Diffusion mechanisms during the osmotic dehydration of Granny Smith apples subjected to a moderate electric field

Simpson, Ricardo; Ramírez, Cristián; Birchmeier, V.; Almonacid, A.; Moreno, Jorge; Núñez, Helena; Jaques, A.

doi:10.1016/j.jfoodeng.2015.05.027

Cited by 71 publications

(52 citation statements)

References 27 publications

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“…A dimensionless moisture ratio (MR t ) was calculated from the drying curves of the dried apple slices as follows:

{MR}_{t} = \frac{W_{t} - W_{e}}{W_{0} - W_{e}}

where W t is the moisture content at any time t (g water/g dry basis), W e is the moisture content at equilibrium (g water/g dry basis), and W 0 is the initial moisture content (g water/g dry basis). The values of W e were estimated when the weight change remained constant (Simpson et al, ).…”

Section: Methodsmentioning

confidence: 99%

“…The second model used was Anomalous diffusion model based on fractional calculus approach : This model was presented by Simpson et al (), in which the diffusion equation is written as follows:

\frac{\partial^{α} W}{\partial t^{α}} = D_{eff} \frac{\partial^{β} W}{\partial x^{β}}

where W corresponds to food water concentration, D eff is the effective diffusion coefficient, α is related to anomalous waiting times between jumps and fractional differentiation order β is related to anomalous jump lengths. Considering only the fractional‐order derivative for time ( α ) and the second order of the spatial derivative as in Fick's second law, the anomalous diffusion Equation can be expressed as depicted in Equation :

\frac{\partial^{α} W}{\partial t^{α}} = D_{eff} \frac{\partial^{2} W}{\partial x^{2}}

…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Anomalous diffusion based on fractional calculus approach applied to drying analysis of apple slices: The effects of relative humidity and temperature

Ramírez

Astorga

Núñez

et al. 2017

J Food Process Engineering

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The objective of this research was to evaluate the diffusion mechanism based on Fick's second law and anomalous diffusion modifying the drying operating conditions temperature (T) and relative humidity (RH) on apple slices (cv. Granny smith). Drying was performed at 30 °C, 40 °C, 50 °C and 30%, 50%, 70%RH based on a 32 experimental design. The drying curves were analyzed to determine the effective diffusion (Deff) using two methods: Fick's second law and anomalous diffusion model based on fractional calculus approach. Our results showed that the anomalous diffusion mechanism fit the experimental data better and revealed a super‐diffusive behavior (α > 1). Therefore, Deff values were estimated using the anomalous diffusion model with α = 1.735. With respect to the use of anomalous diffusion model solution based on fractional calculus at different operations conditions allow to get better fitting of drying data than second Fick's law model, even keeping the Arrhenius behavior of Deff with temperature. Practical applications Diffusion process is typically analyzed using models based on Fick's second law. However, several assumptions inherent in Fick's second law are not fulfilled in food materials (e.g., structural heterogeneity). In addition, Fick's second law does not consider structural variations during the drying process, and it is well known that fruits such as apples experience significant structural changes during drying. Fractional calculus is a tool for mathematically representing the anomalous diffusion of solutes whose movements can be faster or slower than postulated in Fick's second law due to food structure. In general, with second Fick's law model not good fitting to data are obtained, therefore the prediction capacity of the model is limited. Based on this, anomalous diffusion solution based on fractional calculus was applied. The results showed good fit the data to the model, and also by the time exponent (α) is possible to identify the kind of diffusion process.

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“…A dimensionless moisture ratio (MR t ) was calculated from the drying curves of the dried apple slices as follows:

{MR}_{t} = \frac{W_{t} - W_{e}}{W_{0} - W_{e}}

Section: Methodsmentioning

confidence: 99%

“…The second model used was Anomalous diffusion model based on fractional calculus approach : This model was presented by Simpson et al (), in which the diffusion equation is written as follows:

\frac{\partial^{α} W}{\partial t^{α}} = D_{eff} \frac{\partial^{β} W}{\partial x^{β}}

\frac{\partial^{α} W}{\partial t^{α}} = D_{eff} \frac{\partial^{2} W}{\partial x^{2}}

…”

Section: Methodsmentioning

confidence: 99%

Anomalous diffusion based on fractional calculus approach applied to drying analysis of apple slices: The effects of relative humidity and temperature

