Bio-Inspired Flow Field Design for Enhanced Mass Transport in CO₂ Electrolyzers: A Multiphysics Modeling Approach

Abstract

The electrochemical conversion of CO₂ provides a sustainable route to convert it into value-added fuels and chemicals using a membrane electrode assembly at an industry scale. However, achieving high efficiency and selectivity is often constrained by mass transport limitations and high pressure drop. In this study, various flow patterns inspired from nature such as Victoria amazonica leaf, camel’s turbinate, avian lung, and wave flow were systematically investigated through 3D Multiphysics simulations. The developed COMSOL model couples free and porous medium flow using the Brinkman interface and solves for CO₂ transport via the transport of the concentrated species interface under steady-state conditions. Among all the simulated designs, V.amazonica-inspired “A1” and hybrid avian-leaf design “C1” demonstrated high CO₂ concentration on the catalyst surface with the lowest pressure drop, highlighting a balance between mass transport efficiency and pressure drop. On the other hand, wave flow-inspired “D1” exhibited highest CO₂ concentration on the catalyst surface but with a significant pressure drop. A sigmoidal three parameter growth model was used to quantitatively compare the dependence of the CO₂ concentration on the flow rate, indicating that A1 and C1 achieve optimal gas utilization at a lower flow rate than the conventional serpentine flow pattern. The results underscore the potential of bioinspired geometries to improve catalyst utilization, minimize parasitic energy losses, and guide the rational design of scalable, energy-efficient CO₂ electrolyzers.

1. Introduction

The continuous rise in atmospheric CO₂ concentrations, primarily driven by fossil fuel combustion and industrialization, underscores the critical importance of developing carbon capture and conversion technologies to address this challenge. The electrochemical reduction of carbon dioxide (CO₂RR) represents a promising pathway for converting CO₂ into value-added products that can serve as chemical feedstocks or fuels. , Beyond mitigating anthropogenic CO₂ emissions, this reaction offers a route to closing the carbon cycle and enabling more sustainable chemical manufacturing. CO₂RR involves the coupled transfer of electrons and protons and can proceed under both acidic and alkaline environments, with product selectivity influenced by the catalyst and reaction conditions. , In practical applications, the CO₂RR is commonly implemented in CO₂ electrolyzers, which consist of anodic and cathodic compartments separated by an ion-conducting membrane. The cathode facilitates the CO₂RR, while the anodic compartment typically drives the oxygen evolution reaction (OER) to complete the overall electrochemical process. For scaling toward industrially relevant operation, membrane electrode assembly (MEA)-based electrolyzers are considered a particularly suitable design, owing to their high current density capabilities and compact design.

Key components that critically influence the performance of a CO₂ electrolyzer include the membrane, the flow field, and the catalyst. The membrane not only separates the anodic and cathodic compartments but also enables selective ion transport. The flow field governs the distribution of gaseous CO₂ across the catalyst-coated gas diffusion electrode (GDE), while the catalyst itself determines the activity and stability of the reaction. , For industrially relevant operation, achieving high current densities and long-term stability requires careful optimization of all of these components. However, nonuniform gas distribution within the flow field often leads to local CO₂ depletion and unwanted HER. While liquid accumulation and GDL flooding are known to influence the performance of the electrolyzer, understanding the fundamental role of flow-field on gas-phase transport remains a critical step toward rational design. Therefore, engineering optimized flow patterns is essential to ensure uniform reactant delivery, efficient removal of gaseous and liquid products, and mitigation of concentration gradients at the electrode–electrolyte interface. , Optimizing these aspects is critical to bridging the gap between laboratory-scale and commercially viable CO₂ electrolysis systems.

