Hygroscopic Behavior Research Articles

Enhancing green polyethylene composites with filler heat treatment: Pecan nutshells and Pinus sawdust impact

The aim of the present study was to produce sustainable composites using green low-density polyethylene (LDPE) reinforced with heat-treated lignocellulosic residues. The transformation processes were employed to enhance the chemical compatibility of lignocellulosic wastes with the polymer matrices of the composite materials. Sawdust from pine wood (PW) and milled pecan nutshells (NS) were subjected to a thermal treatment at 180°C for 2 h. These heat-treated residues were then homogenized with the polymer matrix and molded through hot compression. The resulting wood polymer composites (WPCs) were subjected to various characterization tests, including density, mechanical properties, infrared spectroscopy, thermal stability, hygroscopic behavior, and morphology. Comparing the composites, the inclusion of heat-treated fillers led to reductions in water absorption and thickness swelling, especially for the NS. Furthermore, the composites didn’t exhibit increased flexural strength and/or tensile strength after the bio-components treatment. The insertion of thermally treated lignocelluloses also resulted in slight decreases in equilibrium moisture content and apparent contact angles.

Tribological and Hygroscopic Behavior of Polybutylene Terephthalate/Acrylonitrile Styrene Acrylate (PBT/ASA) Nanocomposites with Graphene Nanofiller

Fogging in automotive headlamps is a significant issue that affects both aesthetics and functionality. This study investigates the use of graphene-based nanocomposites to mitigate fogging by enhancing the hygroscopic properties of polybutylene terephthalate/acrylonitrile styrene acrylate (PBT/ASA) composites commonly used in headlamps. The incorporation of functionalized graphene improved the tensile and flexural strength of the nanocomposites, though it led to a reduction in elongation and melt flow. Additionally, the solid lubrication properties and increased surface hardness of the graphene contributed to enhanced wear resistance. The presence of graphene in the nanocomposites also reduced moisture diffusion, lowering the rates of both hygroscopic and desorption when compared to commercial PBT/ASA composites. Furthermore, the nanocomposites exhibited a reduction in maximum moisture uptake. These improvements are expected to reduce the absolute humidity inside the headlamp, thereby effectively mitigating the fogging issue.

Hygroscopic behavior and stability of a mixed acerola and watermelon powder

A mistura das polpas de frutas apresenta-se como uma opção vantajosa, por fornecer uma boa variação de vitaminas, minerais e sabores. O objetivo deste trabalho foi avaliar o comportamento higroscópico e a estabilidade do pó misto de acerola com melancia, por meio de análises físico-químicas. O pó misto foi obtido por meio da secagem em camada de espuma (temperatura de 80 °C, com espessura da camada de 1,5 cm). Para o estudo do comportamento higroscópico, foi utilizado o método dinâmico das isotermas de equilíbrio nas temperaturas de 25, 30 e 35 °C. Os dados experimentais foram ajustados aos modelos matemáticos de Peleg, Halsey, GAB e Oswin. Para o armazenamento, o pó misto foi acondicionado em embalagens laminadas por 40 dias sob condições controladas de temperatura (30 e 40 °C) e umidade relativa (≅ 83%). A cada 8 dias foram feitas avaliações dos parâmetros de teor de água, pH, acidez, cor, atividade de água, solubilidade e antocianinas totais. Os resultados do comportamento higroscópico do pó misto evidenciaram que Peleg foi o que melhor se ajustou para estimar as isotermas de adsorção de água nas temperaturas estudadas, por apresentaram R² ≥ 0,98 e P < 10%, e as isotermas foram classificadas como Tipo II (forma sigmoidal). Os resultados demonstraram, ao longo do armazenamento, que ocorreu aumento do teor de água, atividade de água, pH e intensidade de vermelho e redução da solubilidade, antocianinas totais, luminosidade, intensidade de amarelo, ângulo de tonalidade e croma, indicando absorção de água e escurecimento do pó.

