Modelling the kinetics of tea and coffee infusion

Abstract

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.

Aqueous extraction kinetics of soluble solids, phenolics and flavonoids from sage (Salvia fruticosa Miller) leaves

“…Generally kinetics of tea extraction fits reversible first order kinetic model as has been reported by previous researchers (Spiro and Jago 1982;Jaganyi and Price 1999;Stapley 2002).…”

“…1) is revised as reversible first order kinetic model (Eq. 2) for modeling tea infusion (Stapley 2002).…”

Modeling yerba mate aqueous extraction kinetics: Influence of temperature

“…The hypotheses of the model are the following: (1) yerba mate leaves are regarded as infinite flat plates; (2) with non-uniform distribution of components within the leaves, the same component can be found in different forms (associated with each other in the interior of whole cells or cells damaged by the process, stored in parenchymatous tissue or vascular tissue, etc. ); (3) resistance to mass transfer in solid-liquid interface on the liquid side is zero; (4) the solution in the batch reactor is perfectly mixed, and the gradient in the liquid phase is flat; and (5) at the beginning, when the water is taken up, more readily accessible components pass quickly into the solution and form a very large concentration gradient (steptype) in the solid near the interface, causing a very fast mass transfer, which cannot fit with the solution of Ficḱ s law with few terms; its profile is flat inside the solid (the leaf) beyond a narrow border zone (Stapley, 2002). For this stage, we propose a second-order equation in the form: …”

“…There have not been any reports about the aqueous extraction kinetics of yerba mate; nevertheless, there are many studies about extraction kinetics of components of tea and coffee (Jaganyi and Madlala, 2000;Jaganyi and Price, 1999;Spitzer, 1993, 1994;Spiro and Chong, 1997;Spiro and Jago, 1982;Spiro and Selwood, 1984;Stapley, 2002;Zanoni et al, 1992), metabolites extraction kinetics as phenolics, antioxidants and fat substances in other products (Bucić -Kojić et al, 2007;Cacace and Mazza, 2003;Franco et al, 2007;Herodež et al, 2003;Ho et al, 2005;Jaganyi and Wheeler, 2003;Kashyap et al, 2007;Wongkittipong et al, 2004) and a report on yerba mate extraction optimization (Sambiassi et al, 2002). There are several kinetics models for the interpretation of experimental extraction data.…”

“…The most frequently used model for tea and coffee extraction is a pseudo first-order model proposed by Spiro and Jago (1982). However, Herodež et al (2003) applied a solution of Fick's second law for ethanolic extraction of Melissa officinalis L.; Bucić -Kojić et al (2007), the Peleg equation (Peleg, 1988) for the extraction of polyphenols from grape seeds, and Stapley (2002) used the Cranck solution for Fick's law. Rakotondramasy-Rabesiaka et al (2007) used a second-order kinetics model for protopina extraction of Fumaria officinalis L. and Bai et al (2002) applied a twomechanism model for the extraction of b-glucuronidase from defatted canola seed flake.…”