ABSTRACT
The present study provides the first data on the extraction kinetics of polyphenols from algerian Inula viscosa and aims to model the phenomenon of matter transfer involved.
Different models have been applied and evaluated for different conditions of temperature, solid to liquid ratio and stirring speed. The operating conditions affect the kinetic parameters as well as the mass transfer properties.
The diffusion coefficient values ranged from 2.25*10−12 to 31.44*10−12 m2.s−1. The Biot number vary from 45.37 to 92.35 which shows that internal mass transfer limits the extraction process. Activation energy (Ea) was found to be 25.22 KJ .mol−1.
Nomenclature
a | = | Sphere radius |
ap | = | Specific surface area (m2.m−3) |
b | = | Dimensionless constant |
C(eq) | = | Equilibrium concentration |
Cl | = | The liquid phase concentration |
Cs | = | The solid phase concentration |
C(t) | = | Concentration at time t |
C(∞) | = | Concentration at t →∞ |
= | The equilibrium concentration for the diffusion part (g.L−1) | |
= | The equilibrium concentration for the washing portion (g.L−1) | |
cal | = | Calculation |
D | = | Diffusion coefficient (m2.s−1) |
Deff | = | The effective diffusion coefficient (m2.s−1) |
Ds | = | Coefficient of diffusion in the solid phase (m2.s−1) |
DWM | = | Dry weight material (g) |
D0 | = | the Arrhenius constant (m2.s−1). |
Ea | = | The activation energy (J.mol−1) |
exp | = | Experience |
F | = | The fraction of the rapidly released solute |
(1-F) | = | The fraction of the solute released slowly |
GAE | = | Gallic acid equivalent |
H | = | Hydromodule (volume of solvent/mass of plant matter)(g.L−1) |
k | = | The rate constant |
k1 | = | The first order rate constant describing the fast part (min−1) |
k2 | = | The first order rate constant describing the slow release fraction (min−1). |
Ke | = | External mass transfer coefficient (m.min−1) |
Kd | = | The diffusion rate constant (s−1) |
Ke * ap | = | Mass volumetric mass transfer coefficient (min−1) |
KD | = | Partitioning equilibrium = C solute (solid)/C solute (liquid) |
K | = | Transport coefficient (m.s−1) |
L | = | Mass transfer biot number |
M(t) | = | Mass at time t (g) |
M(∞) | = | Mass at t →∞ (g) |
NRMSD | = | Normalized root mean square deviation = |
R | = | Ideal gas constant (J.K−1.mol−1) |
= | washing diffusion model initial extraction rate | |
R2 | = | Determination coefficient |
RMSE | = | root mean square error = |
SSE | = | sum square error = |
t | = | time |
t1/2 | = | The half-life (s) |
x | = | the distance in the direction of diffusion |
ycal | = | calculated yield |
ycal max | = | maximum calculated yield |
yexp | = | experimental yield |
Acknowledgements
The authors gratefully acknowledge the Chemical Engineering Department (Algiers, Ecole Nationale Polytechnique) for their funding of this project, Mr Kamel Mezieche for providing the Inula viscosa samples and for language revision.