Improving the tensile properties of hemicellulose/polylactic acid (PLA) blends prepared by solvent casting

AbstractThe development of new biopolymers has been explored as an alternative to improve the biodegradability of conventional synthetic plastics, such as those used in the packaging industry. Hemicelluloses are biodegradable polymers extracted from plants that, when combined with other biodegradable polymers, such as polylactic acid (PLA), can be easily processed and satisfy the mechanical requirements for commercial application. Thus, this work seeks a biodegradable blend that combines hemicellulose and PLA properties using solvent casting. The influence of hemicellulose content (5, 10, 15, and 20 wt%) on the thermal and mechanical properties was studied. For that purpose, thermogravimetric analysis and differential scanning calorimetry were applied to determine the thermal stability and crystallinity of the materials. Additionally, water uptake and mechanical tests provided information regarding the mechanical and hygroscopic behavior of the blends due to hemicellulose addition. As a result, the blends presented intermediate thermal stabilities between those of hemicellulose and PLA and increased crystallinities with hemicellulose content. The blends are more flexible and hygroscopic than PLA and more resistant than pure hemicellulose. Given the biodegradable nature of PLA and hemicellulose, these blends have the potential for application in sustainable packaging.

Characterization and Hygroscopic Behavior of Mentha crispa Powder Obtained by Foam-Mat Drying

Objective: Characterize and determine the hygroscopic behavior of Mentha crispa powder by obtaining adsorption isotherms and fitting nonlinear regression mathematical models. Theoretical Framework: Mentha crispa is an economically important species in the industry that, due to its perishability, is subjected to drying to increase its shelf life. Hygroscopicity is linked to physical, chemical and microbiological stability and it is necessary to understand its behavior to enable the use of biological products in regions with different climatic characteristics. Method: The powder was characterized according to water content, yield, water solubility index, pH, soluble solids, particle size and color. The adsorption isotherms were obtained by the indirect static method at a temperature of 25 °C. The BET, linear BET, Chung and Pfost, GAB, Halsey, Henderson, Langmuir, Oswin and modified Peleg models were adjusted to the experimental data. Results and Discussion: The results obtained revealed that the increase in drying temperature caused a darkening and degradation of the green hue of the powder. The powder isotherms presented type III behavior, with a sigmoidal shape common to food products. The Oswin and Henderson models are the ones that best represent the adsorption isotherms of Mentha crispa powders under the conditions studied. Research Implications: The research contributes to the literature with practical information on the hygroscopic behavior of the material. Originality/Value: Highlights the importance of adjusting nonlinear regression models to the adsorption isotherms of biological products. The models help to predict the behavior of a material during storage, informing the water content under a given environmental condition.

Experimental investigation on the moisture movement behavior of granites

This study comprehensively investigates the hygric performance of two commonly used types of granite in masonry, each characterized by distinct porosity levels. A series of experimental tests, including capillary absorption, one-dimensional drying, cup methods, vacuum saturation, sorption/desorption isotherms, mercury intrusion porosimetry, and ultrasonic pulse velocity, was conducted in different directions and by using both pure water and NaCl solutions. The results highlight pronounced anisotropy in the granite’s hygric response, with significant directional differences in liquid and vapor moisture movement, as well as ultrasonic wave propagation. Granite with lower porosity and a finer pore structure exhibited hysteresis effects and more pronounced hygroscopic behavior, while granite with higher porosity showed greater capillary activity. The presence of salt crystals within the pore network significantly influences vapor and liquid transport properties, porosity, and moisture storage capacity. The gradual formation of sodium chloride crystals on drying surfaces noticeably altered drying kinetics, influenced by salt concentration and pore characteristics. These findings provide valuable insights into the hygric properties of granite, essential for understanding its durability and informing moisture transfer numerical models.

Hygroscopic and hydrothermal aging behaviors and performance deterioration mechanisms of jute yarn wound composites

The gyratory jute yarn wound composites (JYWCs) manufactured by the filament winding process show significant potential as eco-friendly alternatives to plastic pipes commonly used in outdoor settings. Ensuring the long-term service performance and durability of the JYWCs in hot and humid environments becomes critical. This study investigated the hygroscopic and hydrothermal aging behaviors of the JYWCs to elucidate their performance deterioration mechanisms. Compared with hygroscopic aging, long-term hydrothermal aging posed a more serious threat to the overall performance of the JYWCs. The jute yarns in the JYWCs experienced swelling, shrinkage, and degradation due to hygroscopic and hydrothermal aging, leading to a 47.4 % and 161.5 % increase in the void volume fraction of the JYWCs, respectively. The deterioration in the mechanical properties of the JYWCs was attributed to the attenuation of jute yarn properties, debonding of the fiber-resin matrix interface, and an increase in voids within the composites. Improving the manufacturing process to minimize voids in the JYWCs and control the pathways for moisture absorption is a highly effective strategy to enhance their long-term performance and durability.

