Mass transfer modeling

The SFE process from natural materials generally involves the releasing of solutes from a porous biological matrix into the supercritical solvent via internal and external mass transfer mechanisms. The first part of the extraction, the CER period, is governed by the solubility equilibrium between the CO2 solvent and extract. Once the easily accessible surface extracts are depleted, molecular DC mass transfer occurs and an FER period is seen. Eventually, diffusion of the extracts through the bulk material becomes a more integral part of the extraction process and the accumulation product over time approaches zero (Perakis et al., 2005; Esquivel et al., 1999; Reverchon et al., 2002). Different mathematical aspects related to SFE have resulted in multiple variables and complex equations being derived to model the SFE process. Many models have been proposed; yet, no single model has been universally accepted (Reis-Vasco et al., 2000; Revererchon et al., 2000; Sousa et al., 2005; Sovova, 2005).

Molecular diffusion (Fick's law)

Fick's second law of diffusion defines the molecular diffusion flux of a component with respect to the concentration gradient for a binary mixture. It states that flux is proportional to the concentration gradient and that diffusion of a compound occurs in the direction of decreasing concentration (Mukhopadhyaya, 2000). Fick's second law for a spherical geometry is given as dC = Dfd^C + 2dC) [10.5]

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