Interaction between the electric and concentration fields in the fractionation of two macromolecules using a Hybrid Membrane Cell – CFD study

The numerical study of membrane separation processes with electric interactions requires the simultaneous solution of Poisson-Boltzmann, Navier-Stokes and Nernst-Planck equations. A numerical method was developed, and implemented, to deal with the coupling between the electric field, the flow field and the concentration fields of the ionic species in solution. The numerical method was validated supposing limit conditions: a-for a binary ionic solution, the results are similar to those obtained with a simplified method which assumes the Boltzmann distribution of the ionic species; b-for high molecular diffusivity of the components, the convection is negligible, relatively to the diffusion, and the numerical solution is similar to the one obtained for a stagnant fluid. The numerical code developed was applied to study macromolecules fractionation in a hybrid membrane cell (HMC) composed by negatively charged semi-permeable membranes (impermeable to the solutes and permeable to the solvent) and neutral fully-permeable membranes, alternating in series. The normalized concentration profiles of the species along the normal and tangential directions were obtained, as well as the non-dimensional electric potential along the normal direction. When the charge of the semipermeable membrane is identical to the charge of the component with the highest diffusivity, this component moves away from the membrane and the other, with the lowest diffusivity, approaches the membrane. However, due to the interactions between electric and concentration fields, in the region crossed by the streamlines of the concentrate stream, the separation in the fully permeable membranes is worsened.