Mathematical Modeling of the Effect of Pulsed Electric Field Mode and Solution Flow Rate on Protein Fouling during Bipolar Membrane Electroacidificaiton of Caseinate Solution

Abstract

A one-dimensional non-stationary model was developed for a better understanding of the protein fouling formation mechanism during electroacidification of caseinate solution using electrodialysis with bipolar membranes (EDBM) in pulsed electric field (PEF) mode. Four different PEF modes were investigated with pulse–pause durations of 10 s–10 s, 10 s–20 s, 10 s–33 s, 10 s–50 s. For each current mode 3 different flow rates were considered, corresponding to Reynolds numbers, Re, equal to 187, 374 and 560. The processes are considered in the diffusion boundary layer between the surface of the cation-exchange layer of bipolar membrane and bulk solution of the desalination compartment. The Nernst–Planck and material balance equation systems describe the ion transport. The electroneutrality condition and equilibrium chemical reactions are taken into account. The calculation results using the developed model are in qualitative agreement with the experimental data obtained during the previous experimental part of the study. It is confirmed that both the electrical PEF mode and the flow rate have a significant effect on the thickness (and mass) of the protein fouling during EDBM. Moreover, the choice of the electric current mode has the main impact on the fouling formation rate; an increase in the PEF pause duration leads to a decrease in the amount of fouling. It was shown that an increase in the PEF pause duration from 10 s to 50 s, in combination with an increase in Reynolds number (the flow rate) from 187 to 560, makes it possible to reduce synergistically the mass of protein deposits from 6 to 1.3 mg/cm2, which corresponds to a 78% decrease.