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Adsorption isotherms of pear at several temperatures
Abstract and Figures
The moisture adsorption isotherms of pear were determined at 15ºC, 30ºC and
45ºC using the standard static gravimetric method over a range of water
activity from 0.112 to 0.920. The experimental data were fitted with isotherm
equations recommended in ASAE Standard D245.5. In order to find which
equation gives the best results, large number of numerical experiments were
performed. After that, several statistical criteria proposed in scientific
literature for estimation and selection of the best sorption isotherm
equations were used. For each equation and experimental data set, the average
performance index was calculated and models were ranked afterwards. After
that, some statistical rejection criteria were checked (D’Agostino-Pearson
test of normality, single-sample run test and significance and precision of
the model parameters). The performed statistical analysis shows that the
Guggenheim-Anderson-de Boer (GAB) equation has the highest value of average
performance index, but higher correlation between pair of parameters leads to
lower precision of estimated parameters.[Projekat Ministarstva nauke
Republike Srbije, br. TR 31058]
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... Although most food products generally show typical type II (sigmoidshaped) adsorption isotherms (Andrade et al., 2011;Al Mutaseb et al., 2002), adsorption isotherms of dried kiwifruit slices followed type III (J-shape) isotherm according to BET classifications. In literature, similar to this study, adsorption isotherms of some dried fruits like apple and mango (Falade et al., 2004a, Akoy andvon Hörsten, 2013), pineapple (Falade et al., 2004b), papaya (Thalerngnawachart and Duangmal, 2016), pear (Mitrevski et al., 2015), blueberries (Lim et al., 1995) exhibited type III (J-shaped) behavior. Type III isotherms describes foods rich in soluble components such as sugars Chinachoti et al., 1984). ...
... In this study, BET equation gave P values of higher than 12% for all samples. At different temperatures, the adsorption isotherm data of freeze dried blueberries (Lim et al., 1995), hot air dried pear, banana, apple (Mitrevski et al., 2015;Caballero-Ceron et al., 2018) were recorded to be best described by GAB equation. However in these studies suitability of Peleg equation was not tested. ...
... GAB monolayer values for kiwifruit were close to those reported by Kaymak-Ertekin and Gedik (2004). Kaymak-Ertekin and Gedik (2004) (Akoy and von Hörsten, 2013;Mitrevski et al.,2015;Vega-Galvez et al., 2008). C and K are the factors related to the heat of adsorption of water in the monolayer and multilayer regions, respectively. ...
The aim of this study was to determine the moisture adsorption isotherms of kiwifruit dried by hot air, vacuum and freeze drying methods. Equilibrium moisture contents (EMC) of dried kiwifruits were obtained by using the standard gravimetric method at two different temperatures (25 and 45°C) within a range of water activities from 0.112 to 0.936. The adsorption isotherms of dried kiwifruits decreased with increasing temperature and exhibited type III behavior. Six different isotherm equations (GAB (Guggenheim-Anderson-de Boer), BET (Brunauer-Emmett-Teller), Oswin, Henderson, Halsey and Peleg) were employed to describe the experimental adsorption isotherm data. Adsorption data obtained at both 25 and 45°C for vacuum dried samples and data obtained at 45°C for hot air and freeze dried samples were best represented by Peleg equation. For the samples dried by hot air and freeze drying, GAB equation gave the best description of the experimental data obtained at 25°C.
... Over the past two decades, an increasing number of studies have been concerned with methods for sorption and/or desorption isotherm determination (Mitrevski et al., 2015;Mitrevski et al., 2018), sorption isotherm temperature dependence (Popovski&Mitrevski, 2004), sorption heat determination (Kaymak-Ertekin and Gedik, 2004) and the development of mathematical models for approximating moisture sorption data (Mitrevski et al., 2012;Mitrevski et al., 2015a). ...
