Sorption isotherms and thermodynamics of water sorption of ready-to-use Basundi mix

Basundi mix representing powdered Basundi (an Indian traditional milk product somewhat similar to sweetened condensed milk) is a convenience product developed for enhanced shelf life at ambient temperature. Water sorption isotherms were obtained for this ready-to-use mix over the temperature range of 5-45 °C. There was definite inversion of the temperature effect at high water activity (>0.7). GAB model gave excellent agreement between experimental and predicted values. Other properties of sorbed water viz., monolayer water, number of adsorbed monolayers, density and amount of bound water and surface area of adsorption were also obtained. The net isosteric heat of sorption had strong dependence on moisture content. The enthalpy-entropy compensation suggested that the sorption mechanism involved is enthalpy driven over the entire range of moisture content studied.     

Moisture adsorption isotherms of guar (Cyamposis tetragonoloba) grain and guar gum splits

Moisture adsorption isotherms of guar grain and guar gum splits were determined at 10, 20, 30 and 40 °C and 23-96% relative humidities using gravimetric method. The sorption data were fitted to six well-known sorption isotherm models (modified Chung-Pfost, modified Halsey, modified Henderson, modified Oswin, Chen-Clayton, and GAB models) using non-linear least square method. The GAB model was found the most satisfactory for representation of the equilibrium moisture content data for guar grain and guar gum splits. The equilibrium moisture content of guar gum splits was found to be significantly higher (p < 0.05) than that of guar grain. The isosteric heat of sorption was determined from the equilibrium moisture adsorption data using Clausius-Clapeyron type equation. Exponential relationship described well the dependence of isosteric heat of sorption on the equilibrium moisture content. The enthalpy-entropy compensation theory applied to sorption isotherms indicated enthalpy controlled sorption process.     

Water sorption isotherms for lemon peel at different temperatures and isosteric heats

Lemon peel constitutes a potential source of dietary fiber to formulate new and healthier products, as well as a source of essential oils. The relationship between moisture content and water activity provides useful information for lemon peel processing, especially for drying and storage. Water sorption isotherms of lemon peel were obtained using a standardized conductivity hygrometer at four different temperatures (20, 30, 40 and 50 °C) and wide ranges of moisture content (5.381-0.002 kg water/kg dry solid) and water activity (0.984-0.106). One theoretical (GAB) and four empirical equations (Oswin, Henderson, Halsey and Ratti) were used for modelling sorption isotherms. After evaluating the models according to several criteria, the GAB model appeared as the best option. Isosteric heats of sorption were assessed from experimental sorption isotherm data using different methods.     

Desorption isotherms for fresh beef: An experimental and modeling approach

Desorption isotherms for fresh beef were determined at 30, 40 and 50 °C by the static gravimetric method. The resulting isotherms exhibited a type II sigmoid shape. The BET, GAB and Halsey models were used to fit these experimental data. The GAB model was most accurate for all temperatures and all levels of water activity, followed by the BET and Halsey models. The temperature dependence of GAB constants was estimated. The isosteric heat of desorption and its evolution in relation to moisture content were calculated using Clausius–Clapeyron equations. The monolayer moisture content was determined using the GAB model: it decreased as the temperature increased. The density of bound water, the number of adsorption sites, the sorption surface area and the percentage of bound water were calculated using the Caurie equation: all these quantities decreased as the temperature increased. The Kelvin and Halsey equations were used for calculation of pore size, which increases with an increase in moisture levels and sorption temperature.     

Equilibrium Sorption Isotherms and Isosteric Heat of Rose Hip Fruits (Rosa Eglanteria)

For sorptional data to be useful in simulation and design purposes, they must be represented by equations valid in the conditions usually found in industrial practice. In this regard sorptional models that include the influence of temperature on desorption and sorption equilibrium values are most valuable. In this article, water desorption and sorption isotherms of rose hip fruits (Rosa Eglanteria) were experimentally determined by the gravimetric method, and from these the isosteric heat of sorption was calculated. According to the ANOVA test carried out for this fruits, no significant differences were found between experimental desorption and adsorption isotherms. Seven models were tested to mathematically represent the moisture content as a function of water activity (a_w) in the a_w range of 0.11 to 0.85 and temperatures of 20, 40, and 60°C, for further use in process simulation.