Numerical Investigation of Fracture Behaviour of Polyurethane Adhesives under the Influence of Moisture.

The mechanical behaviour of polymer adhesives is influenced by the environmental conditions leading to ageing and affecting the integrity of the material. The polymer adhesives have hygroscopic behaviour and tend to absorb moisture from the environment, causing the material to swell without applying external load. The focus of the work is to investigate the viscoelastic material behaviour under ageing conditions. The constitutive equations and the governing equations to numerically investigate the fracture in swollen viscoelastic material are discussed to describe the numerical implementation. Phase-field damage modelling has been used in numerical studies of ductile and brittle materials for a long time. The finite-strain phase-field damage model is used to investigate the fracture behaviour in aged viscoelastic polymer adhesives. The finite-strain viscoelastic model is formulated based on the continuum rheological model by combining spring and Maxwell elements in parallel. Commercially available post-cured crosslinked polyurethane adhesives are used in the current investigation. Post-cured samples of crosslinked polyurethane adhesives are prepared for different humidity conditions under isothermal conditions. These aged samples are used to perform tensile and tear tests and the test data are used to identify the material parameters from the curve fitting process. The experiment and simulation are compared to relate the findings and are the first step forward to improve the method to model crosslinked polymers.

Decision Tree Regression vs. Gradient Boosting Regressor Models for the Prediction of Hygroscopic Properties of Borassus Fruit Fiber

This research focuses on the environmental-friendly production of Borassus fruit fibers (BNF), its characterization, and hygroscopic properties determination via Dynamic Vapor Sorption (DVS). The experimental results obtained from the hygroscopic behavior analysis were used to create a primary dataset to train and test Decision Tree Regression (DTR) and Gradient Boosting Regressor (GBR) models. The created primary dataset comprised 294 observations, from which 80% were used to train the models, and the remaining 20% were used for the testing of the two models. The models exhibited high accuracy, easy interpretability on the small-size dataset, and flexibility with regards to the nature of the relationship between the input and output variable. Both models successfully predicted the hygroscopic behavior with the Gradient Boosting Regressor outperforming Decision Tree Regression by indicating values of 0.012, 0.109, 0.059, and 0.999 for MSE, RMSE, MAE, and R2, respectively, during the desorption of the BNF, and values of 0.012, 0.109, 0.059, and 0.999 for MSE, RMSE, MAE, and R2, respectively, during the desorption of the BNF. This suggests that the Gradient Boosting Regressor illustrated the maximum accuracy. The outcomes can be utilized to provide an alternative for traditional methods, which can often be costly and time-consuming by improving the engineering properties of BNF. The models can be used in the construction sector to lower costs as they are able to pinpoint elements influencing the characteristics for specific applications to grasp its various properties through the prediction of its hygroscopic properties.

Assessment of Hygroscopic Behavior of Arctic Aerosol by Contemporary Lidar and Radiosonde Observations

Assessment of Hygroscopic Behavior of Arctic Aerosol by Contemporary Lidar and Radiosonde Observations

Impact of the partial substitution of cement and sand by ash from several types of wood species in cementitious materials manufacture: valorization in the industrial field

The main objective of this article is to evaluate the potential use of wood ash as a substitute for cement and sand in mortars. Three types of wood were selected: Ayous, Sapelli and Fraké, all of which were sourced from carpentry in Cameroon. The sawdust was dried and combusted to obtain ash, then ground and sieved. Six types of mortar were produced, with cement substitution at 0%, 5%, 10%, 15%, 20% and 25%. The physico-mechanical properties of these substitutions were determined after 7, 28 and 56 days. The results of the cement paste consistency show that it increases with the addition of ash, due to the fact that sawdust ash requires a large quantity of water. The addition of ash caused an increase in setting time due to the fact that sawdust ash is less reactive than Ordinary Portland cement, resulting in a delay in the rate of cement hydration. Apparent density values decreased with the addition of sawdust ash, probably due to the hygroscopic behavior of type of ash in mortar specimens. The highest pozzolanic index is that of 5% replacement by ash and almost identical absorption for all mortars at this substitution percentage. Acid attack results revealed a higher durability of mortar specimens with the higher percentage of ash substitution. Optimum compressive strengths for the different substitution percentages were observed at 5%, 15% and 10% respectively for Ayous, Sapelli and Fraké. The best wood ash is Sapelli because of its chemical composition and resistance to compression in mortars. At 56 days, compressive strength values exceed those of the reference composition. This may be due to pozzolanic reactions in the mortars of ash.

