Mass transfer modeling of the antioxidant extraction of roselle flower (Hibiscus sabdariffa)

  • C. E. Ochoa-VelascoEmail author
  • I. I. Ruiz-LópezEmail author
Original Article


The aim of this study was to analyze the equilibrium and dynamic periods for mass transfer during the antioxidant solid–liquid extraction of dry roselle flower (Hibiscus sabdariffa). Extraction kinetics for total phenolic compounds (TPC), total flavonoids (TFL) and total antioxidant capacity (TAC) were obtained at different temperatures (50, 60, 70 or 80 °C) and solvent-to-product mass ratios (100:1, 200:1 or 300:1 g/g) under stirring (220–230 rpm). An analytical solution for unsteady-state mass transfer based on Fick’s second law of diffusion was used to mathematically describe solid–liquid extraction curves and for the simultaneous estimation of diffusion coefficients and the final amount of extracted bioactive compounds, which were further related to experimental conditions by a second order model. The amount of extracted bioactive compounds at equilibrium were in the ranges of 30.8–89.8 g GAE/kg d.m. for TPC (0.154–0.373 g GAE/L extract), 40.0–131.6 g catechin/kg d.m. for TFC (0.269–0.559 g catechin/L extract) and 37.5–227.0 g trolox/kg d.m. for TAC (0.346–0.865 g trolox/L extract). On the other hand, diffusion coefficients for TPC, TFC and TAC were in the ranges of 0.72–2.66 × 10−11, 0.25–2.37 × 10−11 and 1.19–5.79 × 10−11 m2/s, respectively.


Bioactive compounds Diffusion coefficient Equilibrium point Solid–liquid extraction 



Gallic acid equivalents


Total phenolic compounds


Total flavonoids


Total antioxidant capacity

List of symbols

\( A \)

Denotes product surface

\( C \)

Concentration of a given component in solution (g/l solution)

\( D \)

Apparent diffusivity (m2/s)

\( K \)

Equilibrium partition coefficient (kg solid/kg solution)

\( k_{c} \)

Convective mass transfer coefficient (m/s)

\( L \)

Characteristic length for diffusion (m)

\( {\mathbf{n}} \)

Normal unit vector

\( R \)

Solvent-to-product mass ratio (kg/kg)

\( X,\bar{X} \)

Mass fraction of a given component in product (kg/kg product): local and average, respectively

\( Y \)

Mass fraction of a given component in solution (kg/kg solution)

\( t \)

Time (s)

\( T \)

Temperature (°C)

\( V \)

Denotes product volume

\( z \)

Axial coordinate (m)

\( \Delta X \)

Extracted amount of a given component in product (kg/kg product)


\( e \)

At equilibrium

\( i \)

At the solid–liquid interphase

\( l \)

For liquid

\( s \)

For solid

Greek letters

\( \rho \)

Density (kg/m3)

\( \psi ,\varPsi \)

Dimensionless concentration: local and average, respectively



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Copyright information

© Association of Food Scientists & Technologists (India) 2019

Authors and Affiliations

  1. 1.Facultad de Ciencias QuímicasBenemérita Universidad Autónoma de PueblaPueblaMexico
  2. 2.Facultad de Ingeniería QuímicaBenemérita Universidad Autónoma de PueblaPueblaMexico

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