Guggenheim Model Research Articles

Osmotic Dehydration Model for Sweet Potato Varieties in Sugar Beet Molasses Using the Peleg Model and Fitting Absorption Data Using the Guggenheim-Anderson-de Boer Model.

This study investigates the applicability of the Peleg model to the osmotic dehydration of various sweet potato variety samples in sugar beet molasses, addressing a notable gap in the existing literature. The osmotic dehydration was performed using an 80% sugar beet molasses solution at temperatures of 20 °C, 35 °C, and 50 °C for periods of 1, 3, and 5 h. The sample-to-solution ratio was 1:5. The objectives encompassed evaluating the Peleg equation's suitability for modeling mass transfer during osmotic dehydration and determining equilibrium water and solid contents at various temperatures. With its modified equation, the Peleg model accurately described water loss and solid gain dynamics during osmotic treatment, as evidenced by a high coefficient of determination value (r2) ranging from 0.990 to 1.000. Analysis of Peleg constants revealed temperature and concentration dependencies, aligning with previous observations. The Guggenheim, Anderson, and de Boer (GAB) model was employed to characterize sorption isotherms, yielding coefficients comparable to prior studies. Effective moisture diffusivity and activation energy calculations further elucidated the drying kinetics, with effective moisture diffusivity values ranging from 1.85 × 10-8 to 4.83 × 10-8 m2/s and activation energy between 7.096 and 16.652 kJ/mol. These findings contribute to understanding the complex kinetics of osmotic dehydration and provide insights into the modeling and optimization of dehydration processes for sweet potato samples, with implications for food processing and preservation methodologies.

Effect of Heat Treatment on Hygroscopicity of Chinese Fir (Cunninghamia lanceolata [Lamb.] Hook.) Wood

Chinese fir (Cunninghamia lanceolata [Lamb.] Hook.) is a widely planted species of plantation forest in China, and heat treatment can improve its dimensional stability defects and improve its performance. The wood samples were heat-treated at various temperatures (160, 180, 200, and 220 °C) for 2 h. To clarify the effect of heat treatment on wood hygroscopicity, the equilibrium moisture content (EMC) was measured, the moisture adsorption and desorption rates were determined, the hygroscopic hysteresis was examined, and the Guggenheim, Anderson, and de Boer (GAB) model was fitted to the experimental data. The moisture absorption isotherms of all samples belonged to the Type II adsorption isotherm, but the shape of the desorption isotherm was more linear for heat-treated wood samples, especially when the heat treatment temperature was higher. According to the results analyzed with ANOVA, there were significant differences in equilibrium moisture content between the control samples and the heat-treated samples under the conditions of 30%, 60%, and 95% relative humidity (RH, p < 0.05), and the results of multiple comparisons were similar. The decrease in hygroscopicity was more pronounced in wood treated at higher temperatures. The EMC of the 160–220 °C heat-treated samples of the control samples was 14.00%, 22.37%, 28.95%, and 39.63% lower than that of the control sample at 95% RH. Under low RH conditions (30%), water is taken up mainly via monolayer sorption, and multilayer sorption gradually predominates over monolayer sorption with the increase in RH. The dynamic vapor sorption (DVS) analysis indicated that the heat-treated wood revealed an increase in isotherm hysteresis, which was due to the change in cell wall chemical components and microstructure caused by heat treatment. In addition, the effective specific surface area of wood samples decreased significantly after heat treatment, and the change trend was similar to that of equilibrium moisture content.

Properties, Structure, and Acceptability of Innovative Legume-Based Biscuits with Alternative Sweeteners.

The effects of legume incorporation and sweetener substitution on the quality characteristics of innovative biscuits were investigated. The wheat flour was substituted with chickpea and lentil flour at ratios ranging from 0 to 30% legume to whole-meal dicoccum wheat flour. The sugar was substituted by oligofructose at 50 and 100% levels. The quality characteristics, including physicochemical properties (moisture content, water activity, and color), sorption characteristics, structural and textural properties, and sensory properties, were significantly affected by the substitutions. Sorption phenomena were excellently described by the Guggenheim, Anderson, and de Boer (GAB) model, while its parameters were affected by substitutions. Scanning electron microscopy revealed a porous structure with starch granules embedded within the protein matrix, showing restricted gelatinization and keeping largely their form. The incorporation of legume flour increased the biscuit density, hardness, and spread ratio and decreased the color of the products. Furthermore, principal component analysis (PCA) analysis of instrumental and sensory characteristics showed that texture and sweetness were the key quality characteristics for product acceptance. It was found that highly acceptable legume-based biscuits with alternative sweeteners can be produced, with 50% oligofructose substitution and legume flour incorporation (chickpea or lentil) up to 30%.