The five-parameter GAB model was most accurate, with an MRE of ?2,9 % and R²?=?0.989. The values obtained for the isosteric heat of sorption were fitted with a previous published equation, with an MRE%?=??0.05. The isosteric heat of sorption derived from the GAB five parameters equation, for the corresponding monolayer moisture content, only differed by 1.25% with the calculated in this paper.     

Desorption isotherms,net isosteric heat and the effect of temperature and water activity on the antioxidant activity of two varieties of onion (Allium cepa L)

The standard static gravimetric method was used to determine moisture desorption isotherms (MDIs) of two onion varieties (Goudami and Galmi Violet) at 30 °C, 45 °C and 60 °C in the water activity ranging from 0.055 to 0.83. The combined effects of temperature and water activity on the antioxidant activities of the onion varieties were also studied. GAB, Oswin, Smith and BET equations were tested to fit the experimental data. The net isosteric heat of sorption was calculated. Equilibrium moisture content (EMC), total phenolic content (TPC) and antiradical activity were also measured. The isotherm and the EMC vary significantly with the onion variety and drying temperature, irrespective of water activity (a_w). Desorption isotherms were best described by the GAB model. The maximum net isosteric heats for Galmi Violet (32.58 kJ mol^?1) were greater than those of Goudami (23.50 kJ mol^?1) at each EMC. The TPC and antiradical activity of the Galmi Violet were significantly (P ≤ 0.05) higher than that of the Goudami at all investigated temperatures and water activities.     

Moisture sorption characteristics of dried acid casein from buffalo skim milk

Adsorption and desorption isotherms of dried acid casein prepared from buffalo skim milk were determined at 25°, 35° and 45 °C over a water activity range of 0.11-0.97 using static moisture gain/loss from test samples. Both the adsorption and desorption isotherms exhibited sigmoid shape corresponding to type II, typical to many foods. There was generally a negative temperature effect on equilibrium moisture content. The effect of temperature was, however, statistically not significant over the temperature range of 25-45 °C. Of the seven sorption models tested for fitting the sorption data, the GAB model gave the best fit at all the three temperatures. The temperature dependence of GAB parameters has been determined in the form of Clausius-Clapeyron equation. The calculated values of monolayer moisture content from BET isotherm equation have been found to be lower than the corresponding values found by using GAB equation. However, in both cases the monolayer moisture was higher in desorption than the adsorption and deceased with increase in temperature. The net isosteric heat of sorption decreased exponentially with increasing moisture content and approached a constant value of 0.331 kJ/mol at moisture content 28 g/100 g (d.b.). The moisture sorption hysteresis observed at 25°, 35° and 45 C was statistically significant. The extent of hysteresis was negligible in monolayer moisture content region, occurred predominantly in the water activity range 0.35-0.60 and decreased at higher water activities. Total hysteresis energy was evaluated from the sorption data using Everett and Whitton plot. The effect of increase in temperature was to decrease the amount of hysteresis.     

Water Sorption Isotherms and Crispness of Fried Yam Chips in the Temperature Range from 293K to 313K

Water sorption isotherms of fried yam chips were determined using a static gravimetric method with saturated salt solutions in the range of water activity between 0.22 and 0.85 at 293, 303 and 313K. Four sorption models namely GAB, Peleg, modified Mizrahi, and BET were fitted with the sorption data generated. The GAB model followed by Peleg and modified Mizrahi models were found to best represent the experimental data in the a_w range of 0.22–0.85. However, the BET model was more applicable between a_w range of 0.22–0.55. The adsorption isotherm of fried yam chips clearly showed the influence of temperature, decreasing the moisture content at a fixed water activity value with higher temperature. The net isosteric heats of sorption of water were estimated by applying the Clausius–clapeyron equation to the adsorption isotherms at different temperatures. The net isosteric heat of sorption was observed to be decreasing as moisture content increases. Samples stored in desiccators of 0.44 and 0.55 a_w at 303 and 313K, respectively, were rated higher in terms of textural properties investigated.     

