Mass transfer in
 3D
 ‐printed electrolyzers: The importance of inlet effects

This paper investigates the effect of inlet shape, entrance length and turbulence promoters on mass transfer by using 3D printed electrolyzers. Our results show that the inlet design can promote turbulence and lead to an earlier transition to turbulent flow. The Reynolds number at which the transition occurs can be predicted by the ratio of the cross-sectional area of the inlet to the cross-sectional area of the electrolyzer channel. A longer entrance length results in more laminar behavior and a later transition to turbulent flow. With an entrance length of 550mm, the inlet design did no longer affect the mass transfer performance significantly. The addition of gyroid type turbulence promoters resulted in a factor 2 to 4 increase in mass transfer depending on inlet design, entrance length and the type of promoter. From one configuration to another, there was a minimal variation in pressure drop (<16 mbar).


| INTRODUCTION
In recent years, a renewed interest in electrolyzers has emerged. They are expected to play a pivotal role in enabling the ongoing global energy transition, as they are able to directly convert electricity into chemical energy. Moreover, the process can be done cleanly if green energy is used, thereby opening up the way to a sustainable chemical industry.
A key property of an electrolyzer is its mass transfer performance.
A high mass transfer performance indicates that the reactants can quickly reach the electrode, in this way enabling faster reactions and higher currents. Typically, mass transfer is expressed as a Sherwood-Reynolds correlation. In the past decades, many such correlations have been established, [1][2][3][4][5] but there is a large variance in the reported mass transfer performance. For empty parallel plate electrolyzers, the difference can be up to an order of magnitude depending on the configuration and specific design choices that were used, such as the design of the inlet. 1 In literature, several CFD studies are available that investigate these effects. 6,7 However, the comparison of results between reactors remains complicated. Moreover, the importance of certain mass transfer enhancing effects depends on the scale. Smallscale electrolyzers for instance will be affected more by inlet effects than large-scale cells. Therefore, when results from a small cell are extrapolated to a larger electrolyzer, significantly overestimations or underestimations can occur if these scaling effects are not considered.
In order to increase our understanding of mass transfer in electrolyzers more configurations need to be tested. Therein lies another complication since most of the cells described in the literature were built in-house or produced decades ago, resulting in them no longer being available for present-day research. For new research, it can therefore be difficult to find a suitable cell with known mass transfer behavior. Building new ones is not straightforward either, as it requires design work and complex machining. A solution to this problem is to 3D print electrolyzers, as it allows the quick construction of numerous prototypes.
The purpose of this work is to carry out a systematic investigation into electrolyzer mass transfer performance. 3D printed parallel plate electrolyzers are used to investigate the effects of different inlet designs, inlet lengths, and turbulence promoters and results are compared to previous work.

| Measuring mass transfer
The limiting current density method is often used to determine the mass transfer performance of electrolyzers. 8,9 Typically, this involves reversible redox couples such as hexacyanoferrate or hexachloroiridate, for which the rate of reaction is limited by mass transfer at sufficient overpotential. [10][11][12] The limiting current is related to the Sherwood number as shown in Equation (1).
To understand how mass transfer occurs in electrolyzers it is important to realize that there are two different boundary layers (see Figure 1). The first is the hydrodynamic boundary layer, which is the region where the velocity of the flow is lower due to friction with the wall. The second is the diffusive boundary layer, which is where the concentration of reactant species is lower due to the reaction at the electrode surface. In liquids, the diffusive boundary layer is much thin- 3. Hydrodynamically and diffusively developed flow.
Situation A is most common in electrolyzers, where the electrode typically starts directly after the inlet. Situation B occurs when a certain entrance length without electrodes is used in which the flow is allowed to develop before reaching the electrodes. Situation C only occurs after a certain length of electrode and can therefore only be seen in the downstream segments of a segmented electrode.
The distance required for a flow to reach fully developed conditions is known as the hydrodynamic entrance length. More specifically, it is defined as the length needed for the centerline velocity to reach 99% of its fully developed value. In laminar flow, the entrance length depends on the Reynolds number as shown in Equation (2).
where Φ is a parameter that depends on the geometry. For a rectangular channel, it is nonlinearly dependent on the aspect ratio of the cross-section γ 0 . 13 Table 1 lists the six values Han established. 13 To obtain fully developed turbulent flow, a hydrodynamic entrance length is required that is 50 hydraulic diameters d H long, regardless of the flow rate. 14 In Figure 2 the current in a typical mass transfer experiment is shown. In such an experiment, the flow is turned on prior to the potential, giving the hydrodynamic boundary layer time to develop. When the potential is applied (at t = 0), a current appears and quickly trends toward a stable value that is determined by the thickness of the diffusive boundary layer. The high initial current is due to the development of this layer.
At most flow rates, the reaction is fully limited by mass transfer from the bulk after at most 7 seconds. At low flow rates 20 and 30 dm 3 /h, it takes several seconds longer for the diffusive boundary layer to develop. This is because at lower flow rates the diffusive boundary layer is thicker and therefore there is more reactant present in this layer.