... As regression methods (both indirect nonlinear and direct nonlinear regression methods), estimation methods, initial step sizes, initial parameter values, convergence criteria and function forms exert significant effects on the accuracy of the parameters estimated, a large number of numerical experiments were performed (Mitrevski et al. 2015). The method of indirect nonlinear regression analysis and the estimation methods such as the quasi-Newton, Simplex, Simplex and quasi-Newton, Hooke-Jeeves pattern moves, Hooke-Jeeves pattern moves and quasi-Newton, Rosenbrock pattern search, Rosenbrock pattern search and quasi-Newton, Gauss-Newton and Levenberg-Marquardt from computer software Statistica (Statsoft Inc., Tulsa, OK, http://www.statsoft.com) ...
In the scientific and engineering literature, there are various mathematical methods for modelling the equilibrium moisture content of agricultural and food materials. The objective of the present study was to statistically evaluate a total of thirty-two four-parameter moisture sorption isotherm models and subsequently compare their goodness of fit. The moisture sorption isotherm models considered were either originally developed or taken from the reference literature. The coefficient of determination and the graphical evaluation of residual randomness were utilized as the main assessment criteria for statistical evaluation of the moisture sorption isotherm models examined. The statistical performance of the models was tested according to the equilibrium moisture content of quinces. On the basis of the statistical analyses performed, the Popovski&Mitrevski model, i.e. the model with the reference numbers M25 and M30, and the McLaren&Rowen model were found to have the best statistical performance of all the models considered.
... were used to for calculation of the statistical parameters and estimate the parameters in the given models. Because the regression method, estimation method, the initial step size, the start values of parameters, convergence criterion and form of the function have significant influence on accuracy of estimated parameters [24], a large number of numerical experiments were performed. On the basis of thin-layer data and each model from, tab. 1, the values of: coefficient of determina- The analysis of variance (ANOVA) results indicated that the temperature of heatres (p ≤ 0.001), vacuum pressure (p ≤ 0.05), and the interaction of the temperature of heatres and vacuum pressure (p ≤ 0.05) significantly affected the drying time of apple slices. ...
In this study far infra-red vacuum drying kinetics and change of color quality parameters of apple slices were analyzed. The experimental data set of drying kinetics was obtained on the experimental setup designed to imitate an industrial far infra-red vacuum dryer. For approximation of the experimental data with regard to the moisture ratio four well known thin-layers drying models from scientific and engineering literature and new developed model of Mitrevski et al., were used. The performed statistical analyzes show that the model of Mitrevski et al., has the best statistical performance than well-known thin-layer drying models. The estimated values of moisture diffusivity of apple obtained from this study are within the range from 2.80?10-11 to 1.70?10-10 m2 s-1. A negative effect on the total color change of far infra-red vacuum dried apple slices was observed with increasing of temperature of infrared heaters and vacuum pressure
... With regard to food materials, sorption isotherms are of great importance to modelling the drying process, designing and optimising the drying equipment, predicting the shelf-life stability, calculating changes in the moisture content during storage, and selecting the appropriate packaging material (Gal, 1987). Over the last two decades, an increasing number of studies have been reported in the scientific and engineering literature addressing the following issues: methods for determining sorption or desorption isotherms (Mitrevski et al., 2015;Mitrevski et al., 2018), temperature dependence between sorption isotherms (Popovski&Mitrevski, 2004), determination of sorption heat (Kaymak-Ertekin and Gedik, 2004), and mathematical models for approximating the moisture sorption of food materials (Mitrevski et al., 2012;Mitrevski et al., 2015a). Depending on the number of parameters included, models for approximating the moisture sorption data of materials are referred to as one-parameter, two-parameter, three-parameter, or multi-parameter models. ...