Moisture sorption isotherms and isosteric heat for pistachio

The equilibrium moisture contents (EMC) of pistachio were determined using the standard static-gravimetric method at 15, 25, 35 and 40 °C for pistachio powder at 15, 35 °C for pistachio kernel and pistachio nut for water activity (a _w) ranging from 0.11 to 0.9. At a given water activity, the results show that the moisture content decreases with increasing temperature. The experimental sorption curves are then described by the BET, GAB, Henderson, Oswin, Smith and Halsey models. A nonlinear regression analysis method was used to evaluate the constants of the sorption equations. The Smith model was found to be suitable for describing the sorption curves. The isosteric heat of adsorption of water was determined as a function of moisture content from the equilibrium data at different temperatures using the Clasius–Clapeyron equation.     

The fitting of various models to water sorption isotherms of tea stored in a chamber under controlled temperature and humidity

The moisture sorption characteristics of tea stored in a chamber regulated by an atomizing humidification system were investigated at 25, 35 and 45 °C for water activity ranging from 0.1 to 0.9. The sorption isotherms of tea were typical type II sigmoidal curves according to BET classification. In both adsorption and desorption, an increase in temperature resulted in lower equilibrium moisture contents at corresponding values of water activity. The sorption isotherms exhibited hysteresis over the whole water activity range. GAB, BET, Henderson, Iglesias and Chirife, Oswin, Peleg, Smith and Caurie models were applied for analysing the experimental data. Nonlinear regression analysis was used for the determination of the parameters in the equations. Estimated parameters and fitting ability for sorption models were evaluated. The Peleg model was found to be the most suitable for describing the relationship between equilibrium moisture content and water activity for the whole range of temperatures and relative humidities studied. The surface area of monolayer was calculated. The BET equation was solved for the monolayer moisture content and the corresponding a_w values at which monolayer forms were presented. Sorption isotherm data were used to determine the thermodynamic functions such as isosteric heat of sorption, sorption entropy, spreading pressure, net integral enthalpy and entropy. The Clausius-Clapeyron equation was used to evaluate the isosteric heats of sorption. The isosteric heats of sorption and sorption entropy decreased with increasing moisture content. The heat of desorption was little higher than that of adsorption at low moisture content. The enthalpy-entropy compensation theory could be successfully applied to water sorption by tea. This theory showed that the moisture sorption of tea was governed by enthalpy-controlled mechanisms. The spreading pressure increased with increase in water activity and decreased with increasing temperature. The net integral enthalpy decreased with moisture content while the net integral entropy increased.     

Sorption isotherms,GAB parameters and isosteric heat of sorption

The diffusion–sorption drying model has been developed as a physics‐based way to model the decreasing drying rate at low moisture contents. This new model is founded on the existence of different classes of water: free and bound water. The transition between these classes and the corresponding thermodynamics form distinct components of the drying model. This paper shows that the characteristics of the different classes of water and of the transition between them can be deduced from the GAB sorption isotherm. The parameters in the GAB sorption isotherm support the theory of localised sorption, establishing the existence of different classes of water. Moreover, the sorption mechanism retrieved from the GAB parameters is in accordance with the sorption mechanism, which is obtained from the moisture dependence of the net isosteric heat of sorption. This holds for experimental sorption data of corn and starch as well as for literature data on five vegetables and four fortified cassava products. An extremum in the net isosteric heat of sorption coincides with the transition between bound and free water, and the partition moisture content corresponds with the monolayer value derived from the GAB equation. This confirms that the GAB monolayer value can be chosen as model boundary between bound and free water. Moreover, it reveals that this method can be developed into a technique to estimate the bound water content in foods. Copyright © 2005 Society of Chemical Industry     

SORPTION ISOTHERMS OF TURKISH DELIGHT

Moisture sorption isotherms of Turkish delight were determined using the gravimetric static method of saturated salt solutions at 10, 20 and 30C. Isotherms were found to be of type III, typical of high sugar foods. The effect of temperature on moisture content was not significant (P>0.05). The sorption isotherms exhibited hysteresis at low water activities (a_w < 0.5). At higher water activities the moisture content increased sharply as the temperature was increased, resulting in crossing of the isotherm curves at 0.65 water activity. Six models namely the BET, the GAB, the Halsey, the Henderson, the Chung & Pfost and the Iglesias & Chirife were evaluated to determine the best fit for the experimental data. The GAB and the Iglesias & Chirife models fitted well the data of Turkish delight in the temperature and water activity range investigated. However, the GAB model was not appropriate for the estimation of monolayer value. The Clausius-Clapeyron equation was used to examine the isosteric heats of sorption.     