Process modeling and simulation of Gmelina arborea (GmW) and Mansonia altissima (MaW) wood drying

This study simulate the process modeling of drying characteristics of Gmelina arborea (GmW) and Mansonia altissima (MaW) wood under the influence of various process variables such as drying time, drying temperature, and airflow velocity. GmW and MaW moisture desorption isotherms, kinetics, and thermodynamics were also studied. Five (5) thin-layer and desorption isotherm drying models were used to model the moisture ratio and water activity data from the process. According to the anatomical analysis, the GmW sample has an average lumen size of 147.44 m, indicating a high moisture content. The results showed that the Guggenheim, Anderson, and de Boer (GAB) model with the lowest sum of squared error value (0.046) demonstrated the best-fit to the experimental desorption data for GmW samples and the Henderson-P model for MaW samples, while the Demir et al. model emerged as the best kinetics model fit for describing the moisture desorption isotherm and thin-layer drying kinetics. GmW effective diffusivity (Deff) values ranged from 3.671 × 10−8 to 5.378 × 10−8 m2/s and MaW effective diffusivity (Deff) values ranged from 2.923 × 10−8 to 4.678 × 10−8 m2/s. GmW and MaW activation energies were 252.702 kJ/mol and 313.604 kJ/mol, respectively. The thermodynamic studies revealed that the heat and mass transfer coefficients varied linearly with temperature, as the change in enthalpy (ΔH) and change in entropy (ΔS) decreased while the Gibbs free energy (ΔG) increased. The results obtained from this study demonstrated that the proposed drying process modeling and simulation approach could be successfully applied to investigate the wood drying phenomena. The information can be used to reduce the drying costs and improve the wood quality.

Characterization, mathematical modeling of moisture sorption isotherms and bioactive compounds of Andean root flours

Andean roots can be used as an alternative to gluten-free food. The objective of this study was to enhance the technological and nutritional properties of Andean root flours to promote their industrial applicability. The water content and activity of the flour were lower than those required to prevent mold growth. The bulk density of the flour was comparable to that of wheat flour. The flour of Ipomoea batatas (L.) Lam. exhibited the lowest water absorption capacity of the tested samples. However, both this flour and Tropaeolum tuberosum Ruiz & Pavón showed a higher fat absorption capacity. The samples exhibited type-II isotherms, indicating that the flours were highly hygroscopic. The Guggenheim, Anderson, and de Boer GAB model showed a higher coefficient of determination in mathematical modeling. The chroma of T. tuberosum Ruiz & Pavón flour was higher than the other samples, which was related to total carotenoids and lycopene. Furthermore, I. batatas (L.) Lam. exhibited the highest phenol value.

Surface tension and viscosity of Zr–Ti–Cu liquid alloys

Surface tension and viscosity are two main process parameters in the metallurgical industry, especially for high-temperature alloys, such as Zr–Ti–Cu which exhibits excellent characteristics of high strength and high corrosion resistance. However, the surface tension and viscosity of Zr–Ti–Cu alloys are rarely studied. In this work, the surface tension of Zr–Ti–Cu alloy was measured by the pendant drop method. The surface tension and viscosity Zr–Ti–Cu alloy were calculated by our revised modified Guggenheim model and the new CALPHAD-type equation of viscosity proposed in our previous work respectively. The surface tension and viscosity database of the Zr–Ti–Cu system were constructed.

