English

• The electrochemical CO₂ reduction reaction (CO₂RR) converts CO₂ into value-added products under mild conditions, with renewable electricity (e.g., from wind and solar) as the potential energy supply [1–4]. In recent years, apparent progress has been achieved in the development of active electrocatalysts for CO₂RR [5–11]. Meanwhile, the design of suitable electrolyzers for the industrialization of the technique is still under investigation. Specifically, H-cells are used because of the low cost and ease of operation, which are useful for screening electrocatalysts and intrinsic kinetic studies [12]. However, the solubility of CO₂ in aqueous electrolytes is low, resulting in limited operating current densities [1]. Techno-economic analysis highlights the need to run CO₂RR at current densities above 100 mA/cm² to achieve industrial viability [13]. Therefore, gas diffusion electrodes (GDEs), which can provide a thin diffusion boundary layer that helps overcome the CO₂ mass transfer limitations in aqueous systems [14–16], are widely used in combination with flow cells [17,18]. To further lower the cell voltage and promote the energy conversion efficiency in flow cells [12], membrane electrode assembly (MEA) with a zero-gap configuration, similar to that used in fuel cells, has been adopted as the most promising electrolyzer for the practical application of CO₂RR [19,20].

  Although MEAs use GDEs to overcome the solubility problem of CO₂ for achieving high current densities, the uneven CO₂ concentration throughout the entire flow channel with the proceeding of the reaction would affect the functioning of the active sites, especially for those close to the outlet of the reactor [21]. This problem is hard to be solved by the optimization of the catalyst. Regulation of the flow field to enhance the mass transfer of CO₂ within the flow channel, letting it reach the active sites more easily, would be an effective solution [22]. However, the complex mass transfer processes and the zero-gap configuration of MEA make it challenging to experimentally verify the local environments in the GDEs. Therefore, various studies have focused on numerical simulation using computational fluid dynamics (CFD) to understand the mass transfer on porous GDEs, and the mass diffusion-convection caused by complex flow patterns. CFD simulations could provide important data that could hardly be obtained through conventional experiments. It could also be performed at a low cost in a short time. However, it is difficult to take all the experimental conditions into account when using CFD simulation for research, and some simplifications are needed that may cause variations between the simulation results and the real-world scenarios.

  The application of CFD modelling to guide the promotion of mass transfer in MEAs is developing fast [23–28]. Zhang et al. developed a comprehensive three-dimensional (3D) multiphase model of a proton exchange membrane fuel cell (PEMFC) and demonstrated that the addition of baffles in the cathode channel could increase the oxygen concentration in the porous electrode and promote water removal. These effects can effectively prevent the concentration loss in the flow channels of PEMFC [29]. Bao et al. investigated the two-phase flow in a 3D fine-mesh flow field using the volume of fluid (VOF) method. They found the air-guided effect of the 3D baffle enhanced the transport of reactants. In addition, there are some studies based on mass transfer and water management, the design of new flow channels to facilitate mass transfer [30,31]. Although these studies revealed the importance of reactant diffusion, their designs for fuel cells cannot be directly applied to CO₂RR. Therefore, the diffusion of gas-phase CO₂ to the catalyst surface should be carefully considered and new methods to enhance the CO₂ reduction reaction need to be proposed.

  Recently, Weng et al. developed a multiphysics model of a GDE for CO₂RR, which is used to study the interactions between species transport and electrochemical reaction kinetics [32]. Kas et al. developed a two-dimensional transport model for a GDE that performs CO₂ reduction to CO. This model predicts that both CO₂ and buffer electrolyte concentrations decrease gradually along the channel due to electrochemical conversion and non-electrochemical depletion in the presence of parallel gas and electrolyte flow [21]. These computational studies have provided meaningful insights for improving the mass transfer of reactants during CO₂RR. However, further studies with the considerations of the geometric effect and the transport in multiple dimensions, especially for large MEA electrolyzers, are still urgently needed. For instance, the shape of the flow channel cross-section is one of the key factors to influence the transport processes. Different cross-section shapes with varied channel heights and widths affect the velocity and pressure of the gas in the flow channel, thus determining the concentration of CO₂ reaching the gas diffusion layer and the overall performance of the electrolyzer. Considering this point, we conducted numerical simulations of the CO₂RR coupled with mass transfer processes in MEA electrolyzers with rectangular, triangular, trapezoidal, semicircular, and dovetail flow channels. The impact of the cross-section shape of the channels on the distribution of CO₂ concentration and the electrolyzer performance was investigated. The results indicate that wide flow channels with lower heights can provide a uniform flow of CO₂, particularly at high current densities, thereby benefiting CO₂RR. Additionally, the larger the geometric dimensions of the electrolyzer, the more apparent this effect becomes.

