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Modelling the kinetics of tea and coffee infusion
Author(s) -
Stapley Andrew G F
Publication year - 2002
Publication title -
journal of the science of food and agriculture
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.782
H-Index - 142
eISSN - 1097-0010
pISSN - 0022-5142
DOI - 10.1002/jsfa.1250
Subject(s) - mass transfer , thermodynamics , mathematics , constant (computer programming) , chemistry , boundary value problem , slab , term (time) , volume (thermodynamics) , transfer (computing) , diffusion , mathematical analysis , physics , quantum mechanics , geophysics , parallel computing , computer science , programming language
Data from infusion experiments with tea and coffee are commonly fitted to an equation derived by Spiro from a lumped parameter mass transfer model. However, this equation is generally modified by adding an intercept term in order to achieve acceptable fits to data. Spiro has since reported a Fick's second law analysis using a ‘long‐time approximation’ which yields the same form as the modified fit equation, including the non‐zero intercept term. This successfully predicts the high initial rates of mass transfer due to high initial concentration gradients at the surface of the solid. In this paper the value of the intercept is evaluated for both tea leaf (infinite slab) and coffee particle (sphere) geometries under combined boundary conditions of non‐zero interfacial mass transfer resistance and finite volume of extracting solution. Predicted intercepts are similar to experimental values reported in the literature; however, the analysis suggests that fits to data should ignore ‘early’ points where the solution concentration is less than 35% of its final value. This may not be the case with some literature values and this limits the conclusions that may be drawn from them. Solute diffusivities calculated from the observed rate constant using this model differ slightly from those obtained using the original Spiro method. © 2002 Society of Chemical Industry