| Mass transfer in hydrodynamically developed flow
In a perfectly laminar flow, with a perfectly hydrodynamically developed flow, the mass transfer coefficient between parallel plates in a rectangular channel can be described by a theoretical Leveque-type equation, Equation (3a). 14 Here, γ is the aspect ratio of the electrode: B/L. In the work of Ong and Picket no significant effect has been found of the developing diffusive layer on the rate of mass transfer in laminar flow. As a consequence, Equation (3a) is valid for both short and long electrodes. 14 externally. In the former case, a Makergear M3-ID or a Prusa MK3S was used. In both printers, PETG was extruded during the fused filament fabrication process. In the latter case, parts were ordered from the 3D printing company ZiggZagg, who used the multi jet fusion of Nylon. The gaskets were printed in-house using TPU filament Ninjatek-Ninjaflex and the Makergear M3-ID. The electrolyzer is shown in Figure 3 and consisted of exchangeable inlets and electrode assemblies. In Table 2 the characteristic dimensions of the electrolyzer are shown. The electrode assembly was built by affixing a 100 × 50 mm 2 nickel plate to a printed substrate using epoxy resin.
The electrical connection was provided by two wires soldered to the backside of the nickel plate on one end, and 2 banana plugs on the other end.
For the 3D-printed electrolyzer, three different inlets were used in this work: a tube inlet, a conic inlet, and a divider inlet (see   18 A list of the electrolyte properties is available in Table 3.
Before the experiments, the electrodes were pretreated following the recommendations of Szanto et al. 11 The procedure consisted of polishing the electrodes using felt paper and a descending series of Chronoamperometry experiments were performed in order to determine the limiting current density. The procedure was as follows: First, the gear pump was set in motion to produce the desired flow rate. Then, a cell potential of −0.8 V was applied and a waiting time of at least 7 seconds was implemented in order to reach a steady state situation. The limiting current was determined from the average of 30 data points measured over a period of 3 seconds after the current had stabilized.
In our work we record all current data after 7 seconds. Since for low flow rates (see Figure 2) the current has not always completely stabilized after 7 seconds, the Sherwood numbers obtained at lower flow rates (and hence lower Reynolds numbers) may be overestimated slightly in our work.

| 3D-printed electrolyzer with different inlets
To systematically investigate inlet effects, we developed a modular 3D-printed electrolyzer with exchangeable inlets. Three types of inlets were used: a conic inlet, a tube inlet and a divider type inlet (shown in F I G U R E 7 Schematic of the setup. From the electrolyte vessel the electrolyte is pumped by a gear pump through a flow meter and inline UV VIS sensor to the electrolyzer. Right before and after the electrolyzer a T-piece connects to the U-tube in order to measure the differential pressure. The electrolyte vessel is bubbled with nitrogen, and any excess gas is allowed to escape through a waterlock, which prevents backmixing of air The likely reason for this is that the current at low flow rates is not fully stabilized, as shown in Figure 2. The effect likely also contributes to the higher performance in Equation (6)  In our case, the tube inlet has an area ratio of 0.07. The divider inlet is a series of slits, with the ratio of the area of all openings to the channel being 0.52. The conic inlet ends in the same cross-sectional area as the channel, which implies that the ratio is 1.0. Using these values,

