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 isotherms of potato slices

Water vapour sorption isotherms of Norchip, Russet Burbank and Norland potatoes were determined by the salt solution technique at 10, 25 and 40°C. The adsorption isotherms of potatoes were of sigmoid shape and were affected by drying method, temperature and sugars addition. The freeze dried products adsorbed more water vapour than the vacuum dried materials. Addition of glucose, sucrose or lactose to the potatoes caused the equilibrium moisture content to decrease in the low and intermediate water activity ranges. The sorption was temperature independent in the a _w range 0.11–0.35 and showed a hysteresis loop at intermediate moisture levels.     

MOISTURE SORPTION STUDY ON NIGERIAN FOODS: MAIZE and SORGHUM

Adsorption-desorption behavior of maize and sorghum between a_w= 0.10–0.98 at temperatures of 20, 25 and 40C was studied. the grains exhibited type II sorption isotherm. the sorption data were analyzed using six sorption models and the coefficients of determination were between 0.6965–0.9994. the Caurie model gave the poorest fit and the Henderson model the best. Some models were better for adsorption than for desorption. the GAB and BET monolayer moisture contents were not significantly (p > 0.05) different. Monolayer values were temperature-dependent with activation energy from 1.36–10.08 MJ/mol and the maize monolayer values exhibited the highest sensitivity to temperature. Heat of sorption was obtained by applying Claussius-Clapeyron equation to the sorption isotherms at the three temperatures. the heat of sorption decreased with an increase in moisture content and an exponential equation was used to describe the relationship. the processing and storage consequences of this information were discussed.     

Effect of temperature and initial moisture content on sorption isotherms of banana dried by tunnel drier

Sorption isotherms of intermediate moisture content (IMC) products are essential to predict shelf-life of packaged moisture-sensitive product by modelling moisture uptake during storage and distribution. The effect of temperature and initial moisture content (MC) of IMC banana on the relationship between MC and water activity were investigated. Raw bananas were dried in a tunnel dryer at 2% relative humidity (RH), 70 °C, and a 3.2 ± 0.2 m s^–1 air velocity. Drying procedure was carried out a number of times until various IMC levels were obtained (5%, 14%, 22% and 33% db for banana). Sorption isotherms of bananas were determined at 10, 20, 30 and 40 °C. The initial MC of IMC banana had no significant effect on the relationship between MC and water activity according to statistical analysis. All the sorption curves were found to be Type II. BET, GAB, modified GAB, Oswin, Halsey and modified Freundlich models were fitted to the data and it was found that the best results were obtained with a modified Freundlich equation. A secondary modified Freundlich model was built accounting for the effect of a _w and temperature on the sample MC.     

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.     

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.     

Technical note: Sorption isotherms and monolayer moisture content of raw peas, and peas dehydrated after pressure cooking

The moisture sorption isotherms of raw and pre-cooked Century, MP 888 and MP 889 peas at 10, 25 and 40°C were determined by the standard salt solution technique. Pea cultivars, although different in composition, did not differ in equilibrium moisture content. At 40°C and in the water activity range 0.50 a _w 0.90, the sorption capacity of raw peas was higher than that of pre-cooked peas. All adsorption-desorption isotherms were of sigmoid shape and the quantity of sorbed water, at a given relative humidity, increased as the temperature was decreased. The monolayer moisture content of pre-cooked dehydrated peas stored at 40°C was 6.2%, with corresponding equilibrium relative humidity value of about 27%.     

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.     

WATER ADSORPTION PROPERTIES of COATED and NONCOATED POPCORNS

The addition of sugar for coating changed the sorption behavior of popcorn and made it more hygroscopic above a_w value of 0.65. the isotherms for noncoated popcorn exhibited a slight sigmoid shape and for coated showed the shape characteristics of high sugar containing foods. the crossing of both popcorn samples was observed at 0.65 a_w. the BET, the Smith and the GAB models were found to fit the adsorption data of noncoated popcorn; however, the BET and the Iglesias & Chirife models gave a good fit to the data of coated popcorn. the monolayer moisture content values estimated for both samples were considered to be correct values because of low standard error of estimates and their consistency with the literature values. the isosteric heat of noncoated popcorn was higher than the coated popcorn in the entire moisture content range considered for computation.     

