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Description of jambolan (Syzygium cumini (L.)) anthocyanin extraction kinetics at different stirring frequencies of the medium using diffusion models

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Abstract

Anthocyanin extraction kinetics was described for jambolan fruits. The spherical granules obtained were dried at 40 °C and the average radius of the sphere equivalent to the granules was determined. Solid-solvent ratio was fixed at 1:20 and temperature at 35 °C. A mixture of ethyl alcohol and hydrochloric acid (85:15) was used as solvent. Experiments were conducted with the following stirring frequencies: 0, 50, 100 and 150 rpm. Two diffusion models were used to describe the extraction process. The first one used an analytical solution, with boundary condition of the first kind. The second one used a numerical solution, with boundary condition of the third kind. The second model was the most adequate, and its results were used to determine empirical equations relating the process parameters with the stirring frequency, allowing to simulate new extraction kinetics.

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Abbreviations

A,B :

Coefficients of algebraic equations

Bi :

Biot number

D :

Effective mass diffusivity (m2 s−1)

f :

Stirring frequency

h :

Convective mass transfer coefficient (m s−1)

X :

Local value of anthocyanin concentration (mg/100 g)

\( \overline{X} \) :

Mean value of anthocyanin concentration (mg/100 g)

X ∞ :

Equilibrium anthocyanin concentration (mg/100 g)

X 0 :

Initial anthocyanin concentration (mg/100 g)

\( {\overline{X}}_i^{\mathrm{exp}} \) :

Mean anthocyanin concentration measured for the point “i” (mg/100 g)

\( {\overline{X}}_i^{sim} \) :

Mean anthocyanin concentration simulated for the point “i” (mg/100 g)

N p :

Number of experimental points

N :

Number of control volumes

r :

Position in spherical coordinate (m)

R :

Radius of a sphere (m)

t :

Time (s)

V:

Volume (m3)

χ2 :

Chi-square

\( 1/{\sigma}_i^2 \) :

Statistical weight of the point “i”

References

  1. Lapornik B, Prosek M, Wondra AG (2005) Comparison of extracts prepared from plant by-products using different solvents and extraction time. J Food Eng 71(2):214–222

    Article  Google Scholar 

  2. Turker N, Erdogdu F (2006) Effects of pH and temperature of extraction medium on effective diffusion coefficient of anthocynanin pigments of black carrot (Daucus carota var. L.). J Food Eng 76(4):579–583

    Article  Google Scholar 

  3. Pan Z, Qu W, Mab H, Atungulu GG, McHugh THM (2011) Continuous and pulsed ultrasound-assisted extractions of antioxidants from pomegranate peel. Ultrason Sonochem 18(5):1249–1257

    Article  Google Scholar 

  4. D’Alessandro LG, Dimitrov K, Vauchel P, Nikov I (2013) Kinetics of ultrasound assisted extraction of anthocyanins from Aronia melanocarpa (black chokeberry). Chem Eng Res Des 92(10):1818–1826

    Article  Google Scholar 

  5. Garofulic IE, Dragovic-Uzelac V, Jambrak AR, Jukic M (2013) The effect of microwave assisted extraction on the isolation of anthocyanins and phenolic acids from sour cherry Marasca (Prunus cerasus var. Marasca). J Food Eng 114(4):437–442

    Article  Google Scholar 

  6. Tao Y, Zhang Z, Sun D-W (2014) Experimental and modeling studies of ultrasound-assisted release of phenolics from oak chips into model wine. Ultrason Sonochem 21(5):1839–1848

    Article  Google Scholar 

  7. Castillo-Santos K, Ruiz-López II, Rodríguez-Jimenes GC, Carrillo-Ahumada J, García-Alvarado MA (2017) Analysis of mass transfer equations during solid-liquid extraction and its application for vanilla extraction kinetics modeling. J Food Eng 192(1):36–44

    Article  Google Scholar 

  8. Mantell C, Rodríguez M, de la Ossa EM (2003) Kinetics and mathematical modeling of anthocyanin extraction with carbon dioxide and methanol at high pressure. Sep Sci Technol 38(15):3689–3712

    Article  Google Scholar 

  9. Sant’Anna V, Marczak LDF, Tessaro IC (2013) Kinetic modeling of anthocyanin extraction from grape marc. Food Bioprocess Technol 6(12):3473–3480

    Article  Google Scholar 

  10. Chan C-H, Yusoff R, Ngoh G-C (2014) Modeling and kinetics study of conventionaland assisted batch solvent extraction. Chem Eng Res Des 92(6):1169–1186

    Article  Google Scholar 

  11. Wang Y, Herdegen V, Repke JU (2016) Numerical study of different particle size distribution for modeling of solid-liquid extraction in randomly packed beds. Sep Purif Technol 171(1):131–143

    Article  Google Scholar 

  12. Bonfigli M, Godoy E, Reinheimer MA, Scenna NJ (2017) Comparison between conventional and ultrasound-assisted techniques for extraction of anthocyanins from grape pomace. Experimental results and mathematical modeling. J Food Eng 207(1):56–72

    Article  Google Scholar 

  13. Azmir J, Zaidul ISM, Rahman MM, Sharif KM, Mohamed A, Sahena F, Jahurul MHA, Ghafoor K, Norulaini NAN, Omar AKM (2013) Techniques for extraction of bioactive compounds from plant materials: a review. J Food Eng 117(4):426–436