Conventional flow field designs in electrolyzers, such as serpentine and parallel configurations, have been extensively studied and applied across various electrochemical systems. More recently, bioinspired desgins have attracted significant attention, particularly in fuel cell research, owing to their ability to overcome limitations associated with traditional geometries. , Natural systems exhibit hierarchical transport networks optimized over evolutionary time scales for efficient fluid and nutrient distribution with minimal energy input. Mimicking these structures offers an attractive design strategy for electrochemical reactors, where mass transport uniformity and energy efficiency are paramount. , Translating such natural optimization into flow-field design provides a biomimetic route to overcome the CO₂ transport limitations in electrolyzers. By imitating natural branching networks, these designs enable more homogeneous distributions of reactant and pressure across the catalyst surface. Such uniformity enhances reactant accessibility, reduces mass transport losses, and improves device performance, often leading to higher power densities compared with conventional flow patterns.

Several bioinspired configurations including auxiliary fishbone, leaf-vein, tree-like, lung-mimetic, and key-shaped flow fields have been systematically investigated in polymer electrolyte membrane fuel cells (PEMFCs). These structures demonstrate superior performance by reducing pressure drop through hierarchical branching, improving water management to mitigate gas diffusion layer (GDL) flooding, and enhancing the overall mass transport efficiency. Translating these concepts to CO₂ electrolyzers requires an understanding of flow pattern influence on gas-phase transport through the channels and porous media, which is one of the major limitations under high-current density operation. It offers a pathway to improve CO₂ utilization and energy efficiency by enabling efficient reactant delivery and more uniform catalyst layer utilization. Importantly, addressing GDL flooding through optimized bioinspired flow fields can enhance the long-term operational stability of CO₂ electrolyzers while simultaneously reducing energy consumption. , Although the fabrication of such complex architectures often necessitates advanced manufacturing approaches, including additive manufacturing and 3D printing, the associated performance improvements underscore their potential as a promising strategy for next-generation CO₂ electrolysis systems. While several studies have explored the influence of serpentine, parallel, and interdigitated flow fields in CO₂ electrolyzers, , the integration of nature-inspired geometries remains largely unexplored, particularly through detailed 3D multiphysics modeling that couples gas flow and porous medium transport.

Despite the promising performance of bioinspired flow patterns in fuel cell application, not many studies have been reported for CO₂ electrolyzers. The majority of the modeling efforts have investigated conventional flow fields, leaving the transport mechanisms governing bioinspired patterns largely unexplored under realistic electrolyzer operating conditions. There remains a lack of comprehensive three-dimensional multiphysics studies that compare different bioinspired designs under identical boundary conditions to quantify their impact on pressure drop, reactant availability, and transport uniformity. Addressing these gaps is essential to establish clear design principles for integrating bioinspired flow patterns into next-generation CO₂ electrolyzers.

In this work, we investigated several bioinspired flow field designs, including patterns mimicking the structural morphology of the Victoria amazonica leaf which is one of the largest and most mechanically efficient leaves in nature. In addition, we explored hybrid designs that combine features of avian parabronchial lungs with V. amazonica as well as patterns inspired by wave dynamics and camel turbinate structures, each incorporating distinct structural modifications. To evaluate their effectiveness, a three-dimensional Multiphysics model was developed to simulate CO₂ transport and distribution of CO₂ within the flow channels and across the gas diffusion layer. This modeling framework provides a systematic comparison of different bioinspired architectures, enabling us to quantify their influence on CO₂ availability at the catalyst surface, pressure drop characteristics, and mass transport uniformity. By addressing two critical challenges, minimizing pressure losses, and achieving homogeneous delivery of CO₂ to the electrochemically active sites, these designs hold the potential to significantly enhance catalyst utilization, reaction selectivity, and the overall electrolyzer performance. The insights gained from this study contribute to the rational design and upscaling of CO₂ electrolyzers, offering pathways to overcome the key engineering barriers associated with conventional flow fields. Ultimately, such bioinspired strategies may accelerate the transition from laboratory-scale demonstrations to industrially viable CO₂ electrolysis systems with improved energy efficiency and long-term operational stability.

