Document Type : Full length


1 Chemical Engineering Faculty, Sahand University of Technology, Tabriz, Iran

2 sahand uni

3 Urmia University of Technology


Water and solid effective diffusivities and shrinkage were correlated for finite hollow cylinder-shaped apple samples during the candying operation in the osmotic solution. Experiments were conducted in the sucrose solution as an osmotic agent at different temperatures (i.e., 40, 50, and 60 °C) and at a constant concentration of 55 °Brix. The effective diffusivities of water and solid were calculated by fitting the water loss and solid uptake experimental data to Fick’s second law and fractional calculus method, considering the shrinkage of the samples during the candying process. The obtained results exhibited that the volume of the apples reduced linearly by increasing the water loss. For above conditions of the candying process, water effective diffusivities with Fick second law were determined in the range of 3.7×10−10 m2/s–8.73×10−10 m2/s, and those with fractional calculus method were in the range of 2.75×10−10 m2/s–6.98×10−10 m2/s. The results indicated that the coefficient of determination for the fractional calculus method was more than the coefficient of determination for the Fick model. The value of the empirical parameter α for the Non-Fickian diffusion model was always higher than unity, meaning that the dehydration process had a super-diffusive mechanism.


[1]   Shafiee Langari, F., “Experimental study and mathematical modeling of the osmotic drying process”, Iranian Journal of Chemical Engineering (IJChE), 12, 15 (2015).
[2]   Traffano-Schiffo, M. V., Laghi, L., Castro-Giraldez, M., Tylewicz, U., Romani, S., Ragni, L., Dalla Rosa, M. and Fito, P. J., “Osmotic dehydration of organic kiwifruit pre-treated by pulsed electric fields: Internal transport and transformations analyzed by NMR”, Innovative Food Science & Emerging Technologies, 41, 259 (2017).
[3]      Yadav, A. K. and Singh, S. V., “Osmotic dehydration of fruits and vegetables: A review”, Journal of Food Science and Technology, 51, 1654 (2014).
[4]      Ramya, V. and Jain, N., “A review on osmotic dehydration of fruits and vegetables: An integrated approach”, Journal of Food Process Engineering, 40, e12440 (2017).
[5]      Nayak, C. A., Suguna, K. and Rastogi, N., “Combined effect of gamma-irradiation and osmotic treatment on mass transfer during rehydration of carrots”, Journal of Food Engineering, 74, 134 (2006).
[6]      Khin, M. M., Zhou, W. and Perera, C., “Development in the combined treatment of coating and osmotic dehydration of food-a review”, International Journal of Food Engineering, 1, 1 (2005).
[7]      Mayor, L., Pissarra, J. and Sereno, A., “Microstructural changes during osmotic dehydration of parenchymatic pumpkin tissue”, Journal of Food Engineering, 85, 326 (2008).
[8]      Fernandes, F. A., Gallão, M. I. and Rodrigues, S., “Effect of osmotic dehydration and ultrasound pre-treatment on cell structure: Melon dehydration”, LWT-Food Science and Technology, 41, 604 (2008).
[9]      Vilela, A., Sobreira, C., Abraão, A. S., Lemos, A. M. and Nunes, F. M., “Texture quality of candied fruits as influenced by osmotic dehydration agents”, Journal of Texture Studies, 47, 239 (2016).
[10]  Abbasi Souraki, B., Tondro, H. and Ghavami, M., “Modeling of mass transfer during osmotic dehydration of apple using an enhanced lumped model”, Drying Technology, 31, 595 (2013).
[11]  Sareban, M. and Abbasi Souraki, B., “Anisotropic diffusion during osmotic dehydration of celery stalks in salt solution”, Food and Bioproducts Processing, 98, 161 (2016).
