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.     

Moisture sorption characteristics of rice flour

Moisture equilibrium data (adsorption and desorption) of rice flour were determined using the static gravimetric method of saturated salt solutions at three storage temperatures: 10, 20 and 30 degrees C. The range of water activities for each temperature was from 0.11 to 0.85. Equilibrium moisture content decreased with increase in storage temperature at any given water activity. The experimental data were fitted to four mathematical models (modified Oswin, modified Halsey, modified Chung-Pfost and modified Henderson). The monolayer moisture content was estimated from sorption data using the Brunauer-Emmett-Teller (BET) equation. The isosteric heats of sorption were evaluated using Clausius-Clapeyron equation.     

玉米吸湿特性及其等温线类型研究

对测定的我国16个玉米品种的水分吸着等温线数据,采用9个水分吸着方程进行拟合,并根据修正4-参数Guggenheim-Anderson-de Boer方程(4-MGAB)派生的指标划分等温线类型。结果表明,CAE、修正Chung-Pfost(MCPE)、Strohman-Yoerger(STYE)、Brunauer-Emmett-Teller(BET)、3-MGAB、4-MGAB、修正Henderson(MHE)及修正的Oswin(MOE)方程均适合拟合测定的玉米水分吸着等温线,而Modi-fied Halsey(MHAE)不适合。MCPE和CAE被认为是玉米较佳水分吸着方程,方程参数MCPE的C1和C2、CAE的b1在不同玉米品种之间、黄玉米和白玉米之间差异不明显。但是,同一玉米品种吸附等温线的方程参数不同于解吸等温线的对应方程参数。另外,根据D10、Rfi、awn、X4指标判断玉米水分吸着等温线类型,16个玉米品种的吸附和解吸等温线均属于S型等温线(Ⅱ)。结果表明玉米水分吸附与解吸的MCPE和CAE方程参数可用于玉米收获后干燥及储藏通风操作。     

罗非鱼肉干燥过程平衡含水率模型研究

采用静态法测定罗非鱼肉在25、35、45、55℃温度和10%～85%相对湿度范围内的吸湿和解吸平衡含水率,分析温度和相对湿度对罗非鱼平衡含水率的影响。以相关系数和标准误差作为评价指标, 对Henderson模型、Chung-Pfost模型、Halsey模型和Oswin修正模型4个数学模型和平衡含水率曲线进行拟合,比较上述平衡含水率模型对实验数据的拟合精度,发现Oswin修正模型较适合于描述罗非鱼的平衡含水率曲线,并分别给出罗非鱼解吸和吸湿平衡含水率的Oswin表达式。     

Moisture sorption isotherms of broad bean seeds at different temperatures

The equilibrium moisture contents in broad bean seeds were determined using the gravimetric static method at 5, 20, 40 and 60 degrees C over a range of water activities from 0.110 to 0.877. The sorption capacity of seeds decreased with the increase in temperature at constant water activity. Five models, modified Chung-Pfost, modified Halsey, modified Oswin, modified Henderson, and GAB (Guggenheim-Anderson-de Boer) equations, were applied to analyse the experimental data. The modified Oswin and GAB models were found to be the most suitable for describing the sorption isotherms.     

大豆水分解吸-吸附等温线拟合模型

为给在干燥、贮藏及运输过程中保证大豆的品质提供理论依据,实验测定了大豆在室温（25 ℃）条件下的水分解吸-吸附等温线。采用非线性回归分析,应用常见的5 种模型Oswin、Halsey、Hendenson、GAB、Chung-Pfost对大豆在室温条件下测得的水分进行解吸-吸附等温线拟合分析,以确定最佳拟合模型及其参数。结果表明：大豆的解吸等温线属于第Ⅱ种类型;吸附等温线属于第Ⅲ种类型;在整个水分活度范围内,大豆的解吸-吸附等温线均存在着滞后现象;最佳的解吸-吸附等温线拟合方程都是Oswin模型,它们的决定系数均高于0.993;Oswin模型拟合大豆解吸等温线的参数A和B分别为0.075和0.500,吸附等温线的参数A和B分别为0.075和0.498。     

Moisture sorption and thermodynamic properties of cassava starch and soy protein concentrate based edible films