2. Model Development

2.1. Physical Geometry

The design of the cathode flow field in CO₂ electrolyzers was adopted from geometrical motifs derived from natural systems that exhibit highly efficient fluid distribution and mass transport, as illustrated in Figure . These bioinspired design strategies provide physical geometries that mimic naturally optimized transport networks, offering pathways to improve CO₂ distribution, reduce pressure drop, and enhance the overall electrochemical performance in electrolyzer systems.

1.

Flow field designs inspired from different natural systems for the cathode compartment. (A) V. amazonica, (B) Camel’s turbinate, (C) Avian lungs, and (D) wave flow.

The detailed geometrical configurations and corresponding dimensions of these bioinspired designs are presented as follows.

2.1.1. Victoria amazonica

The V. amazonica leaf, one of the largest known aquatic leafs, exhibits a highly optimized venation network, characterized by hierarchical branching and radial reinforcement, and was employed as a design basis owing to its capacity to uniformly distribute reactants across a large surface area with minimal structural resistance. This natural design serves as an effective model for developing flow field patterns that promote uniform reactant distribution in CO₂ electrolyzers. Four designs (A1, A2, A3, and A4) as shown in Figure were developed, which replicate the radial distribution channels, cross-linkage, and hierarchical branching which minimize pressure drop and promote uniform reactant distribution on the catalyst surface. The magnified view highlights the hierarchical venation pattern, interconnected by a lattice of cross-veins that provide uniform nutrient transport.

2.

Flow field designs (A1–A4) inspired from (A) V. amazonica leaf for the cathode compartment.

For all of the designs, inlet and outlet cross-sectional areas were fixed at 1 mm². The parent channel was assigned a width of 1 mm, while the daughter branches were set to 0.7 mm to balance the flow rate and pressure drop across bifurcating channels. The channel-to-rib width was maintained at a ratio of 1:1 in all the designs. Designs A1, A3, and A4 incorporate a single inlet and a single outlet, whereas A2 employs one inlet and two outlets to promote alternative flow distribution and reduce pressure build-up. All configurations include an interconnected network of lateral channels that mimic the cross-vein structure of the V. amazonica leaf. Designs A3 and A4 feature a circular flow-field layout with the carbon paper dimensions kept constant across both configurations. To ensure complete coverage of the active area, extended channel components were incorporated to deliver CO₂ more uniformly across the catalyst surface and minimize regions of limited reactant access. This hierarchical network is intended to enhance reactant delivery by improving the access of CO₂ to the catalyst surface, mitigating local concentration gradients, and promoting more uniform current density distribution across the active area.

2.1.2. Camel’s Turbinate Inspired Flow Pattern

The camel turbinate morphology, featuring spiral and concentric channels within the nasal cavity which dramatically increase the internal surface area enabling efficient heat and moisture exchange during breathing, was adopted as inspiration for promoting enhanced mixing and improving reactant utilization. Inspired by this natural design, four different flow pattern variants (B1, B2, B3, and B4) as shown in Figure were designed. Each design incorporates a series of spiral channel replicating the turbinate to extend the gas flow path and increase the contact with the catalyst surface. The enhanced pathway complexity is expected to promote a more uniform CO₂ distribution, improve gas–liquid interface management, and reduce concentration gradients across the catalyst layer.

3.

Flow-field designs (B1–B4) inspired by the camel turbinate structure (B) for enhanced gas management in CO₂ electrolyzers.

Designs B1, B2, B3, and B4 share identical inlet and outlet cross-sectional areas of 1 mm², with the parent channel width set to 1 mm and the spiral branch channels set to 0.7 mm to enhance the surface coverage of the active area. The dimension of the rib between the parent channel was set to 1 mm. B1 features spiral channels arranged symmetrically on both sides of the main (parent) channel, providing an extended flow path to enhance the gas residence time and surface coverage. In contrast, B3 incorporates spiral channels on only one side of the parent channel, creating an asymmetric flow distribution while maintaining the same parent and branch dimensions. B2 and B4 represent an extended variant of B1 and B3, where baffles are introduced upstream of the spiral channels to deliberately disrupt and redistribute the flow, promoting improved reactant mixing and potentially reducing local concentration gradients. This progressive variation from B1 to B4 allows systematic evaluation of how spiral complexity, flow obstruction, and asymmetry influence the CO₂ transport, pressure drop, and uniformity of reactant delivery to the catalyst surface.

