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

Ramírez, Cristián; Astorga, V.; Núñez, Helena; Jaques, A.; Simpson, Ricardo

doi:10.1111/jfpe.12549

Cited by 38 publications

(31 citation statements)

References 20 publications

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“…Anomalous diffusion model (Equation 5) as reported by Simpson, Ramírez, Nuñez, Jaques, and Almonacid () and Ramírez, Astorga, Nuñez, Jaques, and Simpson (), was also used for modeling the water diffusion and compared with Fick's model.

italicMR = \frac{8}{π^{2}} e^{- D_{ew} \frac{π^{2}}{4 L^{2}} t^{α}}

…”

Section: Methodsmentioning

confidence: 99%

Thin layer drying kinetics of Banana var. Monthan (ABB): Influence of convective drying on nutritional quality, microstructure, thermal properties, color, and sensory characteristics

Kumar

Nambi

Shiva

et al. 2019

J Food Process Engineering

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Banana with good amount of resistant starch (RS) offers greater benefit to human health. Studying the dehydration mechanism of the raw banana slice is very important for subsequent processes and quality of the product. Thus the study was aimed to investigate the influence of varying temperatures viz., 45, 55, and 65°C in a convective dryer on thin layer drying kinetics and to infer their influence on the rheological properties coupled thermal and sensory quality. Time for reducing the moisture content from the initial 71.2 ± 0.2% to a final 4.66–6.13% was found to be 270, 210, and 150 min for the drying temperatures 45, 55, and 65°C, respectively. Moisture ratio decreased exponentially with an increase in drying time. Page and logarithmic models obtained highest r2, lowest chi‐square values and least root mean square error and better reflected drying mechanism of banana slices. Improved rehydration ratio (1:2.4) and RS content (36.26%) was observed with the drying temperature of 55°C. Higher water absorption capacity (WAC) was observed in 55°C (4.86%). Swelling power of the flour was maintained to 4–6% till 70°C but it reached to 22% with the increase in temperature to 90°C. Thermal properties and microstructure of flour differed significantly with the temperatures. The lower value for whiteness index with low temperature drying reflected the better drying than at higher temperatures. Dehydration at 55°C was superior with nutrients like ascorbic acid. The banana flour had the rod shaped starch granules and traces of protein in its surface as evidenced. Irregular spherical shape, surface dents, and shrinkages were observed in powders dehydrated with high temperature (>65°C). Equilbrium relative humidity (ERH) studies revealed that 13.27 and 15.23% were the danger and critical point, respectively, for the banana flour. Descriptive sensory scores of the banana flour endorsed that dehydration at 65°C was found superior to other temperatures. Practical applications Banana flour offers greater potential to increase the resistant starch (RS) content in the food products besides adding minerals and basic nutrients. Drying process should retain the characteristics of fresh fruits by minimizing the cellular and structural changes during the drying. Mathematical modeling offers scope to set the variables which are influencing the drying of banana slices. The dried banana flour could be a replacement or supplement for various formulations. With the better physical properties like swelling capacity and enthalpy along with high RS, banana flour allow the formation of low bulk, high‐fiber products like pasta, noodles, and healthy functional foods with improved sensory descriptors. Banana flour‐based enterprises could be started in places where banana is cultivated and large sum of produced bananas are getting wasted due to poor postharvest management.

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italicMR = \frac{8}{π^{2}} e^{- D_{ew} \frac{π^{2}}{4 L^{2}} t^{α}}

…”

Section: Methodsmentioning

confidence: 99%

Thin layer drying kinetics of Banana var. Monthan (ABB): Influence of convective drying on nutritional quality, microstructure, thermal properties, color, and sensory characteristics

Kumar

Nambi

Shiva

et al. 2019

J Food Process Engineering

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“…Ramírez, Astorga, Nuñez, Jaques, and Simpson () proposed a model based on Fick's Law with a generalized order (α), this model was applied to fit data of apple slices on drying. The results indicate that the α value is fractional and the diffusivity is anomalous.…”

Section: Introductionmentioning

confidence: 99%

The fractional calculus in studies on drying: A new kinetic semi‐empirical model for drying

Matias

Bissaro

Jorge

et al. 2018

J Food Process Engineering

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In this article is introduced a new kinetic semi‐empirical model for drying. The model was developed by arbitrary‐order generalization of Lewis's kinetic equation that was obtained using the Laplace transform and Laplace's Inverse Transform. Kinetic data on soybean drying at 50, 60, 70, and 80 °C were retrieved to test the model which was compared to first‐order Lewis's model and to Page's model by quantitative criteria. Results show that the process is best described by the fractional‐order model and that arbitrary‐order equation may be employed to adjust experimental data on drying, with better results among other models analyzed. Practical applications Drying is one of the most complex and energy‐consuming chemical unit operations. The modeling of drying kinetics can be applied in the project of drying equipment and to reduce costs of energy consumption. In general, the approach used in drying kinetics modeling is based on differential balances to represent the temporal variability of moisture content. In some cases, the Mathematical models cannot fit good the experimental data by to the fact that the models obtained by differential balances are exponential and the experimental data nonexponential. The fractional calculus can be an alternative to generalize the order of differential equations and fit process. The modeling procedure presented in this article presents the use of fractional calculus to generalize the order of a classic differential model. The model obtained by the fractional calculus approach provides best fits and more reliable adjusts than the classic model, the results indicate an anomalous diffusion.

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“…Fractional derivatives are alternative tools to try to explain better anomalous diffusion process with real data. For this reason, Simpson et al [4] studied fractional mass transfer modeling in food drying, also Ramírez et al [5] analyzed the drying analysis of apple slices in view of fractional calculus.…”

Section: Introductionmentioning

confidence: 99%

Kinetic Model for Drying in Frame of Generalized Fractional Derivatives

Özarslan

Baş

2020

Fractal Fract

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In this article, the Lewis model was considered for the soybean drying process by new fractional differential operators to analyze the estimated time in 50 ∘ C , 60 ∘ C , 70 ∘ C , and 80 ∘ C . Moreover, we used dimension parameters for the physical meaning of these fractional models within generalized and Caputo fractional derivatives. Results obtained with generalized fractional derivatives were analyzed comparatively with the Caputo fractional, integer order derivatives and Page model for the soybean drying process. All results for fractional derivatives are discussed and compared in detail.

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

Cited by 38 publications

References 20 publications

Thin layer drying kinetics of Banana var. Monthan (ABB): Influence of convective drying on nutritional quality, microstructure, thermal properties, color, and sensory characteristics

Thin layer drying kinetics of Banana var. Monthan (ABB): Influence of convective drying on nutritional quality, microstructure, thermal properties, color, and sensory characteristics

The fractional calculus in studies on drying: A new kinetic semi‐empirical model for drying

Kinetic Model for Drying in Frame of Generalized Fractional Derivatives

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