[12]  Karim, M. A. and Hawlader, M. N. A., “Drying characteristics of banana: theoretical modelling and experimental validation”, Journal of Food Engineering, 70, 35 (2005).
[13]  Białobrzewski, I., “Simultaneous heat and mass transfer in shrinkable apple slab during drying”, Drying Technology, 24, 551 (2006).
[14]  Ochoa-Martinez, C., Ramaswamy, H. and Ayala-Aponte, A., “A comparison of some mathematical models used for the prediction of mass transfer kinetics in osmotic dehydration of fruits”, Drying Technology, 25, 1613 (2007).
[15]  Jabrayili, S., Farzaneh, V., Zare, Z., Bakhshabadi, H., Babazadeh, Z., Mokhtarian, M. and Carvalho, I. S., “Modelling of mass transfer kinetic in osmotic dehydration of kiwifruit”, International Agrophysics, 30, 185 (2016).
[16]  Ramírez, C., Astorga, V., Nuñez, H., Jaques, A. and Simpson, R., “Anomalous diffusion based on fractional calculus approach applied to drying analysis of apple slices: The effects of relative humidity and temperature”, Journal of Food Process Engineering, 40, e12549 (2017).
[17]  Abbasi, S., Mousavi, S., Mohebi, M. and Kiani, S., “Effect of time and temperature on moisture content, shrinkage, and rehydration of dried onion”, Iranian Journal of Chemical Engineering (IJChE), 6, 57 (2009).
[18]  Simpson, R., Jaques, A., Nunez, H., Ramirez, C. and Almonacid, A., “Fractional calculus as a mathematical tool to improve the modeling of mass transfer phenomena in food processing”, Food Engineering Reviews, 5, 45 (2013).
[19]  Simpson, R., Ramírez, C., Birchmeier, V., Almonacid, A., Moreno, J., Nuñez, H. and Jaques, A., “Diffusion mechanisms during the osmotic dehydration of Granny Smith apples subjected to a moderate electric field”, Journal of Food Engineering, 166, 204 (2015).
[20]  Varea, C. and Hernández, D., “Difusión anómala en sistema complejos”, Rev. Digit. Univ. UNAM, 11, 6 (2010).
[21]  Crank, J., The mathematics of diffusion, 1st Ed., Oxford University Press, (1979).
[22]  Luikov, A. V., Analytical heat diffusion theory, 1st Ed., Academic Press, (2012).
[23]  Carslaw, H. and Jaeger, J., Conduction of heat in solids, Oxford Science Publications, 1st Ed., Oxford, England, (1959).
[24]  Qi, H. and Liu, J., “Time-fractional radial diffusion in hollow geometries”, Meccanica, 45, 577 (2010).
[25]  Podlubny, I., Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, 1st Ed., Academic Press, (1998).
[26]  Torreggiani, D., “Osmotic dehydration in fruit and vegetable processing”, Food Research International, 26, 59 (1993).
[27]  Azuara, E., Cortes, R., Garsia, H. S. and Beristanin, C. I., “Kinetic model for osmotic dehydration and its relationship with Fick's second law”, International Journal of Food Science & Technology, 27, 409 (1992).
[28]  Latimer, G. W., Official methods of analysis of AOAC International, 21st Ed., Gaithersburg, Maryland: AOAC International, (2019).
[29]  Nieto, A. B., Vicente, S., Hodara, K., Castro, M. A. and Alzamora, S. M., “Osmotic dehydration of apple: Influence of sugar and water activity on tissue structure, rheological properties and water mobility”, Journal of Food Engineering, 119, 104 (2013).
[30]  Assis, F. R., Morais, R. M. S. C. and Morais, A. M. M. B., “Mathematical modelling of osmotic dehydration kinetics of apple cubes”, Journal of Food Processing and Preservation, 41, e12895 (2017).
[31]  Moreira, R. and Sereno, A. M., “Evaluation of mass transfer coefficients and volumetric shrinkage during osmotic dehydration of apple using sucrose solutions in static and non-static conditions”, Journal of Food Engineering, 57, 25 (2003).
[32]  Cichowska, J., Żubernik, J., Czyżewski, J., Kowalska, H. and Witrowa-Rajchert, D., “Efficiency of osmotic dehydration of apples in polyols solutions”, Molecules, 23, 446 (2018).