2.1.3. Avian Lung + Victoria amazonica

The avian parabronchial lung served as an archetype due to its unidirectional and efficient gas exchange mechanism, which ensures continuous reactant delivery while minimizing backflow. A hybrid flow pattern was designed by integrating design features from both avian lung and V. amazonica leaf, as illustrated in Figure (C1). The avian lungs are characterized by unidirectional airflow, which facilitates highly efficient gas exchange. This feature was combined with the interconnected venation pattern as the V. amazonica leaf, as discussed in Section , to create a design that promotes both effective reactant distribution and structural uniformity. The inlet and outlet dimensions were fixed at 1 mm², while the channel width was gradually reduced along the direction of flow, reaching 0.5 mm at the outermost channel to mimic the narrowing observed in avian parabronchi. In addition, the interconnected crossflow channels were set to 0.7 mm to maintain consistency with the dimensions used in the other reported designs and the dimension of the rib was kept at 0.7 mm, maintaining a constant channel-to-rib width ratio. This integrated approach is expected to balance unidirectional flow with a uniform lateral distribution, thereby improving CO₂ delivery at the catalyst surface.

4.

Avian parabronchial lung (C)-inspired flow field design (C1) for CO₂ electrolyzers.

2.1.4. Wave Flow Channel

In addition to these biological analogues, a wave-flow-inspired geometry was developed to introduce periodic oscillations in the flow path, thereby enhancing reactant penetration, disrupting boundary layer formation, and facilitating improved mass transfer at the catalyst interface. The flow channels were designed based on wave-inspired geometries that mimic the periodic oscillations of natural fluid motion, as shown in Figure (D1 and D2). Such periodic oscillatory patterns help in enhancing the convective mass transfer and improve the availability of CO₂ at the catalyst surface. Two different designs were considered: in design D1, only periodic oscillations were incorporated, whereas in design D2, elliptical barriers with a major axis of 2 mm and a minor axis of 0.8 mm were introduced in addition to the oscillatory channels to further modulate flow distribution. In both cases, the channel width was fixed at 1 mm to maintain consistency with other designs, while the inlet and outlet cross-sectional areas were kept at 1 mm². To minimize stagnant zones, a fillet of 0.5 mm was applied to all channel curvatures in both D1 and D2. The rib width was set to 1 mm, thereby maintaining a channel-to-rib width ratio of 1:1.

5.

Flow field design (D1,D2) for CO₂ electrolyzers inspired from (D) wave flow.

2.2. Mathematical Model Description

The cathodic compartment of the CO₂ electrolyzer was modeled using COMSOL Multiphysics 5.5 to evaluate transport behavior under different bioinspired flow field configurations. The 3D geometry consists of different bioinspired flow patterns as described in Section and a gas diffusion layer in contact with the flow pattern. The dimensions of the GDL were fixed at 2.5 cm × 2.5 cm × 325 μm throughout the study to ensure comparability across different flow designs. The numerical simulations were performed to model the CO₂ concentration in the gas channel and catalyst surface using the GCRO–DR iterative solver with a relative tolerance of 0.001. For all of the studies, a constant current density of 500 mA/cm² was applied at the catalyst surface. A mesh independence study was conducted for the serpentine flow pattern to ensure that the mesh size does not influence the simulation results, as shown in Figure S1. Successively finer meshes were generated by increasing the number of elements in the computational domain, and the average CO₂ concentration at the catalyst surface, which is one of the key outputs, was compared. The results demonstrated negligible variation beyond fine mesh, indicating that further refinement had no significant impact on the modeled output values. Accordingly, a physics-controlled mesh with 3856302 elements (fine mesh) was selected for all subsequent simulations to balance the efficiency and computational accuracy.

