| To optimise the extraction parameters, a kinetic approach developed during a previous research was adopted. This approach, based on the Fick’s law, uses the following exponential equation to describe the evolution of extracted carotenoids over time (t):
where: Ce = grams of carotenoids extracted at a random time t per gram of biomass submitted to the extraction (adimensional); H* = adimensional constant, ranging from 0 to 1, related to the equilibrium constant H (H* = H/(H+1)); [Cs] = carotenoidic concentration in starting lyophilised material (adimensional); k = kinetic constant (s-1).
The extraction rate (R) calculated as first derivative of the equation 1:
reaches its maximum value (Rmax) at the beginning of extraction, when t is close to 0:
The value of Rmax (s-1) was assumed as an index to evaluate the efficiency of the extraction system versus the carotenoidic fraction. In particular, while the constant k (s-1) gives information on the kinetics of the process, the adimensional product H*×[Cs], representing the asymptotic value of the extraction curve when t ® ¥, measures the maximum amount of carotenoids extractable in the working conditions adopted. In presence of a highly efficient extraction process, H* tends to 1 and therefore the maximum amount of carotenoids extractable per unit of biomass is equal to their concentration in the starting material.
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