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Modeling of Tea Infusion Kinetics Incorporating Swelling Kinetics

  • Raosaheb A. Farakte , Geeta U. Yadav , Bhushan S. Joshi , Ashwin W. Patwardhan ORCID logo EMAIL logo and Gurmeet Singh
Published/Copyright: January 18, 2017
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International Journal of Food Engineering
From the journal International Journal of Food Engineering Volume 13 Issue 2

Abstract

Mathematical model to predict tea infusion kinetics which accounts for swelling kinetics of tea granules is presented. Swelling kinetics of tea granules has never been taken into account for models developed so far. Differential equations (DEs) for concentration of tea constituents inside tea granule with respect to radius and time were derived. Solution methodology for these DEs is developed based on Crank-Nicholson scheme. Tea infusion profile is obtained using this model by knowing the swelling kinetics, partition constant and initial contents in tea granules. Diffusivity and product of interfacial area (As) and backward rate constant (k−1) are the fitting parameters. Model prediction is fitted to the experimental data published previously (R2 = 0.90–0.98). The fitted diffusivity (3.33 × 10−10 m2/s) and Ask−1 (2 m3/(kg.s)) predicted the infusion profile of other sized tea granules very well. This model predicts the infusion during initial stage very accurately without any empirical parameter.

Keywords: tea infusion kinetics; swelling kinetics; partition constant; mathematical model; Crank-Nicholson scheme

Acknowledgments

Authors would like to thank Unilever Industries Limited for funding the research project. One of the authors would like to thank University Grant Commission (UGC) for providing financial support.

List of symbols

a

empirical parameter in Spiro’s kinetic expression

A

surface area of sphere of radius r (m2)

As

specific surface area of the tea granule (m2/kg)

c

concentration inside liquid phase of shell (kg/m3)

ce

experimental value of infusion concentration (kg/m3)

cp

experimental value of infusion concentration (kg/m3)

cs0

initial soluble content of tea granule (kg/m3)

cs

concentration in the solid phase of shell (kg/m3)

cs∗

concentration at the solid liquid interface (kg/m3)

cR

concentration at the surface of tea granule and in the bulk infusion (kg/m3)

cR,∞

concentration at the surface of tea granule and in the bulk infusion at equilibrium (kg/m3)

cs,∞

concentration in the tea granule at equilibrium (kg/m3)

J

flux of transfer of tea constituents across of shell (kg/(m2.s))

kobs

observed rate constant (1/s)

k–1

1st order rate constant for the transfer of soluble from liquid to solid (m/s)

k1

1st rate constant for the transfer of tea constituents from solid to water (m/s)

K

partition constant

M

mass of tea constituent in shell (kg)

n

number of data points

N

number of tea particles taking part in infusion process

r

inner radius of shell (m)

rm

radius of shell to express the volume of shell (m)

rdiss′′

dissolution rate in the shell (kg/(m2.s))

Δr

thickness of shell (m)

R

radius of tea particle at any time ‘t’ (m)

R0

radius of tea particle at any time ‘t = 0’ (m)

R∞

radius of tea particle at any time ‘t = ∞’ (m)

sr

ratio of final (after infusion) to initial volume of tea granule

t

time (s)

Δt

time interval (s)

Vb

volume of infusion at time ‘t’ (m3)

Va

amount of water absorbed per unit weight of tea granules (m3/kg)

V

volume of shell (m3)

w

weight of tea granules used for infusion (kg)

x0

initial soluble content of tea granule (kg/kg)

Z

representation of any variable with respect to time as radius

S, T, U, Y, W, X

lumped parameters as per Crank Nicolson scheme (dimensionless)

Greek symbols

ρ

density of tea granule (kg/m3)

λ

rate parameter for swelling process (1/s)

φ

shape parameter for swelling process

References

1. Spiro M, Jago DS. Kinetics and equilibria of tea infusion part 3. Rotating-disc experiments interpreted by a steady-state model. J Chem Soc Faraday Trans 1982;1:295–305.10.1039/f19827800295Search in Google Scholar

2. Spiro M, Selwood RM. The kinetics and mechanism of caffeine infusion from coffee: the effect of particle size. J Sci Food Agric 1984;35:915–924.10.1002/jsfa.2740350817Search in Google Scholar

3. Price WE, Spiro M. Kinetics and equilibria of tea infusion: theaflavin and caffeine concentrations and partition constants in several whole teas and sieved fractions. J Sci Food Agric 1985;36:1303–1308.10.1002/jsfa.2740361215Search in Google Scholar

4. Spiro M, Siddique S. Kinetics and equilibria of tea infusion. Analysis and partition constants of theaflavins, thearubigins, and caffeine in Koonsong broken pekoe. J Sci Food Agric 1981;32:1027–1032.10.1002/jsfa.2740321012Search in Google Scholar

5. Price WE, Spiro M. Kinetics and equilibria of tea infusion: rates of extraction of theaflavin, caffeine and theobromine from several whole teas and sieved fractions. J Sci Food Agric 1985;36:1309–1314.10.1002/jsfa.2740361216Search in Google Scholar

6. Spiro M, Jaganyi D. Kinetics and equilibria of tea infusion, part 15. Transport of caffeine across a teabag membrane in a modified rotating diffusion cell. Food Chem 2000;69:119–124.10.1016/S0308-8146(99)00251-4Search in Google Scholar