Ramírez

Astorga

Núñez

et al. 2017

J Food Process Engineering

Self Cite

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“…There are many studies on fruit drying (Doymaz, Karasu, & Baslar, ; Ju et al, ; López, Vega‐Gálvez, Rodríguez, Uribe, & Díaz, ; Mahjoorian et al, ; Simpson et al, ; Singh, Guizani, Al‐Alawi, Claereboudt, & Rahman, ) and leather production (Ahmad, Shafi'i, Hassan, Rajab, & Othman, ; Al‐Hinai et al, ; Azeredo et al, ; Basha, Swamy, Ramu, & Sreenivas, ; Chen & Martynenko, ; Domingo & Austria, ; Huang & Hsieh, ; Man & Sin, ; Patil, Shere, Sawate, & Mete, ; Phimpharian et al, ; Roknul Azam, Zhang, Law, & Mujumdar, ; Tontul & Topuz, ; Tontul & Topuz, ; Vatthanakul et al, ; Yılmaz, Yüksekkaya, Vardin, & Karaaslan, ) focusing on drying methods, conditions and kinetics, quality properties of final product. The effects of drying conditions (convective drying, sun drying, osmotic dehydration, and blanching) and parameters (drying temperature and velocity, product thickness and relative humidity) on drying kinetics of persimmon fruit were investigated by Kim et al (), Cárcel, García‐Pérez, Riera, and Mulet (), Doymaz (), Hanif et al (), Demiray and Tülek ()), and Sampaio et al ().…”

Section: Resultsmentioning

confidence: 99%

Production and preference mapping of persimmon fruit leather: An optimization study by Box–Behnken

Dursun

Dalgıç

2018

J Food Process Engineering

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New and additive‐free persimmon fruit leather was planned to produce and obtain a standard product. A Box–Behnken experimental design was employed to characterize the process including hydrocolloid preparation and drying, optimize and investigate the effects of the amount of starch (3, 5, and 7%), product thickness (1, 2, and 3 mm) and convective drying temperature (40, 50, and 60 °C) variables on moisture removal, color, texture profile and sensory attributes. The most preferred leather product was determined evaluating the sensory parameters with Duncan's test (p < .05). A multi‐criteria optimization based on sensory analysis results was achieved using response surface methodology. The optimum process conditions were 4.73% amount of starch, 1.11 mm thickness and 50.26 °C temperature. The amount of starch and its interaction with the other factors had an important effect on leather production. Pearson and principal component correlation analyses were performed to determine whether a correlation existed between the sensory and instrumental analysis parameters. Mutually supportive results were obtained from subjective and qualitative considerations. Practical applications The study presented the production of persimmon fruit leather as a healthy snack and optimization of the process conditions in the scope of an experimental design, which allowed of reducing the number of experiments. This approach enabled the evaluation of individual and interactional effects of each process parameter on important expectations of consumers for a new food product. It is necessary to discuss the results of instrumental and sensory analysis statistically to obtain a standard qualified product.

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“…The rate of dehydration (water loss) during the osmotic dehydration depends upon factors such as: solution concentration, immersion time, solution temperature, size and geometry of the fruit, solution to fruit mass ratio and level of agitation or circulation of the hypertonic solution. A large number of recent publications have described both mathematically and experimentally the influence of these variables on dehydration kinetics and mass transfer rates during osmotic dehydration (Pisalkar et al, 2014;Sutar and Gupta, 2007;Moreira et al, 2007;Silva et al, 2014;Ispir et al, 2009;Alam and Singh, 2010;Zita et al, 2009;Simpson et al, 2015). Mass transfer modeling of osmotic dehydration is necessary for understanding the process as well as to develop design and control schemes.…”

Section: Introductionmentioning

confidence: 99%

Approximate Mathematical Modeling of Osmotic Dehydration of Cone-Shaped Fruits and Vegetables in Hypertonic Solutions

Sirousazar

2017

Turkish JAF Sci.Tech.

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Water loss kinetics in osmotic dehydration of cone-shaped fruits and vegetables was modeled on the basis of diffusion mechanism, using the Fick's second law. The model was developed by taking into account the influences of the fruit geometrical characteristics, initial water content of fruit, water diffusion coefficient in fruit, and the water concentration in hypertonic solution. Based on the obtained model, it was shown that the water diffusion coefficient and the initial water concentration of fruit have direct effects on the dehydration rate and also inverse influence on the dehydration duration. The geometrical parameters of fruit and water concentration in hypertonic solution showed direct effect on the dehydration duration as well as inverse effect on the dehydration rate. The presented model seems to be useful tool to predict the dehydration kinetics of cone-shaped fruit during osmotic dehydration process and to optimize the process prior to perform the experiments.

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Diffusion mechanisms during the osmotic dehydration of Granny Smith apples subjected to a moderate electric field

Cited by 71 publications

References 27 publications

Anomalous diffusion based on fractional calculus approach applied to drying analysis of apple slices: The effects of relative humidity and temperature

Anomalous diffusion based on fractional calculus approach applied to drying analysis of apple slices: The effects of relative humidity and temperature

Production and preference mapping of persimmon fruit leather: An optimization study by Box–Behnken

Approximate Mathematical Modeling of Osmotic Dehydration of Cone-Shaped Fruits and Vegetables in Hypertonic Solutions

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