Hygroscopic behavior of thermo-hygro-mechanical (THM) densified oil palm sawn timber

ABSTRACT To facilitate the drying process and enhance the properties of oil palm wood, oil palm boards were mechanically pre-dewatered and thermo-hygro-mechanically (THM) densified. The thickness of the boards was reduced with compression ratios of 40%, 60% and 75%. Since densified wood tends to recover from compression, especially under humid conditions, this study examined the set-recovery and the hygroscopic behavior of THM densified oil palm wood. The equilibrium moisture content (EMC), differential swelling and swelling coefficient, linear swelling and shrinkage as well as the differential swelling anisotropy were determined under climate conditions with different relative humidity (RH) (20°C/35% RH, 20°C/65% RH and 20°C/85% RH). The maximum swelling was measured after water soaking and the remaining set-recovery was evaluated after re-drying at 103°C. The EMC was reduced by the THM process by around 20%. In the direction of compression (thickness), the densified specimens show higher values for all analyzed swelling and shrinkage parameters than the undensified specimens from the equivalent position within the trunk. The maximum swelling in thickness of 22–38% during water soaking is mostly reversed by shrinkage during re-drying and a comparably low remaining set-recovery of 3–8% is measured at oven dry condition.

Eco-recycled cement's effect on the microstructure and hygroscopic behaviour of compressed stabilised earth blocks

Recycled cement (RCP) retrieved from old cement waste aims to replace carbon-intensive ordinary Portland cement (OPC) in earth stabilisation, improving the mechanical performance and durability of earth construction, without significantly compromising its ecological character and thermophysical properties. This study analyses the microstructure and hygroscopic behaviour of compressed earth blocks (CEB) stabilised with RC. In addition, soil was partially replaced with construction and demolition waste (CDW) to further improve the CEB sustainability. To this end, the sorption-desorption isothermal behaviour of CEB with different soils, types and contents of stabiliser (0–10 % RCP or OPC), and varying percentage replacements of OPC with RCP (20, 50, 100 %) or soil with CDW (0, 15, 25 %) was analysed and related to their microstructure, which was characterised in terms of scanning electron microscopy, mercury intrusion porosimetry and nitrogen adsorption analysis. Unstabilised and OPC CEB were considered for comparison purposes. The microstructure of CEB was refined after RCP stabilisation, which influenced their hygroscopicity and adsorption-desorption hysteresis. Depending on the clay content of the soil, stabilisation reduced or increased the hygroscopic capacity of CEB. After stabilisation, the water adsorption decreased up to 25 % in CEB with clayey soil and increased up to 22 % in CEB with sandy soil. However, the hygroscopic behaviour was not significantly affected by the type of stabiliser. The substitution of OPC with RCP increased the volume of water adsorption up to 3 %, due to its slightly finer porosity. RCP has proven to be effective as an earth stabiliser, leading to CEB with adsorption-desorption properties similar to those of OPC CEB.

Uncovering Effects of Mixing State on Hygroscopic Behavior of Multicomponent Aerosols with In Situ Transmission Electron Microscopy

Uncovering Effects of Mixing State on Hygroscopic Behavior of Multicomponent Aerosols with In Situ Transmission Electron Microscopy

Experimental Analysis of the Low-Velocity Impact and CAI Properties of 3D Four-Directional Braided Composites after Hygrothermal Aging.

Three-dimensional braided composites (3D-BCs) have better specific strength and stiffness than two-dimensional planar composites (2D-PCs), so they are widely used in modern industrial fields. In this paper, two kinds of 3D four-directional braided composites (3D4d-BCs) with different braided angles (15°, denoted as H15, and 30°, denoted as H30) were subjected to hydrothermal aging treatments, low-velocity impact (LVI) tests, and compression after impact (CAI) tests under different conditions. This study systematically studied the hygroscopic behavior and the effect of hygrothermal aging on the mechanical properties of 3D4d-BC. The results show that higher temperatures and smaller weaving angles can significantly improve the moisture absorption equilibrium content. When the moisture absorption content is balanced, the energy absorption effect of 3D4d-BC is better, but the integrity and residual compression rate will be reduced. Due to the intervention of oxygen molecules, the interface properties between the matrix and the composite material will be reduced, so the compressive strength will be further reduced. In the LVI test, the peak impact load of H15 is low. In CAI tests, the failure of H15 mainly occurs on the side, and the failure form is buckling failure. The main failure direction of H30 is 45° shear failure.