7. Spiro M, Price WE. Kinetics and equilibria of tea infusion: part 7 – the effects of salts and of pH on the rate of extraction of caffeine from Kapchorua Pekoe Fannings. Food Chem 1987;25:49–59.10.1016/0308-8146(87)90053-7Search in Google Scholar

8. Spiro M, Price WE, Miller WM, Arami M. Kinetics and equilibria of tea infusion: part 8 – the effects of salts and of pH on the rate of extraction of theaflavins from black tea leaf. Food Chem 1987;25:117–126.10.1016/0308-8146(87)90060-4Search in Google Scholar

9. Spiro M, Chong YY. The kinetics and mechanism of caffeine infusion from coffee: the temperature variation of the hindrance factor. J Sci Food Agric 1997;74:416–420.10.1002/(SICI)1097-0010(199707)74:3<416::AID-JSFA868>3.0.CO;2-0Search in Google Scholar

10. Spiro M, Jaganyi D, Broom MC. Kinetics and equilibria of tea infusion: part 9. The rates and temperature coefficients of caffeine extraction from green Chun Mee and black Assam Bukial teas. Food Chem 1992;45:333–335.10.1016/0308-8146(92)90033-XSearch in Google Scholar

11. Stapley AG. Modelling the kinetics of tea and coffee infusion. J Sci Food Agric 2002;82:1661–1671.10.1002/jsfa.1250Search in Google Scholar

12. Farakte RA, Yadav GU, Joshi BS, Patwardhan AW, Singh G. Role of particle size in tea infusion process. Int J Food Eng 2016;12:1–16.10.1515/ijfe-2015-0213Search in Google Scholar

13. Gujar JG, Chattopadhyay S, Wagh SJ, Gaikar VG. Experimental and modeling studies on extraction of catechin hydrate and epicatechin from Indian green tea leaves. Can J Chem Eng 2010;88:232–240.10.1002/cjce.20271Search in Google Scholar

14. Ziaedini A, Jafari A, Zakeri A. Extraction of antioxidants and caffeine from green tea (Camelia sinensis) leaves: kinetics and modeling. Food Sci Technol Int 2010;16:505–510.10.1177/1082013210367567Search in Google Scholar

15. Linares RA, Hase LS, Vergara LM, Resnik LS. Modeling yerba mate aqueous extraction kinetics: influence of temperature. J Food Eng 2010;97:471–477.10.1016/j.jfoodeng.2009.11.003Search in Google Scholar

16. Miyagawa K, Yamano H, Ogawa I. Calorimetric measurements on the swelling of green tea. Thermochim Acta 1995;257:13–19.10.1016/0040-6031(94)02196-USearch in Google Scholar

17. Joshi BS, Farakte RA, Yadav GU, Patwardhan AW, Singh G. Swelling kinetics of tea in hot water. J Food Sci Technol 2016;53:315–325.10.1007/s13197-015-2023-9Search in Google Scholar PubMed PubMed Central

18. Spiro M, Siddique S. Kinetics and equilibria of tea infusion: kinetics of extraction of theaflavins, thearubigins and caffeine from Koonsong broken pekoe. J Sci Food Agric 1981;32:1135–1139.10.1002/jsfa.2740321115Search in Google Scholar

19. Castillo-Santos K, Ruiz-López II, Rodríguez-Jimenes GC, Carrillo-Ahumada J, García-Alvarado MA. Analysis of mass transfer equations during solid-liquid extraction and its application for vanilla extraction kinetics modeling. J Food Eng 2017;192:36–44.10.1016/j.jfoodeng.2016.07.020Search in Google Scholar

Published Online: 2017-1-18
Published in Print: 2017-2-1

©2017 by De Gruyter

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https://doi.org/10.1515/ijfe-2016-0206
Keywords for this article
tea infusion kinetics; swelling kinetics; partition constant; mathematical model; Crank-Nicholson scheme

Articles in the same Issue

  1. Articles
  2. The Effects of Amyloglucosidase, Glucose Oxidase and Hemicellulase Utilization on the Rheological Behaviour of Dough and Quality Characteristics of Bread
  3. Studies of Boil Treatment on Methanol Control and Pilot Factory Test of Jujube Brandy
  4. Modeling of Tea Infusion Kinetics Incorporating Swelling Kinetics
  5. The Influence of Refractance Window Drying on Qualitative Properties of Kiwifruit Slices
  6. Multiple Parameter Optimizations for Enhanced Biosynthesis of Exo-polygalacturonase Enzyme and its Application in Fruit Juice Clarification
  7. Sugarcane Juice Clarification by Hydrogen Peroxide: Predictions with Artificial Neural Networks
  8. The Stress-Relaxation Behavior of Rice as a Function of Time, Moisture and Temperature
  9. Impacts of Explosion Puffing Drying Combined with Hot-Air and Freeze Drying on the Quality of Papaya Chips
  10. Pulverization Using Liquid Nitrogen Significantly Improves Physical Properties of Powder and Extraction Yield of Polysaccharides of Astragalus mongholicus
  11. Use of Iranian Milkweed Seed Oil to Increase Oxidative Stability of Olive Cultivar Roghani Oil
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