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Effective diffusion coefficient ( D -value) is an important parameter for the extraction process. In this study, a cylindrical model to estimate the  D -value of betanin extraction from red beet roots was developed. The influence of extraction temperature, pH, cylindrical thickness and type of acids on the  D -value was also investigated. The optimal parameters of betanin extraction were 30°C, pH 4.0 adjusted with sulfurous acid or acetic acid.  D -values under the above conditions were 18.95×10 −11  m 2 /s and 17.87×10 −11  m 2 /s, respectively. The result showed that  D -value elevated with the increase of cylindrical thickness, which was consistent with earlier conclusion from spherical model. The modeling may be useful for the investigation into extraction process and practical application.

Mathematical Modeling of Betanin Extraction from Red Beet ( Beta vulgaris L.) by Solid–Liquid Method