The electrochemical conversion of CO₂ can yield a wide spectrum of products, depending on the catalyst and operating conditions. In this study, however, the analysis was restricted to the selective conversion of CO₂ to CO. The reduction reaction takes place in the cathodic compartment of the electrolyzer, where CO₂ is reduced at the catalyst–electrolyte interface. Although the competitive hydrogen evolution reaction (HER) often accompanies the CO₂RR due to the presence of H⁺ ions in the system, the HER was neglected in the present model in order to isolate the transport and consumption behavior of CO₂.

The key parameters used for modeling are shown in Table and the main assumptions considered are as follows:

• All the calculations are conducted at steady-state conditions.

• The reaction takes place at an isothermal condition of 298 K with no thermal diffusion gradient.

• A uniform current distribution is assumed at the catalyst surface.

• Carbon GDL is assumed to be isotropic with constant porosity and permeability.

• Compressible flow and pore–wall interaction are considered for all the calculations.

1. Parameters Used in the 3D Multiphysics Model.

parameter	symbol	value	unit	reference
temperature	T	298	K	this work
reference pressure	P	1	atm	this work
inlet flow rate	Q inlet	20–80	sccm	this work
porosity of GDL	εGDL	0.8	-
permeability of GDL	κGDL	7 × 10–12	m 2
applied current density	i loc	–500	mA/cm2	this work
diffusivity of CO into CO2	DCO2‑CO	1.52 × 10–5	m2 s–1
GDL thickness	h GDL	325	μm
channel depth	w de	1	mm	this work
inlet cross sectional area	A inlet	1	mm2	this work

2.3. Governing Equations

2.3.1. Free and Porous Medium Flow, Brinkman Interface

The flow of a single-phase compressible fluid through a system comprising both free flow and porous media was modeled by using the Brinkman interface approach. The velocity and pressure fields were determined by solving the Brinkman equation within the porous region and the Navier–Stokes equations for the free-flow gas channel. A no-slip boundary condition was applied at the channel walls, while a slip boundary condition was used at the interface between the free flow and porous media. Inlet boundary conditions were defined by a normal inflow velocity corresponding to a specified flow rate $({\mathrm{V̇}}_{\mathrm{i}\mathrm{n}})$ , applied uniformly across the inlet cross-sectional area of the channel. The flow rate was varied from 20 to 80 sccm, based on the validation study of the model. At the outlet, a zero-pressure boundary condition was imposed with backflow suppressed to ensure stable flow conditions.

The equations used to solve for the velocity and pressure field in the free-flowing gas channels are as follows:

$$\rho (\mathbf{u}.\mathrm{\nabla })\mathbf{u}=\mathrm{\nabla }.[-\mathrm{p}\mathbf{I}+\mu (\mathrm{\nabla }\mathbf{u}+({\mathrm{\nabla }\mathbf{u})}^{\mathrm{T}})-\frac{2}{3}\mu (\mathrm{\nabla }.\mathbf{u})\mathbf{I}]+\mathrm{F}$$ 1

$$\mathrm{\nabla }.(\rho \mathbf{u})=0$$ 2

For the porous media, the velocity and pressure were calculated by the following equations:

$$\frac{1}{{ϵ}_{\mathrm{p}}}\rho (\mathbf{u}.\mathrm{\nabla })\mathbf{u}\frac{1}{{ϵ}_{\mathrm{p}}}=\mathrm{\nabla }.[-\mathrm{p}\mathbf{I}+\mu \frac{1}{{ϵ}_{\mathrm{p}}}(\mathrm{\nabla }\mathbf{u}+(\mathrm{\nabla }{\mathbf{u}}^{\mathrm{T}})-\frac{2}{3}\mu \frac{1}{{ϵ}_{\mathrm{p}}}(\mathrm{\nabla }.\mathbf{u})\mathbf{I}]-(\mu {\kappa }^{-1}+\frac{{\mathrm{Q}}_{\mathrm{m}}}{{ϵ}_{\mathrm{p}}^2})\mathbf{u}+\mathrm{F}$$ 3

$$\mathrm{\nabla }.(\rho \mathbf{u})={\mathrm{Q}}_{\mathrm{m}}$$ 4

In the above equations:

