase in macroporosity and hydraulic conductivity next to saturation, and homogenized the pore radius distribution. Re-consolidation after mechanical loosening lasted over 18months until the soil returned to its initial state. The post-tillage trend of soil settlement could be approximated by an exponential decay function. Among environmental factors, wetting-drying cycles were identified as dominant driving force explaining short term hydraulic property changes within the season (r2=0.43 to 0.59). Our results suggested that beside considering average management induced changes in soil properties (e.g. cover crop introduction), a dynamic approach to hydrological modeling is required to capture over-seasonal (tillage driven) and short term (environmental driven) variability in hydraulic parameters.

Performance evaluation of models describing sorption isotherm in cementitious materials between saturation and oven dryness

The objective of this work is to evaluate nine closed-form analytical expressions that describe the sorption isotherm across the complete range of water contents for cementitious materials.To meet this objective, the models were compared in terms of their accuracy root mean square error (RMSE), linearity (coefficient of determination, R2, and adjusted coefficient of determination, Radj2), and prediction potential. Experimental data from controlled drying experiments performed on four cementitious materials were used for the model comparisons. All tested models were found to propose relatively realistic fits, and to have similar performances when tested on different types of materials except for cement paste with lower water to cement ratio.Models involving a large number of parameters do not significantly perform better than more simple ones, especially when one account for extra cost in terms of robustness implied by additional parameters.Overall, the Kosugi model based on a lognormal pore size distribution appears to be the best compromise between goodness of fit and number of parameters to estimate.

Construction of 2D transparent micromodels in polyester resin with porosity similar to carrots

Microscopic visualization, especially in transparent micromodels, can provide valuable information to understand the transport phenomena at pore scale in different process occurring in porous materials (food, timber, soils, etc.). Micromodels studies focus mainly on the observation of multi-phase flow, which presents a greater proximity to reality. The aim of this study was to study the process of flexography and its application in the manufacture of polyester resin transparent micromodels and its application to carrots. Materials used to implement a flexo station for micromodels construction were thermoregulated water bath, exposure chamber to UV light, photosensitive substance (photopolymer), RTV silicone polyester resin, and glass plates. In this paper, data on size distribution of a particular kind of carrot we used, and a transparent micromodel with square cross-section as well as a Log-normal pore size distribution with pore radii ranging from 10 to 110 µm (average of 22 µm and micromodel size of 10 × 10 cm) were built. Finally, it stresses that it has successfully implemented the protocol processing 2D polyester resin transparent micromodels.