Estimation of diffusion and mass transfer coefficients for the microwave-assisted extraction of bioactive substances from Moringa oleifera leaves

In this study, microwave-assisted extraction (MAE) was applied to extract bioactive materials from leaves of Moringa oleifera. The current study was performed in order to clarify and understand the effects of extraction time, temperature, and power on the kinetics and thermodynamics of extraction, diffusion, and mass transfer coefficients and Biot number for the present system. One gram of Moringa oleifera particles with 80 mL solvent (60% ethanol) was extracted under different extraction temperature values (304, 305, 308, and 309 K) and microwave power values (200, 300, 400, and 500 W) for several time periods (30–400 s). According to the kinetic study, activation energy for the present MAE was calculated as 243.367 kj mol−1, where the extraction rate increased with temperature (0.0077, 0.0121, 0.022, and 0.0448 mL mg−1 s−1). Thermodynamic study produced the changes of enthalpy (31.572 kj mol−1), entropy (0.12817 kj mol−1), and Gibbs free energy (− 7.3917, − 7.5199, − 7.90434, and − 8.0325 kj mol−1), respectively. An empirical diffusion model was used for the estimation of diffusion coefficients, mass transfer coefficients, and Biot numbers depending on temperature. The diffusion coefficient (3.058 × 10-10, 3.114 × 10-10, 5.912 × 10-10, and 10.38 × 10-10 m2 s−1), mass transfer coefficient (0.2683, 0.4217, 0.7667, and 1.5613 m s−1), and Biot number (375 × 103, 578.9 × 103, 554.4 × 103, and 624.48 × 103) increased with increase in temperature.