Diffusion of water and caffeine in coffee beans using the hemispherical geometry approach

Abstract

Geometrical, morphological, and shape factors are crucial for the accurate prediction of mass transfer rate of caffeine and water in the extraction of caffeine in aqueous medium from coffee beans. A new expression for the sphericity was deduced considering the hydrated coffee bean as a triaxial semilipsoid with moving boundaries applied to a nonsteady state analytical solution to describe the diffusion phenomena for the hemispherical geometry to best represent the morphology of the coffee bean during the caffeine extraction at varying temperatures from 30 to 60 °C. The sphericity increases with moisture in a power law trend. The hemisphere mathematical model presented an excellent adjustment to the data, with diffusion coefficients between 1.03 ×·10−11 and 9.00 ×·10−10 m2/s for caffeine and 0.69 ×·10−10 and 2.03 ×·10−10 m2/s for water; strongly influenced by temperature with activation energy of 59.93 and 41.24 kJ/mol, respectively, for caffeine and water. Practical applications: The decaffeination of coffee beans satisfies an important segment of the coffee market. Currently, many industries use the decaffeination technology based on organic solvents; others extract caffeine in aqueous medium and on a smaller scale the supercritical fluid extraction process. The present research provides important properties and a mathematical model to better represent the mass transfer phenomena, with the associated diffusion coefficients, along with a suitable expression for the size and shape of the coffee beans changing with the process, which can be used for the proper and accurate design and control of the extraction process. The proposed model used the hemispherical geometry approach with a reduced number of variables (e.g., only one equivalent radius), unlike other approaches that need three dimensions to represent the coffee bean size and the associated shape factor, which makes it time consuming, requiring more complex calculations, and not necessarily more accurate.