Sorption properties of paper treated with silane-modified starch

Sorption properties of paper products are important when applying paper as the packaging material. Hydrophobicity, i.e. reduced affinity of paper surface to liquid water, is of particular importance from the point of view of the direct impact on packed goods. However, hygroscopicity of the material is significant during storage of goods. The analysis of changes in the hygroscopic properties of paper products induced by the treatment with silane modified starch was presented. The results on the hygroscopicity of treated paper were related to the previously published results on the hydrophobicity. The discrete values of equilibrium moisture content allowed constructing adsorption and desorption isotherms. The three-parameter Guggenheim, Anderson, and De Boer (GAB) model, the four-parameter Generalized D’Arcy and Watt (GDW), and Yanniotis and Blahovec (Y-B) sorption isotherm models were used to quantify the hygroscopic properties for all options of untreated and modified paper samples. The effectiveness of silanes for improving hygroscopic properties was determined and compared to their impact on hydrophobicity of the studied materials. It was found that 1H, 1H, 2H, 2H-perfluorooctyltriethoxysilane was the only silane improving hydrophobic and hygroscopic properties. The analysis of the applied models of sorption isotherms depicted that the GAB model was not valid for describing water sorption isotherms in the case of the tested materials, while the GDW and Y-B models provided a much more realistic description of water sorption mechanisms. The evaluation of the results of fitting the GDW model indicated that water molecules bonding to the primary sites was the dominating mechanism of sorption.

Utilization of clay based super-porous hydrogel composites in atmospheric water harvesting

Current research work reports the synthesis and performance evaluation of solid polymer desiccant materials based on the superporous hydrogel composites (SPHCs) comprising superporous hydrogel (SPHs) of sodium acrylate (SA) and acrylamide (AM) with different clays such as Laponite®, bentonite and palygorskite. Synthesized polymer desiccants were characterized using SEM, XRD, TGA and FTIR techniques. All the polymer desiccants followed type-III isotherm and the experimental data correlated well with Guggenheim, Anderson and Boer (GAB) model and suggested that these desiccants belong to macroporous adsorbents and adsorb water vapors largely via capillary condensation process. Parental SPH (i.e. P(SA-co-AM)-SPH) and different SPHCs i.e. SPHC-Laponite®, SPHC-bentonite and SPHC-palygorskite exhibited maximum adsorption capacities of 0.12, 0.17, 0.15 and 0.14 gw/gads, respectively at 50% relative humidity and 25 °C, however, at 90% relative humidity adsorption capacities increased upto 0.77, 1.05, 0.93 and 0.87 gw/gads, respectively, which suggested that the hydrophilicity of synthesized desiccants increased with increasing relative humidity. Exceptionally high adsorption capacities of these desiccants were because of the combined effects of highly porous structure of SPHs and hydrophilic nature of clays. Furthermore, experimental kinetics data correlated well with linear driving force model and suggested that the diffusion of water within polymer structure was via type-II diffusion mechanism. During multiple cycle adsorption, SPHCs exhibited much better re-use efficiency than SPHs which suggested that the incorporation of clays within the polymer matrix not only improved desiccant performance but also improved re-use efficiency of polymer desiccants.

Surface Tension of GaInSnBiZn Liquid High-entropy Alloy

As an emerging alloy material, high-entropy alloy has potential applications that distinguish it from traditional alloys due to its special physicochemical properties. In this work, a low melting point GaInSnBiZn high-entropy alloy was designed based on Miedema model, and its surface tension was measured by the continuous pendant-drop method. The results show that the intrinsic surface tension of GaInSnBiZn high-entropy alloy at 80 °C is 545±5 mN/m, and the surface tension of the liquid alloy is significantly reduced by the formation of surface oxide film. The surface tension of GaInSnBiZn high-entropy alloy was analyzed by using theoretical models (Guggenheim model, GSM (general solution) model and Butler model), and the thermodynamic characteristics of the surface tension formation were further verified by combining with thermodynamic calculations, among which the calculated results of Butler model were in good agreement with the experimental data. Meanwhile, it is found that the surface concentration of Bi in the alloy is much larger than the nominal concentration of its bulk phase, which contributes the most to the surface tension of the alloy, however, it contributes the least to the entropy of the alloy formation in combination with the Butler model.