μ is the dynamic viscosity of the fluid, u is the velocity, ρ is the density of the fluid, p is the pressure, ϵ_p is the porosity of the GDE, κ is the permeability of the GDE, and Q _m is the mass source or sink and accounts for mass deposit and mass creation within the domains. F is the force term which can account for the influence of gravity and other volume forces.

2.3.2. Transportation of Concentrated Species

The species transport was solved by considering the mixture diffusion model, where the diffusion is proportional to a single diffusion coefficient corresponding to the species pairs considered in the model. In this model, only CO₂ and CO were considered, and the thermal diffusion and electromigration were ignored. The following equations were used to calculate the molar flux of the species in the model.

$$\mathrm{\nabla }.{\mathit{j}}_i+\rho (\mathit{u}.\mathrm{\nabla }){\omega }_i=R_i$$ 5

$$N_i=j_i+\rho u{\omega }_i$$ 6

In the above equation, the first and second terms represent the diffusive flux and convective flux, respectively.

$$j_i=-(\rho D_i^m\mathrm{\nabla }{\omega }_i+\rho {\omega }_i{D}_i^m\frac{\mathrm{\nabla }{M}_{\mathrm{n}}}{M_{\mathrm{n}}}-j_{c,i}+D_i^T\frac{\mathrm{\nabla }T}{T})$$ 7

Last two terms in the equation which correspond to the correction flux and thermal diffusion term are not considered as only two species are considered, and the system is solved at an isothermal condition.

$$R_i=\frac{v_i{i}_v}{nF}$$ 8

where N is the total flux vector of species i, R _i is the reaction rate of species i, u is the fluid velocity, j _i is the relative mass flux due to molecular diffusion of species i, ω _i is the mass fraction of species i, i _v is the volumetric current density, v _i is the stoichiometric coefficient of species i, and F is the Faraday constant.

Mixture averaged diffusion coefficient was calculated by the following equation:

$$D_i^m=\frac{1-{\omega }_i}{\sum _{k\ne i}\frac{x_k}{D_{ik}}}$$ 9

Mean molar mass was calculated by using

$$M_{\mathrm{n}}={\left(\sum _i\frac{{\omega }_i}{M_i}\right)}^{-1}$$ 10

The mixture averaged diffusion is corrected by using effective diffusion in the porous media, where it is given by

$$D_{e,ik}=f_e({ϵ}_p,{\tau }_F)D_{ik}$$ 11

f _e is the effective transport factor, which is a function of porosity and tortuosity factor and is calculated by the Bruggeman relationship.

