Understanding of the current density distribution over an electrically heterogeneous surface and its effect on ion transport represents an important issue in electrochemistry, composite materials, geophysics, and some other domains. We report an approach for three-dimensional (3D) modeling (with cylindrical symmetry) of transient ion transfer across a surface composed of conductive and nonconductive areas. In the model formulation and solution we use the electrical current stream function. It allows setting the integral boundary condition for electric current at a heterogeneous surface without any restrictions on the local current density distribution. A very good agreement is found between the numerical solution and the experimental transition time determined from chronopotentiograms. The use of a specially designed membrane allows computation without fitted parameters. We show that the application of specific simplifications for the current density distribution over the surface (uniform distribution throughout all the surface or its conductive area, neglect of tangential current density) results in essential deviations from experimental transition time.
The efficiency of separation processes using ion exchange membranes (IEMs), especially in the food industry, is significantly limited by the fouling phenomenon, which is the process of the attachment and growth of certain species on the surface and inside the membrane. Pulsed electric field (PEF) mode, which consists in the application of constant current density pulses during a fixed time (Ton) alternated with pause lapses (Toff), has a positive antifouling impact. The aim of this study was to investigate the combined effect of three different relatively high flow rates of feed solution (corresponding to Reynolds numbers of 187, 374 and 560) and various pulse–pause ratios of PEF current regime on protein fouling kinetics during electrodialysis with bipolar membranes (EDBM) of a model caseinate solution. Four different pulse/pause regimes (with Ton/Toff ratios equal to 10 s/10 s, 10 s/20 s, 10 s/33 s and 10 s/50 s) during electrodialysis (ED) treatment were evaluated at a current density of 5 mA/cm2. It was found that increasing the pause duration and caseinate solution flow rate had a positive impact on the minimization of protein fouling occurring on the cationic surface of the bipolar membrane (BPM) during the EDBM. Both a long pause and high flow rate contribute to a more effective decrease in the concentration of protons and caseinate anions at the BPM surface: a very good membrane performance was achieved with 50 s of pause duration of PEF and a flow rate corresponding to Re = 374. A further increase in PEF pause duration (above 50 s) or flow rate (above Re = 374) did not lead to a significant decrease in the amount of fouling.
Fouling is one of the major problems in electrodialysis. The aim of the present work was to investigate the effect of five different solution flow rates (corresponding to Reynolds numbers of 162, 242, 323, 404 and 485) combined with the use of pulsed electric field (PEF) current mode on protein fouling of bipolar membrane (BPM) during electrodialysis with bipolar membranes (EDBM) of skim milk. The application of PEF prevented the fouling formation by proteins on the cationic interface of the BPM almost completely, regardless of the flow rate or Reynolds number. Indeed, under PEF mode of current the weight of protein fouling was negligible in comparison with CC current mode (0.07 ± 0.08 mg/cm2 versus 5.56 ± 2.40 mg/cm2). When a continuous current (CC) mode was applied, Reynolds number equals or higher than 323 corresponded to a minimal value of protein fouling of BPM. This positive effect of both increasing the flow rate and using PEF is due to the facts that during pauses, the solution flow flushes the accumulated protein from the membrane while in the same time there is a decrease in concentration polarization (CP) and consequently decrease in H+ generation at the cationic interface of the BPM, minimizing fouling formation and accumulation.
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