  A three-dimensional isothermal steady-state model was developed as the cathode of an MEA electrolyzer for CO₂RR (Fig. S1 in Supporting information). The computational domain includes the cathode flow field in the channel, gas diffusion layer, and catalyst layer. The detailed mesh of the model is shown in Fig. S1a. The number of grid cells for the rectangular flow channel model is 97,427, the minimum mesh is 0.12, and the average mesh element quality is 0.66. Five different cross-section shapes of the flow channels are selected namely rectangle, triangle, trapezoid, dovetail, and semicircle. Grid elements with other cross-section shapes are shown in the supporting information (Figs. S2-S5 in Supporting information).

  In this model, the gas diffusion layer is assumed to be isotropic [33]. The length of the gas diffusion layer (L_GDL) is 315 µm [34,35]. The catalyst layer consists of spherical Ag nanoparticles with the radius of r_np that are loosely bound by a binder with the substrate possessing an intrinsic porosity of ε_CL^O. The solid volume fraction is 1−ε_CL^O. The volume fractions of liquid and gas are ε_CL^OS and ε_CL^O(1−S), where S represents the catalyst layer saturation [32,33]. The MEA electrolyzer is assumed to operate at a steady state with gaseous mixtures are incompressible ideal gas in laminar flow. The effect of gravity is ignored [32–34].

  The characteristic dimensions, airflow velocity, and pressure of the CO₂RR electrolyzer determine the flow state of the gas, thus requiring the selection of the appropriate control equation. Two charge transfer reactions are assumed to occur in the catalyst layer: the CO₂RR (Eq. 1) and the H₂ evolution reaction (Eq. 2) in alkaline environment [18].

  (1)

  (2)

  The mass balance of each species in the flow channel, gas diffusion layer and catalyst layer can be written as follows (Eq. 3):

  (3)

  where n_i is the mass flux, R_CT,i are the bulk charge transfer reactions [32]. R_CT,i are applied to both gas and liquid phase species.

  The gaseous species fluxes include a diffusion term and a convection term (Eq. 4),

  (4)

  where j_i is the diffusion mass flux of species i, ρ_i is the mass density of species i, u_g is the mass-averaged fluid flow rate [32]. The diffusion fluxes were calculated using a mixture averaged diffusion model [34], the equation is formulated as follows (Eq. 5):

  (5)

  where ω_i is the mass fraction of species i, ρ_g is the density of the gaseous mixture, M_n is the average molar mass of the mixture (Eq. 6) [32].

  (6)

  D_i^eff is the effective diffusion coefficient of species i. The diffusion coefficient consists of the mass-averaged Stefan-Maxwell diffusivity and the Knudsen diffusivity (Eq. 7) [34], The formula for calculating the mass-averaged Stefan-Maxwell diffusivity (Eq. 8) and the Knudsen diffusivity (Eq. 9) is shown below:

  (7)

  (8)

  (9)

  r_p,m is the average pore radius of porous media, y_i and M_i are the molar fraction and molar mass of substance i, respectively. The binary gas-phase diffusion coefficients, D_in, are estimated following derivation by Fuller et al. [36], the calculation formula is as follows (Eq. 10):

  (10)

  where ν_p,i is the special diffusion parameter to be summed over atoms, groups, and structural features of the diffusing species.

  In addition, for flow through porous media (catalyst layer and gas diffusion layer), the effective diffusivity is corrected according to the porosity (ε_m) and tortuosity (τ_m) of the media, using the Bruggeman relation (Eq. 11) [32–34],

  (11)

  where ε_m is the porosity of the porous medium.

  To describe the mass-averaged velocity field in porous media, u_g, Darcy's law is used (Eq. 12),

  (12)

  where κ_m^eff is the effective permeability of the porous medium, μ_g is the fluid viscosity, and p_G is the total gas pressure [33]. The calculation method for effective permeability is calculated as follows (Eq. 13):

  (13)

  κ_sat,m is the saturated permeability, κ_r,m is the relative permeability. κ_sat,m is determined by the structure of the medium, according to Carman–Kozeny equation (Eq. 14) [37].

  (14)

  The values of κ_sat,m^o are given in Table 1. Relative permeability (Eq. 15) is assumed to be cubically related to saturation [38], and therefore

  (15)

  Table 1

  

  Table 1.  Simulation settings and parameters.

