Modelling the osmosis effect on solute migration through porous media

Abstract

In spite of an increasing number of publications that deal with the osmotic phenomenon that occurs within mineral barriers for pollutant control, the related models and their applications are not always correct, and they some times present inconsistencies between the initial assumptions and the results obtained. In order to investigate this topic thoroughly, a model has been proposed to describe the osmosis effect on solute migration within fine-grained porous media. This model is based on sound fundamental principles of thermodynamics, and complies with the basic physics postulates such as mass conservation and momentum balance. Its basic assumptions are incompressibility of the solid skeleton and the solvent, and infinite dilution of the solute. The osmotic phenomenon has been considered together with advective and diffusive one-dimensional transport of a bulk electrically neutral or uncharged solute under isothermal conditions, and the material constants of the governing differential equations are linked to the well-known parameters used in current geotechnical and chemical engineering practice. Therefore the proposed model can easily be used to assess the influence of the osmotic efficiency (ω) on the performances of mineral barriers for subsoil pollutant control, referring in particular to geosynthetic clay liners (GCL), whose behaviour, at low solute concentrations, can be considered very close to that of an ideal semi-permeable membrane. The proposed model has been tested using limit values of the input parameters in order to verify its consistency in terms of the physical meaning of the related outputs. The proposed theoretical approach has also been used to re-interpret some experimental data taken from specialised literature. The interpretation of the results, in terms of osmotic efficiency (ω), effective solute porosity (n*), bulk diffusion coefficient (D) and tortuosity factor (τ), seems to be intrinsically consistent and reliable. Nevertheless, the encouraging results of the proposed model require further ad hoc experimental tests in the laboratory before its definitive validation and calibration.