Effects of maltodextrin on physicochemical properties of freeze-dried avocado powder

The effect of maltodextrin on the moisture sorption isotherm, glass transition temperature (Tg), and degree of caking of freeze-dried avocado samples at room temperature (25°C) was investigated. The incorporation of maltodextrin reduced the water sorption capacity of the powder due to its less hygroscopic nature. Parameters derived from the Guggenheim, Anderson, and de Boer (GAB) model describing the properties of absorbed water are discussed. The water absorption isotherm possessed the characteristic sigmoid-shaped type II isotherm curves and the model gave the best fit over the whole range of aw tested. The differential scanning calorimetric method was used to measure the Tg of freeze-dried avocado samples. Increasing the water content decreased the Tg, and Tg was increased with increasing maltodextrin content. Increased maltodextrin content to solid material in the freeze-dried sample was associated with less sensitivity to caking as evidenced by Tg values. In addition, increased maltodextrin content in the powders caused brighter, less yellowish, and more greenish coloration and protected color change including browning index. The antioxidant capacity was significantly decreased with increasing maltodextrin content. Thus, the effect of maltodextrin concentration on physicochemical properties was a promising way to preserve the physical property and chemical compounds in freezedried avocado powder.

Water sorption characteristics of freeze-dried bacteria in low-moisture foods

Water sorption isotherms of bacteria reflect the water activity with the change of moisture content of bacteria at a specific temperature. The temperature-dependency of water activity change can help to understand the thermal resistance of bacteria during a thermal process. Thermal resistance of bacteria in low-moisture foods may differ significantly depending on the physiological characteristics of microorganisms, including cell structure, existence of biofilms, and growth state. Previous studies demonstrated that the incremental change of aw in bacterial cells during thermal treatments resulted in changes in their thermotolerance. In this study, a pathogen associated with low-moisture foods outbreaks, Salmonella Enteritidis PT30 (in planktonic and biofilm forms), and its validated surrogate, Enterococcus faecium, were lyophilized and their water sorption isotherms (WSI) at 20, 40, and 60 °C were determined by using a vapor sorption analyzer and simulated by the Guggenheim, Anderson and De Boer model (GAB). The published thermal death times at 80 °C (D80 °C-values) of these bacteria in low-moisture environments were related with their WSI-derived aw changes. The results showed that planktonic E. faecium and biofilms of Salmonella, exhibiting higher thermal resistance compared to the planktonic cultures of Salmonella, had a smaller increase in aw when thermally treated from 20 to 60 °C in sealed test cells. The computational modeling also showed that when temperature increased from 20 to 60 °C, with an increase in relative humidity from 10% to 60%, freeze-dried planktonic E. faecium and Salmonella cells would equilibrate to their surrounding environments in 0.15 s and 0.25 s, respectively, suggesting a rapid equilibration of bacterial cells to their microenvironment. However, control of bacteria with different cell structure and growth state would require further attentions on process design adjustment because of their different water sorption characteristics.

The Effect of Chitosan Type on Biological and Physicochemical Properties of Films with Propolis Extract.

The aim of the research was to determine the influence of chitosan type and propolis extract concentration on biological and physicochemical properties of chitosan-propolis films in terms of their applicability in food packaging. The films were prepared using three types of chitosan: from crab shells, medium and high molecular weight and propolis concentration in the range of 0.75–5.0%. The prepared polysaccharide films were tested for antimicrobial properties, oxygen transmission rate (OTR) and water vapor transmission rate (WVTR). Moreover, sorption tests and structural analysis were carried out. Microbiological tests indicated the best antimicrobial activity for the film consisting of high molecular weight chitosan and 5.0% propolis extract. Both the type of chitosan and propolis concentration affected transmission parameters—OTR and WVTR. The best barrier properties were recorded for the film composed of high molecular weight chitosan and 5.0% propolis extract. The results of sorption experiments showed a slight influence of chitosan type and a significant effect of propolis extract concentration on equilibrium moisture content of tested films. Moreover, propolis extract concentration affected monolayer water capacity (Mm) estimated using the Guggenheim, Anderson and de Boer (GAB) sorption model. The obtained results indicate that chitosan films with an addition of propolis extract are promising materials for food packaging applications, including food containing probiotic microorganisms.

