Hybrid Fickian-Darcian flow model for high pressure impregnation of fluids into porous biomaterials

Pressure-driven fluid flow is an inevitable consequence which occurs during the high pressure processing of porous biological materials confined in a fluid phase. A hybrid numerical model was adopted to simulate the mass flow of fluids into an enclosed biological porous matrix under constant high hydrostatic pressure treatments. The numerical model was based on the finite element simulation of time-dependent Fickian mass transfer represented as saturation rate of fluid flow in the unsaturated media. The Kozeny-Carman model was used for correction of relative permeability because of the pressure-induced textural changes. As a case study, the proposed methodology was applied to simulate the high pressure impregnation of apple cubes by ascorbic acid solution (1% by mass). The proposed model demonstrated the existence of a low-pressure zone in the geometrical centre of the computational domain associated with the operating pressure level which provides a sufficient driving force for liquid migration. The numerical results were corroborated through implementing gravimetric and image processing experiments. Finally, a linear flow front rate of 0.03 cm s−1 was estimated along the porous matrix, and the analytical solutions to the Darcian model were used to determine the lumped permeability as a function of pressure difference at the impregnation flow front.