Moisture sorption isotherms and thermodynamic properties of cassava starch and soy protein concentrate–based edible films were investigated. Equilibrium moisture content was determined at various temperatures (10, 20, 30 and 40 °C) and relative humidities (17–83%) using gravimetric method, and the results were analysed using four sorption isotherm models. The equilibrium moisture of edible films (both adsorption and desorption modes) decreased with soy protein concentrate addition and temperature at constant water activity. The monolayer moisture content values of cassava starch–soy protein concentrate edible films decreased with increase in temperature and soy protein level. GAB and Oswin models (%RMS ≤10) best described the isotherms of the biofilms with the monolayer moisture contents, isosteric enthalpy and entropy higher for adsorption with significant kinetic compensations. The moisture sorption and thermodynamic properties of cassava starch–soy protein concentrate edible films showed that they are suitable for packaging applications.     

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.     

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.     

Equilibrium moisture content and heat of desorption of saffron

The equilibrium moisture contents of saffron (Crocus sativus L.) stigmas were determined experimentally using the standard gravimetric method at temperatures 30, 45 and 60 °C and water activity ranging from 11% to 83%. The sorption isotherm curves of saffron were sigmoidal in shape and decreased with increased temperature at constant relative humidity. Five selected isotherm models GAB, modified Henderson, modified Chung‐Pfost, modified Halsaey and modified Oswin were tested to fit the experimental isotherm data. Modified Oswin and modified Henderson models were found acceptable for predicting desorption moisture isotherms and fitting to the experimental data, respectively. The isosteric heats of desorption, determined from equilibrium data using the Clausius‐Clapeyron equation, were found to be a function of moisture content. The net isosteric heat of desorption of saffron varied between 1.38 and 5.38 kJ mol^?1 at moisture content varying between 2% and 20% (d.b).     

豆粕平衡水分及吸着等热研究

采用静态称重法测定了国产6个豆粕样品的平衡水分吸附/解吸等温线,并采用修正MCPE、MHAE、MHE、MGAB、MOE及STYE 6个方程进行拟合,得出MGAB、MHAE、MOE均适合描述豆粕平衡水分-平衡相对湿度之间的关系,并可用于分析豆粕水分吸附/解吸等热。当水分小于15%时,豆粕吸附/解吸等热均随水分增大而快速减小,同温度下的解吸吸着等热显著高于吸附吸着等热。当水分大于15%时,豆粕吸附/解吸等热均随水分增大而变化平缓,同温度下的解吸吸着等热趋同于吸附吸着等热。当水分小于15%时,较低温度下的豆粕吸附吸着等热与解吸吸着等热均高于较高温度下的。在水分17.5%的游离水临界点,豆粕的吸着等热(汽化热)接近纯水的潜热,约为2 500 kJ/kg。由等温线分析的25℃豆粕绝对安全水分为12.48%,相对安全水分为13.90%。     

Moisture desorption isotherms of medium-grain rough rice

Moisture desorption isotherms (EMC/ERH) of medium-grain rough rice (Japonica variety) were determined using a constant environment chamber for various combinations of air temperature (11.8-51.0 degrees C) and relative humidity (37.1-89.7%). The initial moisture contents were in the range of 24.7-41.6% dry basis. A thin-layer technique was used to achieve uniform drying. Each test was continued until the moisture content change in 24h was less than 0.1% dry basis. The final moisture content was considered as the dynamic equilibrium moisture content. Four three-parameter EMC/ERH equations, the modified Henderson, modified Chung-Pfost, modified Oswin and modified Halsey equations, were compared for their ability to fit the experimental EMC/ERH data. The residual sum of squares (RSS) and standard error of estimate (SEE) were adopted as the criteria to evaluate the fitting performance of the models. The modified Chung-Pfost equation was identified as the most appropriate equation for representing the EMC/ERH desorption isotherms of rough rice. Coefficients for equilibrium moisture content as a function of equilibrium relative humidity and temperature are given. The EMC/ERH data obtained in this study agreed well with previously published data. However the average isotherm, combining desorption and adsorption data, of ASAE does not predict the desorption EMC of rough rice accurately.     

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.     

