On One Mathematical Model of the Extraction Process of Polydisperse Porous Material

Abstract

We consider a mathematical model which represents the extraction process of a target component from the polydispersed porous material. The suggested model is demonstrated by the example of a at solid material with bidispersed pores of dierent size in the form of a system of channels of macropores with micropores facing their walls. The macropores and the micropores in the material have homogeneous size. We model a case when micropores of the solid material (dispersed medium) are initially lled with an oil (dispersion phase), which is our target component. The macropores are lled in with a pure solvent. In the process of extraction the oil diuses from the micropore to the macropore, and then from the micropores to the external solvent volume, wherein the ratio of concentrations in the macropore and the micropore is taken in accordance with the linear law of adsorption. The well-posedness of the formulated mathematical model has been justied.