Abstract
Purpose
A new approach was proposed to model the extraction kinetics according to the operating parameters. This approach is based on the determination of the critical time
t
c
(a characteristic time which depends on the operating parameters).
Methods
It is necessary to start by collecting the experimental values of
t
c
from experimental kinetics using the second derivation of extraction yield. Then, a full factorial design 2
3
is used to model
t
c
as function of studied factors: temperature, solid-liquid ratio and ultrasonic power. The obtained expression of
t
c
was used in second time as the basis of the modeling of extraction kinetics. It made possible to locate the inflection point that separates the two intervals of the extraction. To assure continuity in this point, we changed variable of time for the second phase of extraction and we started fitting from the last calculated point from the first phase. Seven models were tested to fit studied kinetics.
Results
A mathematical model was proposed to express
t
c
according to the operating parameters of the studied extraction. Patricelli (composed of two exponential terms) and the exponential models showed the best fitting results for all experiments. Patricelli model fitted very well the first phase of experiments and the exponential model fitted the second phase.
Conclusion
This confirms a new coupled washing/diffusion hypothesis of extraction performing in three steps: washing, first diffusion step, and second diffusion step.