Mathematical modelling of moisture sorption isotherms and determination of isosteric heat of blueberry variety O'Neil

The sorption isotherms of blueberry variety O'Neil were determined at 20, 40 and 60 °C, for a range of water activity of 0.10–0.95. The isotherms showed that the equilibrium moisture content increased when temperature decreased at constant water activity. The BET, GAB, Halsey, Henderson, Caurie, Smith, Oswin and Iglesias-Chirife equations were tested for modelling the sorption isotherms. The results showed that GAB, BET and Halsey models gave the best fit quality for the experimental desorption data, and BET, Oswin and Henderson for adsorption data as suggested by the statistical tests employed. The net sorption heat was calculated using the Clausius–Clapeyron equation giving 38.62 kJ mol⁻¹ (desorption) and 30.88 kJ mol⁻¹ (adsorption) at a moisture content of 0.01 g water (g d.m.⁻¹). Tsami equation was applied to estimate the net isosteric heat of sorption as function of equilibrium moisture content with satisfactory results.     

方便米粉的水分吸附和热力学特性

为了给方便米粉的加工和贮藏过程提供理论指导,根据吸附原理,在环境温度分别为15、25 ℃和35 ℃时,采用静态称量法研究方便米粉的吸附等温线。采用7 个常见的非线性回归方程对吸附实验进行拟合,以决定系数、平均相对偏差和标准估计误差为评价指标,确定最佳拟合模型及其参数,探讨方便米粉水分吸附过程中净等量吸附热、微分吸附熵和焓熵互补等热力学性质的变化。结果表明,方便米粉的水分吸附特性属于II型等温线,Peleg和GAB模型都适合描述方便米粉的水分吸附特性。用GAB模型拟合得到的单分子层水分含量X0在15、25 ℃和35 ℃下分别为9.23%、8.34%和7.65%（干基）。在水分吸附过程中,方便米粉的净等量吸附热和微分吸附熵都会随着平衡水分含量的升高而明显下降;同时,存在焓熵补偿现象;根据实验结果绘制净等量吸附热与微分吸附熵的关系图,计算获得方便米粉的吸附过程属于焓驱动和自发过程。本研究对方便米粉贮藏条件选择和进一步评估不同贮藏条件下方便米粉的贮藏期具有指导作用。     

Sorption isotherms and thermodynamic properties of grated Parmesan cheese

This study focuses on isotherms, isosteric heat of sorption and enthalpy–entropy mechanism of water sorption of grated Parmesan cheese at simulating conditions of storage and drying processes. Isotherms were determined by gravimetric method using different saturated salt solutions. Samples were submitted to different temperatures, and several models were used to fit experimental data, GAB and modified GAB being those which best represented experimental data in all temperature ranges. The isosteric heat of sorption was calculated by Clausius–Clapeyron equation, and higher values of integral isosteric sorption heat were verified for storage temperatures. Besides it, both conditions showed higher values of sorption heat corresponding to low water content. This phenomenon was supported by the enthalpy–entropy compensation study, which demonstrated a higher spontaneity of water sorption for storage temperatures, confirming that the lower the water content of food products is, the stronger the intermolecular bonds of water are.     

Effect of drying method on the moisture sorption isotherms for Inonotus obliquus mushroom

Moisture sorption isotherms of Inonotus obliquus mushroom were studied over a selected temperature range (20-50 °C). Sigmoid sorption isotherms were observed for these samples. The sorption data were analyzed using various conventional models. The Oswin model was found to be the best model for predicting the equilibrium moisture content of mushroom in the range of water activity 0.08-0.96. The monolayer moisture content decreased as temperature increased and was affected by the drying method used. The net isosteric heat of sorption was determined using the Clausius-Clapeyron equation and the value decreased with increase in moisture content of mushroom.     