Eutectic mixtures containing the active pharmaceutical ingredient ezetimibe: Phase diagrams, solid state characterization and dissolution profiles

Cardiovascular disease represents the leading cause of death worldwide, according to the World Health Organization (WHO) report. One of the treatment strategies is the use of the drug ezetimibe (EZT). This drug is a cholesterol absorption inhibitor with low aqueous solubility, which affects its therapeutic efficacy. The purpose of this paper was to obtain eutectic materials of EZT with methylparaben (MPB), salicylic acid (SCA) and nicotinamide (NTM) coformers, and to study their phase diagrams, dissolution properties and hygroscopicity to assess possible enhancements. Phase and Tamman diagrams were constructed using differential scanning calorimetry (DSC) results. The eutectic materials were characterized by powder X-ray diffraction (PXRD) and polarized light optical microscopy (OM). The hygroscopicity of the materials was assessed at different relative humidities (RH) through dynamic vapor sorption (DVS). The dissolution study was conducted with the materials in powder form, with paddle dissolution, rotating at 50 rpm, in 900 mL of aqueous buffer solution at pH 6.8 and 37 °C. The phase diagrams demonstrated that EZT formed eutectic systems with eutectic molar fractions of 0.59, 0.67 and 0.69 for EZT-SCA, EZT-NTM and EZT-MPB, respectively. The three eutectic materials are characterized as microcrystalline conglomerates of their components. In terms of the hygroscopic behavior of EZT at different RHs, eutectic materials demonstrated lower susceptibility to monohydrate formation compared to the anhydrous form. In dissolution studies, EZT-SCA and EZT-MPB solubilized EZT in amounts 22 % higher than the pure drug in 15 min. On the other hand, EZT-NTM eutectic suppressed the dissolution of EZT down to 56 % at the same time. The results indicated the possibility of obtaining materials with enhanced properties using eutectic mixtures, with improved dissolution rates and hygroscopic stability.

Effect of hygrothermal aging on mechanical properties of continuous flax fiber composites

AbstractThe influence of hygrothermal aging on the mechanical properties of flax fiber‐reinforced polymer (FFRP) composites was studied by examining the mechanical properties and failure mechanism of the composite laminates exposed in distilled water at different temperatures. The resin transfer molding (RTM) process was used to manufacture FFRP laminates, which were then subjected to accelerated aging tests in distilled water at different temperatures. The moisture absorption characteristics of FFRP were analyzed by a water absorption test. Tensile, bending, and low‐velocity impact tests of laminates after different aging conditions were performed. Combined with DSC and FTIR tests, the failure mechanism of FFRP exposure to hygrothermal aging was analyzed. The result indicated that the increase in temperature will accelerate the moisture absorption process of FFRP, and the hygroscopic behaviors at different temperatures conform to Fick's law. In the early stage of hygrothermal aging, the composites undergo post‐curing, and the tensile and bending strengths increase. After that, the tensile and bending strengths are decreased because of the thermo‐oxygen aging of materials and fiber/matrix interface damage. After hygrothermal aging, the impact peak force of FFRP decreases obviously while the absorbed energy increases due to the increase of internal defects and plasticization of composites. The increase of hygrothermal aging temperature aggravates the aging of materials, resulting in a more obvious decline in the tensile, bending, and impact properties of the composites.Highlights The effect of hygrothermal aging on the mechanical properties of FFRP is investigated. With the increase of hygrothermal aging time, the tensile and bending strength of FFRP increased at the early stage of aging and then decreased. After hygrothermal aging, the impact peak force of FFRP decreases and the absorbed energy increases due to the increase of internal defects and plasticization of composites.