Hybrid super-porous hydrogel composites with high water vapor adsorption capacity – Adsorption isotherm and kinetics studies

Water vapors adsorption capacity of deliquescent salts is very high, but they dissolve in the adsorbed water by forming crystalline hydrates which restricts their use in different water vapor adsorption applications. This limitation can be overcome by incorporating deliquescent salts within a polymer matrix which will keep the salt solution in place. Furthermore, if the polymer matrix used is also capable of adsorbing water vapor, it will further improve the overall performance of desiccant systems. Therefore, in this work, we are proposing the synthesis and use of a highly effective new solid polymer desiccant material, i.e. superporous hydrogel (SPHs) of sodium acrylate and acrylic acid P(SA+AA), and subsequently its composite with deliquescent salt, i.e. calcium chloride (CaCl2), for the adsorption of water vapors from humid air without the dissolution of deliquescent salt in the adsorbed water. Synthesized SPH composite was characterized using different techniques like scanning electron microscopy (SEM) and Fourier-transform infrared spectroscopy (FTIR). Parental P(SA+AA)-SPHs matrix alone exhibited the adsorption capacity of 1.02 gw/gads which increased to 3.35 gw/gads after incorporating CaCl2 salt in the polymer matrix. For both materials, experimental isotherm data agreed with Guggenheim, Anderson and Boer (GAB) isotherm model and exhibited type-III adsorption isotherm. The adsorption kinetics followed linear driving force model. Furthermore, adsorbents were used successively for ten cycles of adsorption and regeneration. Therefore, the proposed polymer desiccant material overcomes the problem of dissolution of deliquescent salts and purposes a new class of highly effective solid desiccant material.

Linking water vapor sorption to water repellency in soils with high organic carbon contents

AbstractWater repellency (WR) significantly affects the hydraulic behavior of soils. Although WR often is regarded as a phenomenon with implications for dry soils, it is prevalent at water contents (w) exceeding the wilting point water content. Because the measurement of the WR–w relationship is laborious, alternative more time‐efficient methods are desirable to estimate parameters of the WR‐w curve. Using 32 high organic carbon (OC) soils from Denmark and South Greenland, we characterized the water vapor sorption isotherms (WSIs), investigated the interrelated effects of OC and clay contents on WSIs and the WR–w relationship, and further evaluated if parameters of the WR‐w curve may be derived directly from WSIs. The samples exhibited OC and clay contents ranging from 0.014 to 0.369 kg kg–1 and from 0.02 to 0.16 kg kg–1, respectively. The WSIs measured for relative humidity (RH) values between 3 and 93%, were strongly hysteretic, were OC dependent, and could be accurately characterized with the Guggenheim, Anderson, and de Boer model. Further, the WRarea and wnon parameters, derived from WR measured for several w, were well estimated with linear regressions based on OC content and multiple linear regressions based on OC and clay contents. Estimations for WRarea and wnon based on the WSI parameter wm‐a were superior to OC and clay content. Finally, we established mathematical expressions that estimate WRarea or wnon from any air‐dry w obtained from either the desorption or adsorption isotherms between 10 and 90% RH.

Changes in physical and biochemical properties of spray dried camel and bovine milk powders.

This study aimed at investigating the changes in skim camel milk (SCMP) and skim bovine milk (SBMP) powders produced by spray-drying. The physical (sorption isotherms at 25 °C and the glass transition temperature Tg at 0.13, 0.23 and 0.33 of water activities (aw)) and the biochemical (LC-MS, before and after drying) properties were assessed. Compared to SBMP, the results for SCMP indicated lower protein denaturation extent, lower critical aw for lactose crystallization (aw = 0.60 instead of 0.70), and lower Tg at 0.13 of aw (54.6 ± 1.4 °C instead of 57.8 ± 0.4 °C). Fitted to Guggenheim, Anderson and De Boer (GAB) model, the water sorption isotherms showed that both powders exhibited the same monolayer moisture content (Xm = 2.0 g 100 g−1, p > 0.05). These findings were linked to the absence of β-lactoglobulin, the high surface lactose content, the high initial lactose crystallization and the low size distribution (d50 < 10 μm) of SCMP.

Solid polymer desiccants based on poly(acrylic acid-co-acrylamide) and Laponite RD: Adsorption isotherm and kinetics studies