Equation ((7) results in a good prediction for the divider inlet at
Re > 500 (max deviation <8%) and to a lesser extent the tube inlet (max deviation <18%). On the other hand, for the conic inlet the prediction appears to be inaccurate. This is because the ratio of 1.0 implies that there is no expansion, but expansion is occurring in the inlet. Therefore, we used the geometric mean to determine the ratio:   [5]. Here we report the latter.
By finding the intersect of the laminar and turbulent correlations, the Reynolds number at which the transition occurs Re t can be determined. When combined, and solved for Re, Equations (6) and ((7) lead to Equation (8), which gives Re t as a function of the cross-sectional area ratio of the inlet to the channel.

Re t = 925
A in A ch Equation (8) predicts that the flow transition occurs at Re t = 223 for the conic inlet, Re t = 463 for the divider inlet and Re t = 56 for the tube inlet. The transition for the conic and divider inlet are observed in Figure (9). For the tube inlet Re t is near the first datapoint of the graph and therefore the transition cannot be seen.
When A in /A ch = 1, no expansion takes place and Re t = 925. This is far earlier than expected from the work of Ong and Pickett,14,17 possibly due to the imperfections in the printed parts and the assembly thereof.

| 3D-printed electrolyzer with different entrance lengths
In Figure 10 the effect on mass transfer of adding a calming section between the inlet and the electrolyzer is shown. When no calming section is used, the type of inlet is important as the turbulence generated by it greatly enhances mass transfer. By adding a calming section, this effect is diminished and for a calming section of 550 mm the type of inlet no longer seems to matter. According to Equation (5a) and (5b) the laminar entrance length is 240 mm at the highest Reynolds number measured (Re = 1200). Therefore, it makes sense that an inlet well beyond this distance would no longer influence the mass transfer to the electrodes. Furthermore, the divider type inlet seems to perform similar at any length of calming section.
This implies that a good inlet design can enable hydrodynamically fully developed laminar flow.
Despite using a 550 mm long calming section, our correlations still do not completely match the hydrodynamically fully developed F I G U R E 8 Sherwood-Reynolds plot of the correlations shown in Table 4. Lines in this graph denote literature correlations within their respective Reynolds ranges. Except for the developed flow correlation, all correlations were plotted using the geometric parameters given for the electrolyzer the correlation was established with. For the developed flow correlation, the geometric data of the printed electrolyzer used in this work was used. This was done to offer a comparison between our experimental data and the developed flow prediction. The circle, triangle, and diamond markers are experimental data obtained with the 3D-printed electrolyzer whose correlations are shown in Table 6. Electrolyte data are available in Table 3. The dashed box (extending from the origin to Sh = 400 and Re = 2000) marks the region of this graph that is used for Figure 9 [Color figure can be viewed at wileyonlinelibrary.com] laminar flow correlation established by Ong at Reynolds numbers below 500. As previously mentioned, an overestimation of mass transfer occurs at low Reynolds numbers, since the current is not fully stabilized after 7 seconds. Apart from this effect, additional experimental error is expected due to the limitations of 3D printing. A first limitation is that due to the print process imperfections may be introduced into the channel wall. These imperfections lead to increased surface roughness, which may result in higher mass transfer and an earlier transition to the turbulent regime. Second, because the longest dimension of a print is limited to around 200 mm, the assembly consists out of multiple smaller parts with joints between them. At these joints, minor protrusions may exist that can introduce turbulence.