Numerous mathematical models for approximating the water sorption data of food materials are available in the scientific literature. Depending on the number of parameters included, such models are referred to as one-parameter, two-parameter, three-parameter, or multi-parameter models. The objective of this study was to evaluate a total of sixty two-parameter sorption isotherm models for approximating the equilibrium moisture content data of quince and to compare the goodness of fit between the models examined. On the basis of the statistical analyses performed, it can be concluded that the Popovski&Mitrevski model has the best statistical performance of all the models examined. The coefficient of determination was the main criterion for assessing the model performance, totalling R2 = 0.9913 for the best model performance.
... The experimental moisture content data obtained at different heater temperatures, 120, 140, 160, 180 and 200 o C and different absolute vacuum pressures, 20, 40, 60 and 80 kPa for potato [15] and apple [16] were converted to the moisture ratio, MR, and then fitted to the two thinlayer drying models given in Table 1. Because the regression method, estimation method, the initial step size, the start values of parameters, convergence criterion and form of the function have significant influence on accuracy of estimated parameters [22], a large number of numerical experiments were performed. The method of indirect non-linear regression and estimation methods of Quasi-Newton, Simplex, Simplex and quasi-Newton, Hooke-Jeeves pattern moves, Hooke-Jeeves pattern moves and quasi-Newton, Rosenbrock pattern search, Rosenbrock patternsearch and quasi-Newton, Gauss-Newton and Levenberg-Marquardt from computer program StatSoft Statistica (Statsoft Inc., Tulsa, OK, http://www.statsoft.com), ...
In this paper the drying kinetics of far-infrared vacuum drying of some vegetables and fruits are presented. The experimental data of drying kinetics were obtained on experimental drying setup designed to imitate industrial dryer. Two well-known thin layer drying models from scientific literature were used to approximate the experimental data of drying kinetics in terms of moisture ratio. The performed statistical analysis shows that the model of Aghbashlo gives the best results for approximation of experimental drying data. ARTICLE HISTORY
Numerous mathematical models for approximation of sorption data of food and agriculture materials are available in the referent scientific and engineering literature. Depending on the number of parameters included in the model for approximation of moisture sorption data, the models may be one, two, three, four, five or more parametric. Also the sorption models may be included or not the temperature as a parameter into the equation. The objectives of the presented article was a review of one hundred seventy-two sorption no temperature dependent sorption isotherm models which used to for approximation equilibrium moisture data of food materials. For statistics evaluation of those models the equilibrium moisture data of quince were used. The value on coefficient of determination the root mean squared error, the mean relative deviation and graphical evaluation of the residual randomness were the main assessment criterions for statistical evaluation of the sorption isotherms model. Based on the performed statistical analysis it was concluded that the model of Popovski & Mitrevski i.e. M161 has the best statistical performances.
Natural antioxidants are a research topic of increased attention due to the fact that some synthetic antioxidants are now suspected to be potentially harmful to human health. The biomass like mirabelle plum stones valorisation considered as agro-industrial residues seems to be a prospective way for new natural antioxidants. Therefore, an experimental study of sorption isotherm and drying kinetic and antioxidant activities of shell and kernel of mirabelle was carried out. The gravimetric method is used to determine adsorption and desorption isotherms. The experimental results were fitted by GAB and Owswin models. Moreover, a set of drying experiments were studied at five air temperatures (75, 85, 95, 105 and 110°C). Experimental drying curves were fitted with Page, single-term and two-term exponential models. It is found that exponential models are suitable for fruit stones drying. Moreover, the antioxidant activity of kernel extracts is evaluated using the methods of oxygen uptake method (OUI) and the scavenging of 2-2-diphenyl-1-picrylhydrazyl (DPPH) radical. The OUI measurement showed that the extracts had considerably high antioxidant activity (83–90%). The close correlation between DPPH and OUI assays is confirmed. Hence, the mirabelle kernel extracts can be used as effective natural antioxidant.