Exploring the hygroscopic behavior of highly energetic oxidizer ammonium dinitramide (ADN) at different temperatures and humidities using an innovative hygroscopic modeling

Ammonium dinitramide (ADN) is a new type of green energetic oxidizer with excellent energy density and low pollution combustion characteristics. However, the strong hygroscopicity has a significant impact on its practical application. To assist in the research on moisture-proof modification of ADN materials, an innovative hygroscopic modeling approach was proposed to evaluate the hygroscopicity of ADN at various temperatures and humidities. By investigating the diffusion coefficient of water molecules in molecular dynamics processes, a visual insight into the hygroscopic process of ADN was gained. Furthermore, analyzing the non-covalent interactions between ADN and water molecules, the hygroscopicity of ADN could be evaluated qualitatively and quantitatively. The energy analysis revealed that electrostatic forces play a dominant role in the process of water adsorption by ADN, whereas van der Waals forces impede it. As a whole, the simulation results show that ADN presents the following hygroscopic law: At temperatures ranging from 273 K to 373 K and relative humidity (RH) from 10% to 100%, the hygroscopicity of ADN generally shows an increasing trend with the rise in temperature and humidity based on the results of three simulations. According to the non-hygroscopic point (298 K, 52% RH) of ADN obtained by experiment in the literature, a non-hygroscopic range of temperature and humidity for ADN can be depicted when the simulation results in relative hygroscopicity is less than or equal to 17%. This study can provide effective strategies for screening anti-hygroscopic modified materials of ADN.

An Experimental Investigation of the Mechanism of Hygrothermal Aging and Low-Velocity Impact Performance of Resin Matrix Composites.

Resin matrix composites (RCs) have better thermal and chemical stability, so they are widely used in engineering fields. In this study, the aging process and mechanism of two different types of resin-based three-dimensional four-way braided composites (H15 and S15) under different hygrothermal aging conditions were studied. The effect of aging behavior on the mechanical properties of RCs was also studied. Three different aging conditions were studied: Case I, 40 °C Soak; Case II, 70 °C Soak; and Case III, 70 °C-85% relative humidity (RH). It was found that the hygroscopic behavior of RCs in the process of moisture-heat aging conforms to Fick's second law. Higher temperatures and humidity lead to higher water absorption. The equilibrium hygroscopic content of H15 was 1.46% (Case II), and that of S15 was 2.51% (Case II). FT-IR revealed the different hygroscopic mechanisms of H15 and S15 in terms of aging behavior. On the whole, the infiltration behavior of water molecules is mainly exhibited in the process of wet and thermal aging. At the same time, the effect of the aging process on resin matrices was observed using SEM. It was found that the aging process led to the formation of microchannels on the substrate surface of S15, and the formation of these channels was the main reason for the better moisture absorption and lower mechanical strength of S15. At the same time, this study further found that temperature and oxygen content are the core influences on post-aging strength. The LVI experiment also showed that the structural changes and deterioration effects occurring after aging reduced the strength of the studied material.

Additive Water Uptake of the Mixtures of Urban Atmospheric HULIS and Ammonium Sulfate

AbstractThe hygroscopicity of atmospheric aerosols affect the global climate and human health. However, the hygroscopic behavior of mixtures of inorganic salts and organics in atmospheric aerosols have not been well characterized for ambient complex organic mixtures. Here, the hygroscopic growth of humic‐like substances (HULIS), which represent the complexity of organic aerosol compounds, from urban aerosols and their mixtures with ammonium sulfate were investigated with measurements from a hygroscopicity tandem differential mobility analyzer and model analyses. The Zdanovskii–Stokes–Robinson (ZSR) relationship, which assumes that the water uptake of each component is additive, was examined for the mixtures. The dependence of the hygroscopicity parameters (κ) of the mixtures on the volume fraction of HULIS is generally represented by the ZSR relationship with the deviations of κ on average of 16% (4%–27% in different mixing ratios), and 0.03 (0.02–0.04) on absolute basis. An assumption of asphericity for the dry particles reduced the deviations (14%). Approximations for the surface tension depression by surfactants and surface‐bulk partitioning were predicted to account for the deviations to a small extent. Furthermore, a thermodynamic model for simplified compound systems showed that the non‐ideality of the solutions potentially explained the deviations from the ZSR relationship. The results of this study support the use of the ZSR relationship for organic‒inorganic mixtures as a practical approximation in atmospheric models, provide a guide for the uncertainty associated with this approximation, and suggest directions for future studies.