$$f_e=\frac{{ϵ}_p}{{\tau }_F}$$ 12

$${\tau }_F={ϵ}_p^{-1/2}$$ 13

2.4. Boundary Conditions and Model Validation

Boundary conditions were defined with a no-slip condition (u = 0) along the walls of the flow field and at the interface between the flow channels and GDL, ensuring zero tangential velocity at the solid boundaries. At the outlet of the flow channel, the pressure was set to 0 Pa with backflow suppression to prevent the reverse flow into the computational domain. The catalyst surface was treated as an active reaction boundary, where a constant current density of 500 mA/cm² was applied, which corresponds to the continuous conversion of CO₂ to CO. These boundary conditions as shown in Figure collectively ensure physically consistent flow, pressure, and electrochemical constraints within the modeled cathodic domain. The developed model was validated against the study conducted by Siddhartha et al., who reported the spatial distribution of CO₂ on the catalyst surface under three distinct cases. For validation, case C was adopted, wherein the authors accounted for CO₂ consumption due to its reaction with OH^– ions and incorporated this into the model through a modified current density parameter. To ensure consistency, a serpentine flow field was designed following the geometric specifications reported in their study. The average CO₂ concentration on the catalyst surface was then simulated by using the same modified current density values, allowing direct comparison between the present model and the published results. The corresponding flow rates and current densities employed for model validation are summarized in Table S1. Figure S2D depicts the comparison of the average CO₂ concentration on the catalyst surface obtained from this study with the simulated concentration values reproduced from Siddhartha et al., confirming the reliability of the present model for describing CO₂ transport under reactive conditions. The validated model was subsequently employed to investigate various bioinspired designs discussed in this article.

6.

Schematic illustration of the flow pattern and GDL system, and boundary conditions employed in the developed Multiphysics model.

3. Results and Discussion

In gas-fed CO₂ electrolyzers, the inlet flow rate plays a crucial role in determining the concentration of CO₂ at the catalyst interface and pressure drop within the flow channels. At lower flow rates, limited convective transport leads to CO₂ depletion near the electrode surface, thereby limiting reaction kinetics and adversely affecting the overall performance of the electrolyzer. Regions of the catalyst surface that have insufficient CO₂ concentration become prone to the competitive HER, which not only reduces the selectivity but also reduces the overall efficiency of the system. On the other hand, at higher flow rates, the enhanced convective mass transport not only facilitates replenishment of CO₂ at the catalyst surface but also increases the overall pressure drop. , Achieving an optimal balance between the CO₂ concentration on the catalyst surface and pressure drop is therefore for ensuring high efficiency and stability in CO₂ electrolyzers. Understanding this trade-off through quantitative modeling is therefore essential for designing energy-efficient flow-field designs.

3.1. Comparative Analysis of Bioinspired Flow Patterns

The simulated data represent the variation of average CO₂ concentration at the catalyst surface and the corresponding pressure drop across different flow pattern designs over a range of inlet flow rates varying from 20 to 80 sccm. For all the designs, both the CO₂ concentration and pressure drop exhibit a clear dependence on the flow rate. At higher flow rates, the catalyst surface attains a sufficiently high CO₂ concentration for efficient working of the electrolyzer primarily due to enhanced convective mass transport that mitigates local reactant depletion near the electrode interface. Figure (i) represents the average CO₂ concentration on the catalyst surface at different applied flow rates for flow patterns A1, A2, A3, and A4 inspired by the V. amazonica leaf and conventional serpentine flow pattern. Among the simulated flow field patterns, A1 consistently achieved the highest average CO₂ concentration at the catalyst surface across all of the investigated flow rates, outperforming the conventional serpentine flow pattern. This superior performance can be attributed to the hierarchical branching and vein-like structure, which promotes uniform CO₂ distribution on the catalyst surface. , Figure (ii) represents the CO₂ streamline, depicting the gas flow distribution within the flow pattern at a flow rate of 40 sccm. The maximum CO₂ concentration of 40 mM is represented in red, indicating regions of high reactant availability. The corresponding average CO₂ on the catalyst surface at different flow rates (20, 40, 60, and 80 sccm) is presented in Figure S3. As observed, at higher flow rates, the catalyst surface is uniformly covered with CO₂ unlike at lower flow rates. The A2 design exhibited the lowest average CO₂ concentration on the catalyst surface, which can be attributed to the dual outlet configuration. In this flow pattern, the inlet stream is divided into four different flow paths, two of which are directly connected to the outlets without any flow restrictions. This makes the reactants move preferentially toward the outlet, resulting in insufficient penetration into the remaining regions of the catalyst layer. Additionally, it has nonuniform pressure distribution and asymmetric flow, which collectively lead to the generation of low-concentration areas on the catalyst surface. This confirms the influence of flow rate on maintaining enough CO₂ on the catalyst surface at a current density of 500 mA/cm² to sustain catalytic activity and suppress the competing HER thereby achieving efficient and selective CO₂ conversion. Figure (iii,iv) represents the variation in pressure drop across different flow rates for A1, A2, A3, and A4 and serpentine flow pattern. It can be observed that all the bioinspired designs show lower pressure drop as compared to conventional serpentine flow, with A1 demonstrating the lowest pressure drop. This can be attributed to its well optimized branching structure, which facilitates uniform flow distribution and minimizes flow resistance within the flow pattern. ,

