Моделювання процесу екстрагування речовини у системі: тверде тіло–рідина

Abstract

The paper reports the basic principles of modeling of extraction process through the cell walls. A solid body is assumed to be an aggregate of deformable particles, inside of which there is an extractable substance. Two stages of the process are considered: diffusion and hydrodynamic ones. The mass exchange stage inside the solid is diffusive because it has not fluidity. As far as the diffusion stage is concerned, we propose to consider the process of internal transfer as a set of pseudocatalytic reactions between the solvent molecules and the extractable substance. Based on this approach, the relationship between the diffusion coefficient and the particles structure hasbeen derived under the condition of a cellular structure of the particles. The equations for describing the time change of the mean concentrations of a substance are given, taking into account the effect of the external mass discharge condition at interphase boundaries. It has been proved that the applied approach makes it possible to find a sufficient number of parameters for describing the different effects of extraction and gives physical meaning to interpretations of kinetic curves of extraction. As regards the hydrodynamic stage, a proper frame model of the pore space was formulated, which is deterministic and two-scale. It takes into account possible shear and volume deformations of the particles. Such two-phase medium was considered as a collection of variable intensity sources. The equations for calculating the mass transfer coefficient for the system are solid particles–liquid, taking into account the rheology of the liquid phase as a mixture of extractant and extractable substance. It has been proved that the proposed models have sufficient universality to withstand adaptation to different specific situations.