Characterization and modeling of the polarization phenomenon to describe salt rejection by nanofiltration

Abstract

In this work, dead-end filtration was applied to the nanofiltration of synthetic ionic solutions. In order to study the phenomenon of polarization in the boundary layer, we chose NaCl, CaCl ₂ and Na ₂(SO ₄) solutions to pH = 6.8 which concentrations varies from 0.3 to 1.5 g L ⁻¹ and the filtration pressure varied from 6 to 16 bar. In this study, the results of these experiments show a correlation between the initial concentration of the solution and the pressure applied with the polarization. The polarization intensifies for the high concentrations and pressures. The ionic balance between the microscopic zone of polarization and the macroscopic state of the solution is described by the following key equation of the model:

$${\int }_{\delta (t)}^0(C(x,t)-C_o)\cdot v_x(t)=(C_r(t)-C_o)\cdot V_s(t)$$

The novelty of this model that it is sufficient to know the conductivity and volume flow of permeate solution to calculate precisely the polarization concentration at the membrane surface, the thickness of the polarization layer and the concentration profile inside the boundary layer polarization. It is important to note that the model developed does not take into account the clogging phenomenon because the experiments were done on low concentration synthetic ionic solutions.