Localized Electroconvection at Ion-Exchange Membranes with Heterogeneous Surface Charge


 Operating electrochemical membrane processes beyond the limiting current density bears the potential to decrease the investment cost of desalination plants significantly. However, while there are strategies for successfully reducing energy demand by shortening the plateau region, their influence on the formation of electroconvection is still unknown.

This study demonstrates control over the electroconvective vortices' rotational direction and position using a surface patterning method. We compare the development of electroconvection at two membranes modified with patterns of different surface charges. We analyze the electroconvective vortex field's build-up, the vortices' rotational direction, and structural stability in the steady-state. Finally, we showcase the control possibilities by enforcing a specific structure along an asymmetric letter pattern. Such tailor-made patterns have the potential to diminish the plateau region's energy loss completely. Furthermore, the scale-up of these membranes to industrial processes will allow the economic operation in the overlimiting regime, significantly increasing their space-time yield.

The operation range of electrically driven membrane processes like electrodialysis (ED), capac-2 itive deionization (CDI), and flow-capacitive deionization (FCDI) is limited by the fluid-sided 3 resistance evolving during operation at high driving force [1]. In these processes, ions are trans-4 ported through charge-selective membranes by an electric field. The ion flow, measured as a 5 current density, increases linearly with increasing driving force in terms of an electric poten- 6 tial between two electrodes. However, the current increase is disrupted by a diffusion-limited 7 plateau region (see Fig. 1 a)) [1]. Today, it is known that a significant share of the current 8 increase is due to a hydrodynamic instability called electroconvection (EC). EC overcomes the 9 Figure 1: Current density over potential graph for a homogeneous and heterogeneous membrane and difference in electric field lines. a) Sketch of the current density over potential graph for an electrically driven membrane process with a homogeneous (solid line) or heterogeneous (dashed line) membrane. For both cases, three distinct regimes appear with a difference in the limiting current density i lim . b) Electric field lines at a homogeneous and heterogeneous membrane surface. limiting current density due to the formation of convective 3D vortices, recently quantified by 10 Stockmeier et al. [2], which mix the depleted layer close to the membrane. In fact, EC balances 11 with unwanted water splitting and a maximum contribution of EC to the overlimiting current 12 density is desired [3].

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The possibility to evoke and intensify EC also at low driving forces has been the focus of 15 multiple studies [4][5][6][7][8][9][10][11][12][13]. In general, the limiting current density and the length of the plateau re-16 gion have been found to depend on the ion concentration, distance between the bulk electrolyte 17 and membrane (i.e., the laminar boundary layer), and membrane characteristics like surface 18 heterogeneity [1]. A heterogeneous membrane surface causes a disturbance of the electrical field 19 lines close to the membrane, which, in turn, triggers EC, see Fig. 1 b). As a result, the plateau 20 is shortened. The results of Roghmans et al. [11] suggest that EC even emerges in the ohmic 21 region at their pattern structure, increasing the limiting current density. 22 Modifying membranes as a means to control surface heterogeneity has gained increasing 23 interest in the literature. Various studies focused on heterogeneity in surface geometry, con-24 ductivity, hydrophobicity, and zeta potential. It has been shown that these four parameters, in  Recently, we presented a method to simultaneously engineer the surface geometry, conductiv-51 ity, and charge of membrane surfaces in a controlled manner [11]. An ink-jet printing technique 52 was used to apply a pattern of circular patches of polymer microgels with varying zeta po-53 tential. Such modified membranes were found to double the limiting current density with a 54 40% reduced plateau length and only slightly increased membrane resistance. The hypothesis 55 behind this successful modification was a combination of an early start of EC even at limiting 56 current densities, the ion conductivity of the pattern, an altered rotational direction due to the  The examples mentioned above show the vast potential that engineered ion-exchange mem-61 branes with tailored surface properties possess to increase the efficiency of electrically driven 62 membrane processes. However, the physics behind the current density increase, especially of 63 Roghmans et al.'s multi-influential microgel patterns, are still unclear. Therefore, the EC vor-64 tex field structure at such patterns needs to be analyzed, isolating important properties for 65 future membrane modifications.

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In this paper, we evaluate the effect of patterning a cation-exchange membrane surface, with   The simulations with patches both show a shortened plateau region that ends at 15 V t .

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The overlimiting current region starts at 17.5 V t . However, the graphs do not steadily increase. The images in Fig. 2 c) show the steady-state of simulations at 20 V t for all three cases.     Fig. 4 a) and c) show two Nafion membranes patterned with P2VP microgels with a 400 µm 188 diameter and a 600 µm diameter, respectively.

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The vortex field reconstruction of the experiments at both membranes is shown in Fig. 4 b) 190 and d). In both images, coherent vortex rings emerge that resemble the patterns.  ingly, the vortices also resemble the slight imperfections in the pattern for the 400 µm case.

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The rotation of the vortex rings is directed towards the patches as in the experiments at lower 193 magnification with larger particles, see Fig. 3.

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The results show that the patches enforce their structure on EC's build-up in its development  These results prove that the P2VP microgel pattern enforces the build-up of vortex pairs at 208 the structure, completely resembling its shape. The emergence of strong EC vortices only at 209 the structure also shows that a P2VP pattern structure leads to a faster EC build-up. It also 210 gives additional proof that vortices move towards P2VP-coated surfaces.  the ion transport will also decrease. Additionally, the modification method is easily upscalable 236 to cover larger membrane areas. Further progress will enable efficient use of the overlimiting 237 current region in industrial-scale processes leading to decreased material and investment costs.
where c i is the concentration, D = D + = D − = 1 × 10 −9 m 2 s −1 is the diffusion coefficient.   The cathode has a circular hole (d = 9 mm) which is sealed by a glass slide glued on top. The 319 electrolyte (1 mM CuSO 4 ) is filled in the electrolyte chambers above and below the membrane.

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The bottom chamber's height matches the microscope's maximum focal depth of L z = 0.8 mm.

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The diameter of the chamber of 8 mm results in a large aspect ratio of 10, which is desired to The bulk concentration c B is approximated with a linear gradient between electrode and

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In post-processing, the implemented VIC# method is used for transforming the particle