| 3D-printed electrolyzer with turbulence promoters
Often, turbulence promoters are added to parallel plate electrolyzers in order to enhance mass transfer. 1,5 This degree of mass transfer F I G U R E 9 Sherwood-Reynolds plot of the experimental data obtained with the shortest empty channel printed electrolyzer. A divider inlet (Diamonds), conic inlet (Triangles), and tube inlet (Circles) were measured. The full line is the correlation for hydrodynamically developed laminar flow shown in Table 4 and Equation (3a). Electrolyte data are available in Table 3 [  Table 4 and Equation (2). Electrolyte data are available in Table 3 [Color figure can be viewed at wileyonlinelibrary.com] enhancement is also widely seen in literature. 2,4,5,19,21,23,25 However, the opposite is observed in the work of Frías-Ferrer et al, 22 where the turbulence promoter reduces mass transfer. The difference is probably due to the design of the inlet device: the electrolyzer used by

| Pressure drop in the printed cell
The pressure drop of the 3D-printed electrolyzer without turbulence promoters was small and varied between 2600 ± 200 Pa and 3800 ± 200 Pa at Reynolds 1000 depending on the configuration (see also Figure S1).
The highest pressure drop was found for the tube inlet, the lowest for the divider inlet. Since these differences are small, it is likely that their accuracy is strongly affected by the imperfections in the print and the gasket joints between components of the cell. Furthermore, because the pressure drop was measured across the entire electrolyzer, it may be possible that factors such as the placement of the external tubing or the tightness of the fittings lead to further inaccuracy. Turbulence promoters did not significantly affect the pressure drop. For the divider inlet without calming section, the pressure drop at Reynolds 1000 was 2700 ± 200 Pa for every promoter (see also Figure S2). In the cell with divider inlet and a

| CONCLUSION
The different design choices made in the construction of an electrolyzer greatly affect the mass transfer performance. Between the electrolyzers found in literature, up to a factor 10 difference is observed (see Figure 8).
This variation is the result of several different geometric design choices in the electrolyzer. Using a 3D-printed electrolyzer, we were able to investigate the effect of some of these choices.
F I G U R E 1 1 Effect of turbulence promoters on mass transfer, without (on the left) and with (on the right) a 150 mm long calming section. The divider inlet was used in each case. Electrolyte data are available in  20 This correlation uses the ratio of cross-sectional area of the inlet and channel as parameter to predict the magnitude of expansion turbulence. In the conic inlet, the cross-sectional area varies throughout the inlet and this was accounted for by using the geometric mean cross-sectional area. The correlation deviated from the experimental results by <18% for the tube inlet, <8% for the divider inlet, and < 6% for the conic inlet.
The addition of a calming section minimized these effects. With a calming section of 550 mm, the type of inlet no longer seemed to affect the rate of mass transfer. This length is over twice the predicted hydrodynamic entrance length of 240 mm at Re = 1200 (based on Equation (5)). Therefore, it is reasonable to assume that the flow is fully developed and that the inlets no longer matter. Despite this, our results did not completely match the correlations for hydrodynami- with an entrance length a larger variance in performance was found.
Inlet turbulence therefore greatly influences the effect of a turbulence promoter.
The pressure drop was measured for the different configurations of inlet length, inlet type, and turbulence promoters. Overall, only very small differences between each configuration were observed (in the order of 100 Pa). Though the difference is marginal, it appears that higher pressure drops result in higher mass transfer rates.
Mass transfer in electrolyzers can be significantly enhanced by turbulence promoters or turbulence causing inlets. The added pressure drop for these is minimal, which implies that large performance increases can be achieved for little extra pumping costs. However, due diligence must be taken in extrapolating results from the lab-scale to the industrial scale.
Since the importance of the inlet effect diminishes as the electrolyzer scales up, mass transfer may be slower than expected from the lab-scale.
As we have shown, a good inlet design or a calming section can reduce inlet turbulence in smaller electrolyzers, so that they are more representative of their larger counterparts.

ACKNOWLEDGMENTS
This project has received funding from Nouryon as part of the HIGHSINC project. We thank Nouryon for their contributions. We thank A.W. Vreman (Nouryon, TU Eindhoven) for the discussions surrounding mass transfer in electrolyzers and assistance in furthering our understanding in the material.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.