    Article  Google Scholar 

  14. Lin C, Xia G, Liu S (2017) Modeling and comparison of extraction kinetics of 8 catechins, gallic acid and caffeine from representative white teas. LWT - Food Sci Technol. https://doi.org/10.1016/j.lwt.2017.04.028

    Article  Google Scholar 

  15. Espinoza-Pérez JD, Vargas A, Robles-Olvera VJ, Rodríguez-Jimenes GC, García-Alvarado MA (2007) Mathematical modeling of caffeine kinetic during solid–liquid extraction of coffee beans. J Food Eng 81(1):72–78

    Article  Google Scholar 

  16. Hojnik M, Skerget M, Knez Z (2008) Extraction of lutein from Marigold flower petals - Experimental kinetics and modelling. LWT - Food Sci Technol 41(10):2008–2016

    Article  Google Scholar 

  17. Tao Y, Zhang Z, Sun DW (2014) Kinetic modeling of ultrasound-assisted extraction of phenolic compounds from grape marc: Influence of acoustic energy density and temperature. Ultrason Sonochem 21(4):1461–1469

    Article  Google Scholar 

  18. Silva WP, Silva CMDPS, Precker JW, Gomes JP, Nascimento PL, Silva LD (2012) Diffusion models for the description of seedless grape drying using analytical and numerical solutions. Agric Sci 3(4):545–556

    Google Scholar 

  19. Silva CMDPS, Silva WP, Farias VSO, Gomes JP (2012) Effective diffusivity and convective mass transfer coefficient during the drying of bananas. Engenharia Agrícola 32(2):342–353

    Article  Google Scholar 

  20. Silva WP, Farias VSO, Neves GA, De Lima AGB (2012c) Modeling of water transport in roof tiles by removal of moisture at isothermal conditions. Heat Mass Transf 48(5):809–821

    Article  Google Scholar 

  21. Silva WP, Silva CMDPS, Gomes JP (2013) Drying description of cylindrical pieces of bananas in different temperatures using diffusion models. J Food Eng 117(3):417–424

    Article  Google Scholar 

  22. Cissé M, Bohuon P, Sambe F, Kane C, Sakho M, Dornier M (2012) Aqueous extraction of anthocyanins from Hibiscus sabdariffa: experimental kinetics and modeling. J Food Eng 109(1):16–21

    Article  Google Scholar 

  23. Tao Y, Wu D, Zhang QA, Sun DW (2014c) Ultrasound-assisted extraction of phenolics from wine lees: modeling, optimization and stability of extracts. Ultrason Sonochem 21(2):706–715

    Article  Google Scholar 

  24. Francis FJ (1982) Analysis of anthocyanins. In: Markakis P (ed) Anthocyanins as food colors. Academic Press, New York, pp 181–207

    Chapter  Google Scholar 

  25. Luikov AV (1968) Analytical heat diffusion theory. Academic Press, New York

    Google Scholar 

  26. Crank J (1992) The Mathematics of Diffusion. Clarendon Press, Oxford, UK

    MATH  Google Scholar 

  27. Silva WP, Precker JW, Silva CMDPS, Silva DDPS (2009) Determination of the effective diffusivity via minimization of the objective function by scanning: application to drying of cowpea. J Food Eng 95(2):298–304

    Article  Google Scholar 

  28. Patankar SV (1980) Numerical heat transfer and fluid flow. Hemisphere Publishing Corporation, New York

    Book  Google Scholar 

  29. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1996) Numerical Recipes in Fortran 77. The art of Scientific Computing. Cambridge University Press, New York v. 1

    MATH  Google Scholar 

  30. Da Silva WP, Rodrigues AF, Silva CMDPS, Castro DS, Gomes JP (2015) Comparison between continuous and intermittent drying of whole bananas using empirical and diffusion models to describe the processes. J Food Eng 166(1):230–236

    Article  Google Scholar 

  31. Da Silva WP, Silva CMDPS, Cavalcanti CGB, Silva DDPS, Soares IB, Oliveira JAS, Silva CDPS (2004) LAB Fit curve fitting: a software in Portuguese for treatment of experimental data. Revista Brasileira de Ensino de Física 26(4):419–427

    Article  Google Scholar 

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Acknowledgements

The first author would like to thank CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) for the support given to this research and for his research grant (Processes Number 302480/2015–3 and 444,053/2014–0).

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Authors and Affiliations

  1. Federal University of Campina Grande, Campina Grande, Paraiba, Brazil

    Wilton Pereira da Silva, Jarderlany Sousa Nunes, Josivanda Palmeira Gomes, Auryclennedy Calou de Araújo & Cleide M. D. P. S. e Silva

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  1. Wilton Pereira da Silva
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  2. Jarderlany Sousa Nunes
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  3. Josivanda Palmeira Gomes
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  5. Cleide M. D. P. S. e Silva
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Correspondence to Wilton Pereira da Silva.

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da Silva, W.P., Nunes, J.S., Gomes, J.P. et al. Description of jambolan (Syzygium cumini (L.)) anthocyanin extraction kinetics at different stirring frequencies of the medium using diffusion models. Heat Mass Transfer 54, 3275–3285 (2018). https://doi.org/10.1007/s00231-018-2349-8

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