This study investigates the potential application of superporous hydrogels (SPHs) and their composites with Laponite-RD (Lap-RD) for the adsorption of water vapors from humid air. Super-hydrogel composites (SPHCs) wee synthesized via gas blowing and foaming technique. Synthesized adsorbents were characterized using different techniques such as fourier-transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), X-ray diffraction (XRD) and thermos-gravimetric analysis (TGA). The incorporation of Lap-RD within the polymer matrix increased its thermal stability. Further, P(AA-co-AM) SPHs as well as SPHCs were used to adsorb water vapors from humid air. The adsorption of water vapors in both of these materials exhibited type-III isotherm with a maximum adsorption capacity of 1.03 and 1.24 gw/gads for P(AA-co-AM) SPH and SPHC at 25 °C, respectively. Higher adsorption capacity of SPHC was due to the combined effects of capillary condensation and the presence of hydrophilic Lap-RD particles within the polymer matrix. Adsorption isotherm for both materials followed Guggenheim, Anderson and Boer (GAB) model which suggested that the main driving force for water vapors adsorption was capillary condensation. The adsorption capacity of both materials decreased with increasing temperature. Furthermore, the adsorption capacity for these materials was quite low in the relative humidity range of 20–50 % which increased abruptly with increasing the relative humidity above 50 %. The isosteric heat of water vapors adsorption for P(AA-co-AM) SPHs and SPHC were found to be in the range of 59−48 and 57−49 kJ/mol, respectively. Adsorption kinetics followed linear driving force model and the diffusion of water molecules followed non-Fickian type diffusion mechanism. Finally, the synthesized adsorbents showed very good reusable efficiency and used successfully for ten cycles of adsorption.

Measurement and Modelling of Moisture Sorption Isotherm and Heat of Sorption of Fresh Feces

The drying (or dewatering) of fresh feces and fecal sludge is a productive step in the management of sanitation, waste treatment, and resource recovery services. An improved understanding of fresh feces and fecal sludge drying would contribute to the development and deployment of fecal sludge management services. However, there is a lack of available literature on the fundamental drying characteristics of fresh feces. In response to this gap, this work shares experimental results for equilibrium moisture content of fresh feces at different water activity levels (aw) and proposes the use of the Guggenheim, Anderson, and de Boer (GAB) model for predicting aw, calculating the heat of sorption, and estimating the corresponding energy requirements for drying of fresh feces. This is the first time this work has been done with fresh feces. The total heat of evaporation was significant up to a moisture content of about 0.2 kg water per kg dry solids. In addition to informing drying process design, the sorption isotherm can be used to predict microbial activity, which could improve the management of feces and fecal sludge from a public health perspective. These data in turn will be used to promote access to dignified, safe, and sustainable sanitation.

Synthesis and Characterization of Ti–Fe Oxide Nanomaterials: Adsorption–Degradation of Methyl Orange Dye

Organic solvent-free impregnation method was used to synthesize titanium-iron oxides (TIOs) nanomaterial. The physical properties of synthesized TIOs materials were characterized by XRD, SEM–EDX, BET, UV–Vis, and FTIR analytical techniques. The appearance of iron oxide (IO) on SEM image, XRD, and EDX spectra, the redshift on UV–Vis spectra of TIO compared to titanium oxide (TO), and intensity reduction in FTIR spectra proves the good impregnation of IO in TO lattice. The Langmuir and Dubinin–Radushkevich adsorption isotherm test in the dark show the domination of physical adsorption. Furthermore, the Flory–Huggins isotherm model that has $$\Delta G$$ = −11.40 kJ/mol and Fowler–Guggenheim model that has $$w$$ = −106.5 kJ/mol confirm the spontaneity of the reaction and the presence of adsorbate–adsorbate repulsive interaction, respectively. The passing of the linear Weber–Morris intraparticle adsorption–diffusion plot through the origin and well-fitting of its coefficient of determination (R2) value relative to pseudo-first-order indicates the domination of adsorption–diffusion mechanism. On the methyl orange degradation experiment, as the percentage of IO increases from 4 to 12, its degradation efficiency decreases, i.e., TIO with 4% calcined at 500 °C (TIO-4) has higher degradation efficiency with k values of 0.03025.