Diffusion coefficients of water and organic volatiles in carbohydrate-water systems

Summary. The diffusion coefficients of water, D _w, and acetone, D _a, in aqueous solutions of malto-dextrin have been determined over a range of moisture contents of the malto-dextrin above 10%. At a few selected moisture contents, the diffusion coefficients of ethyl acetate, benzene, carbon tetrachloride, camphor and methane have also been determined. Diffusion coefficients were derived from measurements of sorption and desorption by a malto-dextrin layer.
The diffusion coefficient was found to be dependent on both the moisture contents and the size of the diffusing molecule. Over the range of moisture contents investigated, log D _w was found to be proportional to C _w-1 and log D_a proportional to C _w-1/2, where C _w is the concentration of water (kg/m³) in the malto-dextrin. For the compounds studied, the logarithm of the diffusion coefficient measured at a moisture content of 20.1% was found to be approximately proportional to the molecular 'diameter' of the diffusant.
This knowledge helps to explain the phenomenon of flavour retention during the drying of liquid foods.     

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.     

Desorption isotherms and isosteric heat of desorption of previously frozen raw pork meat

Some meat products involve drying previously frozen pork meat, which makes the knowledge of sorption characteristics very important for the design and management of meat dehydration processes. The sorption isotherms of raw pork meat from the Biceps femoris and Semimembranosus muscles were determined at four temperatures: 25, 30, 35 and 40 °C. The experimental results were modelled using the GAB (Guggenheim, Anderson and De Boer) model. The effect of temperature was also taken into account to model the experimental sorption isotherms using four models (GAB, Oswin, Halsey and Henderson). The best results were provided by the GAB model. From the experimental sorption isotherms the isosteric heats of sorption were determined. For a moisture content higher than 0.15 kg water/kg dm, the isosteric heat of meat was similar to the latent heat of vaporization for pure water. For a lower moisture content, an increase in the isosteric heat was observed when the moisture content decreased.     

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.     

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.     

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 characteristics of dried red peppers (Capsicum annum L.)

The water sorption isotherms of whole dried red pepper pods at 15, 25, 40°C were measured, and the results were used to test the applicability of the GAB equation, BET equation, and modified BET equation. the GAB, BET, and modified BET equations fitted the data well for water activities up to 0.93, 0.43, and 0.75, respectively. the monolayer values were found to range between 6 and 10 g H₂O per 100g solid, depending on temperature and the equation used for estimation. the excess heat of sorption as a function of moisture content was also determined.     

Effect of moisture content on glass transition and sticky point temperatures of sugarcane, palmyra-palm and date-palm jaggery granules

Sorption isotherms of sugarcane (SC), palmyra-palm (PP) and date-palm (DP) jaggery granules were obtained at 25 and 35 °C following isopiestic vapour transfer technique. Glass transition temperatures ( T _g) and sticky point temperatures ( T _sc) at different moisture contents were determined using DSC and rotational viscometer, respectively. All sorption isotherms fitted well to the GAB equation while no apparent difference in equilibrium moisture content (EMC) was seen among them at either of the temperatures. T _g values for dry granules were 316.89, 335.24 and 325.07 K for SC, PP and DP respectively. T _g could be predicted well with both Gordon and Taylor equation, and combined Gordon and Taylor and GAB equations. T _sc for palmyra-palm was highest (347.3 K), followed by DP (339.6 K) and SC (334.9 K). A generalised linear equation correlates T _g and T _sc. Critical moisture contents for SC, PP and DP are 1.0–2.0, 3.1–4.3 and 1.9–2.9% db, respectively.     

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.     

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 Sorption Characteristics of Freeze Dried Blueberries

Moisture sorption isotherms of freeze dried lowbush blueberries at 4, 16, 25, 35, and 45°C were determined using indirect gravimetric method. Moisture sorption kinetics at these temperatures and 75% RH were also investigated. The isotherms followed a type III shape with a temperature inversion effect at 0.9 water activity. They were best described by the GAB equation. Net isosteric heat of moisture sorption in freeze dried blueberries, determined using the Clausius Clapeyron equation, varied from 5.5 to 0.25 kJ/mol as moisture content changed from 8 to 36% (dry basis). Moisture adsorption kinetics in freeze dried blueberries were well described by the first order kinetics equation. The rate constant followed the Arrhenius relationship with an activation energy of 38.6 kJ/mol.