Mathematical Modeling of Concentration Dependences of Electric Conductivity and Diffusion Permeability of Anion-Exchange Membranes Soaked in Wine

The formation of organic colloidal particles in the pores and on the surface (fouling) of membranes used in the food industry is a significant constraint on the further development of membrane technology. A model to describe the effect of these particles on electric conductivity and diffusion permeability has been proposed. It is based on a microheterogeneous two-phase model constructed in terms of the concepts of nonequilibrium thermodynamics and effective medium theory. The model takes into account the presence of two phases: (i) the gel phase comprising a polymer matrix and fixed ions whose charge is compensated for by mobile ions and (ii) the electrically neutral solution filling the intergel spaces. Each of the phases is characterized by intrinsic thermodynamic and kinetic parameters. The model takes into account changes in the values of these parameters caused by the formation of organic nanoparticles in meso-and macropores (fouling). It is assumed that the formation of colloidal particles in the intergel solution leads to a decrease in the ion mobility. In addition, these particles are capable of deprotonating a portion of the fixed ions and thereby decreasing the exchange capacity of the membrane. A high degree of hydration of these particles is responsible for an increase in the volume fraction of intergel spaces. Selection of relevant model parameters provides good agreement between calculation and experimental results.