  DownLoad: CSV

  The fraction of the Nth gaseous species is determined by (Eq. 16)

  (16)

  The conservation of charge (Eq. 17) and Ohm's law (Eq. 18) govern the electron potential ϕ_s and the current i_s.

  (17)

  (18)

  i_s is the current density in the solid phase. i_l is the current density in the liquid phase. i_k is the local partial current density of the reaction k. a_v is the active surface area defined in the following (Eq. 19). σ_s,m^eff is the effective conductivity of the solid material in the medium, corrected by the Bruggeman relation (Eq. 11).

  (19)

  Charge transfer reactions (Eq. 20) occur at the electrode/electrolyte interface [33].

  (20)

  F is Faraday's constant. n is the number of electrons transferred, and ν_i is the stoichiometric coefficient of species i (negative for reactants, positive for products). i_loc is the local current density of electrochemical reactions. The current density of the electrode reaction at the electrochemical interface is defined by means of a custom current density value.

  Regarding the coupled theory of mass transfer and electrochemical reactions, the general chemical reaction equation (Eq. 21) when linking the species flux at the electrode surface to the current is as follows.

  (21)

  Ox denotes oxides and Red denotes reducing substances.

  The inlet flux is 50 sccm, and the outlet boundary of the flow channel is a pressure condition, which inhibits reflux. The boundaries are flux-free conditions except for the inlet, outlet and electrochemical reaction interface.

  It is assumed that the CO₂ in the feed is wet and the water vapor is saturated [33]. The saturated water vapor pressure is calculated as below (Eq. 22) [33,39].

  (22)

  The formula for calculating the mass fraction of water is as follows (Eq. 23):

  (23)

  According to Eq. 16, the mass fraction of CO₂ (ω_co2) can be obtained.

  During the reaction in the MEA electrolyzer, the reactants CO₂ and H₂O reach the catalyst layer through the gas diffusion layer to participate in the reaction. The products CO and H₂ are generated in the cathode catalyst layer, which are discharged from the cell through the gas diffusion layer and the flow channel by gas diffusion and purging. As discussed above, the uniform distribution of CO₂ through the channel is essential to achieving high activity. According to the simulation model with the five different channel designs (Fig. S6 in Supporting information), the performance is evaluated by observing the concentration changes of the reactants on the contact surface between the flow channel and the gas diffusion layer.

  When the areas of the five different cross-sections of flow channels are the same (Fig. S6a and Table 2), the CO₂ concentration distributions at the interface between the flow channel and the gas diffusion layer are shown in Fig. 1a. The left side is the inlet and the right side is the outlet (applicable for all the simulations conducted in this work). When the simulation is steady, the CO₂ concentration becomes smaller in the direction parallel to the flow channel, from the inlet to the outlet with the proceeding of the reaction. The CO₂ concentration distribution at the outlet section of the flow channel is shown in Fig. S7a (Supporting information). A certain concentration difference can be observed between the channel and the rib. The uniformity of gas concentration distribution is good for channels with triangle, trapezoid, and semicircle shapes. The semicircular flow channel has the most uniform gas concentration distribution. However, the rectangular and dovetail channels have uneven distributions of the reactant. It is worth noting that the uniformity of the CO₂ concentration has a close relationship with the width of the channel (Table 2). The wider the channel is, the better the CO₂ is distributed.

  Table 2

  

  Table 2.  Geometric parameters of the five different cross-sections of the flow channels with the same area.

  DownLoad: CSV

  Figure 1

  

  Figure 1.  CO₂ distributions at the interface between the flow channel and the gas diffusion layer. (a) The five different flow channels with the same cross-section areas. (b) The five different flow channels with the same cross-section area and the same channel width. (c, d) The five different flow channel cross-sections with the same channel width and channel height, but different areas. The gas flow rate at the inlet is the same for a-c. The gas flow velocity at the inlet is the same for d. The shape of the flow channel cross-section is rectangular, triangular, trapezoidal, semicircular, and dovetail. The left side is the inlet and the right side is the outlet.

  DownLoad: Full-Size Img PowerPoint

  In addition to the apparent impact of the width of the channel, the height of the channel may also be important. The effect of channel height on gas distribution was investigated with models possessing the same channel cross-section area and channel width (Fig. S6b and Fig. 1b). The CO₂ concentration distribution at the outlet section of the flow channel is shown in Fig. S7b (Supporting information). Compared with the rectangular flow channel, the uniformity of the gas concentration distribution is promoted for the dovetail model, while it becomes worse for the triangular, trapezoidal, and semicircular shapes. The main reason for such change lies in the different channel heights of the flow channel cross sections (Table S1 in Supporting information). The smaller the channel height, the more uniform the gas concentration distribution at the contact interface between the channel and the gas diffusion layer.