Moisture sorption study on Nigerian foods: Kuka

Kuka is an important vegetable in the Nigerian food chain. The moisture sorption characteristics of the vegetable studied at 34, 37 and 45°C between a_w 0.10–0.96, revealed a BET type II behaviour. The Kuka exhibited hysteresis and an increase in EMC with increase in a_w and decrease in temperature. Four sorption models (Oswin, Halsey, Kuhn, and GAB) were studied and the Oswin model was the most suitable. The constants in the Oswin model and GAB monolayer moisture contents were obtained and found to be temperature-dependent. Heats of sorption were greater for desorption than adsorption and in either mode, they reduced with an increase in moisture content. An exponential equation was obtained to relate heat of sorption with moisture content.     

Modelling moisture sorption isotherms for maize flour

The sorption isotherm of food material is pertinent in the processing and storage of food products. Adsorption and desorption isotherms for maize flour were investigated using the static gravimetric method over the range of temperature (27–40 °C) and water activity (a_w) (0.10–0.80) commonly experienced in the tropical environment. The experimental data were compared with five widely recommended models in the literature for food sorption isotherms (GAB, modified GAB (MGAB), modified Oswin (MOE), modified Henderson (MHDE), and modified Chung–Pfost (MCE)). The GAB, MGAB, and MOE models were found to be acceptable in predicting the moisture sorption isotherms for maize flour. Overall, the MGAB appears to be most suitable for fitting the adsorption and desorption moisture isotherms data for the maize flour.     

Modelling the Water Sorption Isotherms of Quinoa Seeds (<Emphasis Type="Italic">Chenopodium quinoa</Emphasis> Willd.) and Determination of Sorption Heats

Adsorption and desorption isotherms of quinoa seeds (Chenopodium quinoa Willd.) were measured using the static gravimetric method at three temperatures (20, 40 and 60 °C). Water activity ranged from 0.118 to 0.937. The moisture sorption behaviour of quinoa was temperature dependent, as indicated by a decrease in equilibrium moisture content, at all levels of a _w, with increasing temperature. Eight mathematical equations available in the literature were used to model the experimental data, namely, GAB, BET, Caurie, Henderson, Oswin, Halsey, Smith and Iglesias–Chirife. All the equations showed generally a good fit; however, the Iglesias–Chirife and Oswin equations were considered the best to predict the experimental data for both isotherms. Effect of temperature on model parameters was analysed and studied through an Arrhenius-type equation. The net isosteric heats of desorption and adsorption were determined by applying the Clausius–Clapeyron equation resulting in 69.24 kJ mol⁻¹ for desorption and 61.26 kJ mol⁻¹ for adsorption. The experimental heat data were satisfactorily modelled by Tsami’s equation.     

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.     

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.     

Moisture sorption characteristics of mango–soy-fortified yogurt powder

Moisture adsorption isotherms of plain yogurt, mango–soy-fortified yogurt (MSFY) and MSFY containing 0.4% gelatin stabilizer (MSFYG) powder were determined at 20, 30, 40 and 50°C. A gravimetric static method was used under 0.11–0.81 water activity ranges for the determination of sorption isotherms that were found to be typical type II sigmoid. Experimental data were fitted to five mathematical models viz. modified Henderson, modified Chung–Pfost, Oswin, Smith and Guggenheim–Anderson–de Boer (GAB). It was found that both Oswin and GAB models were acceptable in describing equilibrium moisture content–equilibrium relative humidity (EMC–ERH) relationships for yogurt powder samples over the entire range of temperatures.     

Water sorption isotherms of fresh and partially osmotic dehydrated pumpkin parenchyma and seeds at several temperatures

Experiments were conducted to determine the equilibrium moisture content of pumpkin (cv Cucurbita Pepo L.) at different temperatures (278.1 K, 298.1 K and 318.1 K) and relative humidities (8–91%). Fresh and partially osmotically dehydrated (using sucrose solutions) samples of pumpkin parenchyma were employed. The desorption isotherm of pumpkin seeds at 298.1 K was determined as well and was found to be similar to other sorption isotherms of other seeds with similar fat and protein compositions. No significant dependence of the equilibrium experimental data on the temperature or osmotic pre-treatment was found. Several common mathematical models were used to fit the experimental data. For the parenchyma tissue, statistical analysis proved that those of Halsey, Oswin, Chirife and GAB were the best, while for the seeds, the Henderson, GAB and Peleg models are preferable.