Desorption Isotherms and Net Isosteric Heat of Chestnut Flour and Starch

The desorption isotherms of chestnut flour and chestnut starch were determined at different temperatures (20°C, 35°C, 50°C, and 65°C) using gravimetric method. Desorption isotherms of potato starch were also determined in order to establish a comparison against desorption isotherms of chestnut starch. Several saturated salt solutions were selected to generate different water activities in the range of 0.09 to 0.91. Obtained desorption isotherms were of type II, according to Brunauer’s classification. Three-parameter Brunauer–Emmett–Teller and Guggenheim–Anderson–de Boer (GAB) models satisfactorily fitted the experimental data for all systems studies, although the last one can be considered better based on obtained statistical parameters and because it is applicable in a broader water activity range. The average monolayer moisture content (kilograms per kilogram d.b.) calculated by GAB model was 0.059 ± 0.007 for chestnut flour, 0.103 ± 0.021 for chestnut starch, and 0.060 ± 0.028 for potato starch. The net isosteric sorption heat, calculated by means of Clausius–Clapeyron equation, decreased when moisture content increased. The maximum values of net isosteric sorption heat (kilojoules per mole) were approximately 27.5 for chestnut flour, 16.0 for chestnut starch, and 33.0 for potato starch in the range of temperature from 20°C to 50°C.     

Moisture sorption isotherms and thermodynamic properties of walnut kernels

The moisture sorption isotherm data of walnut kernels stored in a chamber, the relative humidity (r.h.) of which is regulated by atomizing humidifier, were determined at three different temperatures (25, 35 and 45 °C) and r.h. ranging from 10% to 90%. Eight models, namely the GAB, BET, Henderson, Iglesias and Chirife, Oswin, Peleg, Smith and Caurie equations, were fitted to the sorption data. Several statistical tests were adopted as the criteria to evaluate the fitting performance of the models. Of the models tested, the Peleg model gave the best fit to experimental data. The surface area of a monolayer was calculated. The BET equation was applied to the monolayer moisture content and the corresponding a_w values at which a monolayer forms are presented. The experimental data were also used to determine the thermodynamic functions such as isosteric heat of sorption, sorption entropy, spreading pressure, net integral enthalpy and entropy. The sorption isosteric heats for walnut kernels were determined by the application of the Clausius-Clapeyron equation to sorption isotherms obtained from the best-fitting equation. Isosteric heats decreased with increase in moisture content and approached the latent heat of pure water. Adsorption entropy increased with increasing moisture content, and then it decreased sharply with increase in moisture content. The spreading pressures (adsorption and desorption) increased with increasing water activity. Net integral enthalpy of adsorption increased slightly with moisture content to a maximum value. Thereafter, it remained constant. Net integral entropy of adsorption was negative in value and it decreased with increase in moisture content to a minimum value, and then increased slightly with increase in moisture content.     

Thermodynamic properties of moisture adsorption of whole wheat flour. Calculation of net isosteric heat

The moisture sorption isotherms of whole wheat flour were determined at 10, 20 and 30 °C over a relative humidity range of 10–90%. Two models were applied to the sorption experimental data: the Guggenheim–Anderson–de Boer (GAB) and the Caurie models. The goodness of fit of the mathematical models was statistically evaluated by means of the root mean square per cent error (%RMS), obtaining values between 1.44 and 1.05 for GAB, and between 2.69 and 2.57 for the Caurie model. Hence, both models provided a good fit to the experimental data. The isosteric heat of sorption was calculated using two methods: the Clausius–Clapeyron expression and the Caurie equations, showing in both cases maximum values (11.03 and 12.39 kJ mol^?1, respectively) when moisture content was minimum (2.5 g H₂O per 100 g dry matter), and gradually diminishing to the value of the heat of vaporisation of pure water when moisture content reached a maximum value.     

Adsorption isotherms of pinhão (Araucaria angustifolia seeds) starch and thermodynamic analysis

The seeds of Araucaria angustifolia, commonly known as pinhão, are widely consumed in both Southern and Southeastern Brazil due to their high nutritious value comprised basically by starch. The literature on the technological aspects of this seed is still very scarce. Moisture adsorption isotherms of pinhão starch were determined at 10, 20, 30 and 40 °C using the gravimetric method. Results show that the Peleg model most appropriately represents the experimental data. Other models (Chung–Pfost, GAB, Henderson, BET and Chirife) also were found to adjust well. The isosteric heat of sorption (differential enthalpy) was calculated by using the moisture adsorption isotherm and decreased as moisture content increased. The enthalpy–entropy compensation theory was applied to adsorption isotherms and the isokinetic temperature for pinhão starch was calculated by plotting the differential enthalpy versus differential entropy. It was found that the adsorption process investigated was enthalpy-controlled and spontaneous.