  According to the study above, both the channel width and channel height could influence the uniformity of CO₂ gas concentration distribution. Further investigation about the effect of channel shape on the uniformity of CO₂ distribution was conducted by ensuring the same channel width and channel height (Fig. S6c and Fig. 1c). The CO₂ concentration distribution at the outlet section of the flow channel is shown in Fig. S7c (Supporting information). It can be observed that the uniformity of CO₂ distribution for the five different shapes of the cross sections does not differ much under the same flow rate. Among them, the uniformity of concentration distribution of triangular and trapezoidal channels is slightly better than that of the rectangular one. The uniformity of gas concentration distribution of the semicircular and dovetail channels is slightly worse than that of the rectangular channel, but the difference is not significant. Therefore, it can be concluded that channel width and channel height are essential to affect the distribution of CO₂ during the reaction at a constant flow rate. Wide and low channels are beneficial for the uniform distribution of the reactant. In wide channels, the area for direct contact between CO₂ and the gas diffusion layer is large, which could be good for the dispersion of the reactant. When the channel height is small, the diffusion distance of the gas in the direction perpendicular to the flow channel is short, which could further lead to a more uniform CO₂ concentration distribution.

  As discussed above, the impact of the channel shape is not significant when the width and the height of the channel are fixed with a constant flow rate of CO₂. To further search for the optimized cross-section shape of flow channels, simulations with a constant flow velocity were conducted for the five different channels (Fig. 1d). The CO₂ concentration distribution at the outlet section of the flow channel is shown in Fig. S7d (Supporting information). The triangular, trapezoidal, and semicircular channels have worse distribution of the reactant. Compared with the flow channel with the rectangular cross-section, the flow channel with the dovetail cross-section has better gas distribution uniformity. It is worth noting that the uniformity of the CO₂ distribution correlates with the cross-section areas of the channel (Table S2 in Supporting information). A larger channel cross-section area leads to a more uniform distribution. Therefore, the channels in a MEA electrolyzer for CO₂RR should better be wide and low with a large cross-section area.

  To further verify the obtained design principle, whether similar trends could be achieved at different flow conditions was tested [21]. When the areas of the cross sections are the same (Fig. S6a), the trends of CO₂ concentration distributions for the five different cross-section shapes at flow rates of 10 sccm (Fig. 2a and Fig. S8a in Supporting information), 30 sccm (Fig. 2b and Fig. S8b in Supporting information), 70 sccm (Fig. 2c and Fig. S8c in Supporting information), and 90 sccm (Fig. 2d and Fig. S8d in Supporting information) were consistent with that at the flow rate of 50 sccm (Fig. 1a). In addition, the higher the flow rate, the better the distribution is (Fig. 2). Similar results could be obtained for other conditions when the channels with the same areas and widths are used or the channels with the same widths and heights are applied (Figs. S9-S12 in Supporting information).

  Figure 2

  

  Figure 2.  CO₂ distributions at different flow rates: (a) 10 sccm, (b) 30 sccm, (c) 70 sccm, (d) 90 sccm. The shape of the flow channel cross-section is rectangular, triangular, trapezoidal, semicircular and dovetail. Flow channel designs are similar to those used in Fig. S6.

  DownLoad: Full-Size Img PowerPoint

  The difference between the maximum CO₂ concentration and the minimum CO₂ concentration at the interface between the gas diffusion layer and the catalyst layer was calculated as an indicator of the uniformity of CO₂ (Fig. 3). As the flow rate increases, the CO₂ concentration difference becomes smaller. At low flow rates, such as 10 sccm and 30 sccm, an increase in flow rate increases the degree of uniformity. However, under high flow rate conditions, such as 70 sccm and 90 sccm, a further increase in flow rate has little impact on the degree of uniformity, when mass transfer is no longer a limiting factor. Although increasing the flow rate will improve uniformity, it will sacrifice the single-pass conversion of CO₂. When the cross-section area of the flow channel is the same, the concentration difference of the semicircular cross-section flow channel is the smallest, indicating a more uniform concentration distribution (Fig. 3), which is in consistence with the previous result (Fig. 1a). For the other cases, the trends of CO₂ distribution at different flow conditions also follow those of the results above (Figs. S13-S15 in Supporting information).

  Figure 3

  

  Figure 3.  Difference between the maximum and the minimum CO₂ concentrations at the contact interface between the flow channel and the gas diffusion layer at different flow conditions. The five different flow channels with the same cross-section area.