A mathematical modelling of the drying process of food materials is important for scientific and engineering calculations. Thin-layer drying models are important tools in mathematical modeling of drying curves and estimate drying time. These models have wide application due to their ease of use and requirement of less data unlike in complex mathematical models. In this paper, the drying kinetics of two fruits (namely, pear and quince) were studied. The experimental data set of thin-layer drying kinetics at five drying air temperatures 30, 40, 50, 60 and 70 oC, and three drying air velocities 1, 1.5 and 2 ms-1 were obtained on the experimental setup, designed to imitate industrial convective dryer. For approximation the experimental data in terms of moisture ratio the new thin-layer model was developed. The performed statistical analysis shows that this model has the best statistical performance than well-known thin-layer drying models from scientific literature.
In this paper, a procedure for the statistical verification and validation of a newly generated sorption isotherm M01 model is defined. A basic approach to the evaluation of a model for approximating experimental sorption data is presented. Based on the accuracy within an acceptable range, a model is considered valid for a set of experimental conditions conducive to its intended purpose. The matching of experimental data to the data obtained in the calculations was examined. Several statistical criteria, proposed in the literature, and indicators (the coefficient of determination (R2), the root mean squared error (RMSE) and the mean relative deviation (MRD)) were used for the quantitative verification of the newly generated sorption isotherm model. A qualitative statistical analysis was performed by the validation of statistical assumptions relative to the residuals obtained from the regression analysis. This was achieved by creating a normal quantile-quantile diagram with a normal residual distribution, and a Scatter plot diagram with a random residual distribution. Fitted with the newly generated three-parameter sorption isotherm model, the validation of the experimental data on the sorption isotherms of pear flesh tissue (determined at four temperatures 15˚C, 30˚C, 45˚C and 60˚C, and over a range of water activity from 0.110 to 0.920) was performed relative to the results of the Guggenheim, Anderson and De Boer (GAB) model. The success of the newly generated model was confirmed in relation to this reference model.
In this paper some numerical experiments are made in which the parameters of the GAB model are calculated. It is shown that the problem has more than one solution. In that way it is proved that the parameters of the GAB model have not any physical meaning.
In the paper a generator of water desorption isotherm models is presented. It can be defined as: any sum of water desorption isotherm models is a water desorption isotherm model. Ten examples are given.
In the paper it is shown how four parameter models for moisture sorption isotherms can be created using two parameter models with nonlinearly related parameters. Ten new four parameter models are presented. Some numerical experiments are made in order to examine the efficiency of the models.
In the paper a method for extension of the water sorption isotherm models is given. It is shown how some n-parameter models can be extended into (n+1)-parameter models. Twelve new models are presented.
KEYWORDS Water sorption isotherms, sorption isotherm models. ABSTRACT In this paper two methods for generating new water sorption isotherm models are given. They can be defined as: logarithm or exponential function of water sorption isotherm model is water sorption isotherm model. Five examples are given.
KEYWORDS Water sorption isotherms, sorption isotherm models ABSTRACT In the paper a method for generating water sorption isotherm models is presented. It can be defined as: any product of water sorption isotherm models is a water sorption isotherm model. Twelve examples are given.
In the paper the method of free parameter for extension of the water sorption isotherm models is presented. It is shown how some n-parameter models can be extended into (n+1)-parameter models. Twenty seven new models are given.
In recent years many efforts have been made to determine the sorption isotherms of foods at different temperatures. Ten years ago Wolf et al. (110) published a comprehensive collection of sorption isotherms measured by the authors or taken from literature. The same authors (111) measured several foods and spices in the temperature range from 5 to 60°C. Chirife et al. (23, 24, 26) and Iglesias and Chirife (52, 53, 55) frequently used these data in their important articles on the calculation of sorption isotherms and heat of sorption. Recently Iglesias and Chirife (56) published a book containing more than a thousand isotherms.
In this paper is shown that the trigonometric and cyclometric functions can be successfully used in generating water sorption isotherm models. Twelve new trigonometric and twelve new cyclometric twoparameter models are presented.