Water Vapor Sorption Properties of Illinois Shales Under Dynamic Water Vapor Conditions: Experimentation and Modeling

AbstractWater vapor adsorption/desorption isotherms are measured on five shales from Illinois basin by dynamic vapor sorption method. The experimental adsorption data are modeled by the Guggenheim, Anderson, and De Boer model and the Freundlich model over the entire range of measured relative humidity (Rh) values (0–0.95). Modeling results show that shale hydration is controlled by surface chemistry at low Rh through a strong intermolecular bonding, while is mainly influenced by the pore structure at high Rh (&gt;0.9) through capillary condensation. This is consistent with the progressive decrease of isosteric heat of adsorption with water content, obtained by the Clausius‐Clapeyron equation. Exceptionally, for the one shale containing 8.6% montmorillonite, mesopore condensation only accounts for 33% of the measured water adsorption even at Rh ~0.95 due to the limited external pores and the important role of clay swelling. The specific surface area defined by Guggenheim, Anderson, and De Boer analysis as available for water adsorption is larger than that available for low‐pressure N2 adsorption due to the complex surface chemistry. The one shale rich in expansive montmorillonite and with a large interlayer capacity for water but inaccessible to N2 molecules conditions this result. Among the other four shales, one with high kerogen content behaves the highest water adsorption, possibly due to the high content of oxygen‐containing functional groups and the potentially high pore volume of kerogen. These findings contribute to a better understanding of water storage and transport behavior in shales and impact behavior relevant to structures and reservoirs founded in such media.

Adsorption isotherms modeling of herbicides bispyribac- sodium and metribuzin on two common Egyptian soil types

تجارب الأدمصاص الحرارى للمبيدات المختبرة بيسبيرباك صوديوم والمتريبيبوزين من المحلول المائي فى التربة الطينية اللومية والتربة الرملية اللومية. أدمصاص مبيد بيسبيرباك صوديوم كان أعلى من المتريبيبوزين فى التربة الطينية اللومية والتربة الرملية اللومية. تم استخدام عشرة نماذج رياضية : نماذج لانجموير )خمسة أشكال خطية(، فراوندلخ، تيمكين، دوبينين رادوسكينك، الوفيك، فولرجوجنهيم، كيسيليف، جوفانيك، هاركين جورا وهاليس ي تم تطبيقهم على نتائج تجارب مبيدات الحشائش بيسبيرباك صوديوم والمتريبيبوزين فى التربة الطينية اللومية والتربة الرملية اللومية. ولوحظ أن قيم معادلة لانجموير التي تم الحصول عليها من التعبيرات الخطية مختلفة فيما بينها. تشير قيم معامل ا لارتباط المتحصل عليها من قيم معادلات لانجموير المختلفة إلى أن نوع التربة هو العامل الأساس ي المؤثر على تطبيق النموذج المناسب. كانت قيم معامل ا لارتباط منخفضة للمبيدات المختبرة في الترب المختلفة فى جميع معادلات لانجموير باستثناء قيم معامل ا لارتباط الخاصة بمعادلة لانجموير الثالثة والرابعة لمبيد المتريبيبوزين فى التربة الطنية اللومية. وقد أظهر نموذج فراوندلخ توافقا مع النتائج التجريبية لبيسبيرباك صوديوم والمتريبيبوزين في تربة الطينية اللومية، بالنسبة لبيسبيرباك صوديوم والمتريبيبوزين في التربة الرملية اللومية. نموذج تمكين يصف تماما أدمصاص بيسبيرباك صوديوم في التربة الطينية اللومية والتربة الرملية اللومية بسبب القيم العالية لمعامل ا لارتباط وانخفاض قيم الخطأ القياس ي في حين أنه غير صالح لوصف ادمصاص المتريبيبوزين في كل من التربة الطينية اللومية والتربة الرملية اللومية. نموذج دوبينين رادوسكينك لوحظ أن معامل قيم ا لارتباط منخفض، لذلك لا يناسب هذا النموذج وصف نتائج الأدمصاص للمبيدات المختبرة المختلفة. نموذج الوفيك لوحظ فيه أن قيم معامل لارتباط منخفضة أقل من 0.86 لمبيدات الآفات المختبرة في الترب المختبرة مشيرة إلى صورة خطية سيئة. القيم المحسوبة ل θ والتي تعتمد على نموذج فراوندلخ أقل من 0.6 . لذلك، يمكن استخدام فولرجوجنهيم لوصف ادمصاص المبيدات التي تم اختبارها. نموذج جوفانيك كانت قيم معامل ا لارتباط للمبيدات المختبرة لبيسبيرباك صوديوم والمتريبيبوزين هي 0.7971 و 0.9130 في التربة الطينية اللومية و 0.9144 و 0.9077 في تربة الرملية اللومية. نماذج هاركين جورا وهاليس ي مناسبة لوصف النتائج التجريبية المتحصل عليها.