  DownLoad: Full-Size Img PowerPoint

  The CO₂ distributions at the contact interface between the flow channel and the gas diffusion layer were also calculated at different current densities (Fig. S16 in Supporting information). The CO₂ distributions at the flow channel exit interface were also calculated at different current densities (Fig. 4). At low current density, the CO₂ concentration distribution is relatively uniform, without apparent difference for different channel cross-section shapes. With the increase of current density, the CO₂ concentration distribution varies. These results indicate that mass transfer is not the main limiting factor at low current densities. Only when the current density is high, the uniformity of the CO₂ concentration distribution needs to be considered with the careful design of the channels in the MEA electrolyzer. It is worth noting that the design of the channels should also consider the manufacturing difficulties, especially for practical applications.

  Figure 4

  

  Figure 4.  CO₂ distributions at the flow channel exit interface at different current densities: (a) 100 mA/cm², (b) 200 mA/cm², (c) 600 mA/cm², (d) 1000 mA/cm². The shape of the flow channel cross-section is rectangular, triangular, trapezoidal, semicircular and dovetail. Flow channel designs are similar to those used in Fig. S6. The flow rate is a constant value of 50 sccm.

  DownLoad: Full-Size Img PowerPoint

  In this study, numerical simulations of CO₂RR MEA electrolyzers with rectangular, triangular, trapezoidal, semicircular, and dovetail flow channels were carried out using computational fluid dynamics. The effects of the cross-section dimensions on the uniformity of CO₂ concentration distribution were investigated. The results show that under the same flow rate condition, the larger the channel width and the smaller the channel height, the more uniform the CO₂ distribution. Under the same flow velocity condition with channels with the same width and height, large cross-section area is beneficial for the uniformity the CO₂ distribution. Besides, this effect is more significant at low flow rates and high current densities. This work provides theoretical guidance for the design of high-performance MEA electrolyzer for CO₂RR.

  Declaration of competing interest

  The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

  CRediT authorship contribution statement

  Lili Zhang: Writing – original draft, Methodology, Investigation. Hui Gao: Methodology. Gong Zhang: Investigation. Yuning Dong: Investigation. Kai Huang: Methodology, Investigation. Zifan Pang: Methodology, Investigation. Tuo Wang: Writing – review & editing, Supervision. Chunlei Pei: Writing – review & editing, Methodology. Peng Zhang: Writing – review & editing, Methodology, Investigation. Jinlong Gong: Writing – review & editing, Methodology, Investigation, Conceptualization.

  Acknowledgments

  We acknowledge the National Key R&D Program of China (No. 2021YFA1501503), the National Natural Science Foundation of China (Nos. 22250008, 22121004, 22108197), the Haihe Laboratory of Sustainable Chemical Transformations (No. CYZC202107), the Natural Science Foundation of Tianjin City (No. 21JCZXJC00060), the Program of Introducing Talents of Discipline to Universities (No. BP0618007) and the Xplorer Prize for financial support.

  Supplementary materials

  Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.cclet.2024.110204.

  
  
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• 

  Figure 1  CO₂ distributions at the interface between the flow channel and the gas diffusion layer. (a) The five different flow channels with the same cross-section areas. (b) The five different flow channels with the same cross-section area and the same channel width. (c, d) The five different flow channel cross-sections with the same channel width and channel height, but different areas. The gas flow rate at the inlet is the same for a-c. The gas flow velocity at the inlet is the same for d. The shape of the flow channel cross-section is rectangular, triangular, trapezoidal, semicircular, and dovetail. The left side is the inlet and the right side is the outlet.

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  Figure 2  CO₂ distributions at different flow rates: (a) 10 sccm, (b) 30 sccm, (c) 70 sccm, (d) 90 sccm. The shape of the flow channel cross-section is rectangular, triangular, trapezoidal, semicircular and dovetail. Flow channel designs are similar to those used in Fig. S6.

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  Figure 3  Difference between the maximum and the minimum CO₂ concentrations at the contact interface between the flow channel and the gas diffusion layer at different flow conditions. The five different flow channels with the same cross-section area.

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  Figure 4  CO₂ distributions at the flow channel exit interface at different current densities: (a) 100 mA/cm², (b) 200 mA/cm², (c) 600 mA/cm², (d) 1000 mA/cm². The shape of the flow channel cross-section is rectangular, triangular, trapezoidal, semicircular and dovetail. Flow channel designs are similar to those used in Fig. S6. The flow rate is a constant value of 50 sccm.

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  Table 1.  Simulation settings and parameters.

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  Table 2.  Geometric parameters of the five different cross-sections of the flow channels with the same area.

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