7.

Simulated data for the flow pattern inspired by V. amazonica. (i) Average CO₂ concentration on the catalyst surface, (ii) CO₂ streamline showing the direction of the flow for A1, (iii,iv) pressure drop at different flow rates for A1, A2, A3, and A4.

Figure (i) represents the average CO₂ concentration on the catalyst surface for the designs B1, B2, B3, and B4 and serpentine flow. It can be observed that all of the designs underperform relative to the serpentine flow, with B4 showing the highest CO₂ concentration among them. Designs B1 and B3 feature basic spiral layouts, whereas B2 and B4 include additional baffles intended to perturb the inlet flow stream. In designs B1 and B3, the flow remains largely unidirectional, resulting in poor penetration into the circular vortex regions due to the absence of barriers in the straight flow path. To overcome this limitation, baffles were introduced in B2 and B4, which significantly improved the average CO₂ concentration on the catalyst surface by promoting flow diversion and mixing. However, with the introduction of baffles, an increase in pressure drop is observed, as shown in Figure (iii). Among all four designs, B4 demonstrated the most favorable balance, achieving CO₂ concentrations nearly comparable to the serpentine flow field at flow rates beyond 50 sccm. This improvement can be attributed to the effective flow redirection and enhanced convective mass transfer induced by the baffles, although it comes at the expense of increased pressure drop, which intensifies with an increasing flow rate. On the other hand, B1 has the lowest average CO₂ concentration due to the least flow diversion and mixing. Figure (ii,iv) represents the CO₂ streamline corresponding to B4 and B2 designs, depicting the gas flow distribution at a flow rate of 40 sccm with a maximum concentration equal to 40 mM achieved at the inlet of the flow pattern. The presence of baffles can be clearly seen, diverting the flow into the vortex region, thereby enhancing the mixing and promoting convective mass transfer within the flow channel. The corresponding average CO₂ on the catalyst surface of B4 design at different flow rates (20, 40, 60, and 80 sccm) is shown in Figure S5.

8.

Simulated data for the flow pattern inspired by camel’s turbinate. (i) Average CO₂ concentration on the catalyst surface, (ii,iv) CO₂ streamline showing the direction of the flow for B4 and B2, respectively, (iii) pressure drop at different flow rates for B1, B2, B3, and B4.

Figure (i) illustrates the variation of average CO₂ concentration on the catalyst surface as a function of flow rate for the designs C1, D1, and D2, compared with the serpentine flow pattern. At lower flow rates, all three designs exhibit comparable CO₂ concentration, following an increasing trend with the rising flow rate. Both D1 and D2 demonstrate higher average CO₂ availability on the catalyst surface as compared to the serpentine flow pattern, while C1 exhibits nearly identical performance. This suggests that all three designs are capable of enhancing the CO₂ availability comparable to or better than the conventional serpentine flow. However, the pressure drop associated with D1 and D2 as shown in Figure (iv) is significantly higher than the serpentine flow pattern. Both D1 and D2 have oscillatory design which promote convective mass transfer but simultaneously induce greater pressure drop. In particular, D2 incorporates elliptical baffles which promote the movement of CO₂ to the catalyst surface but further increases the pressure drop, an effect analogous to conditions of partial channel blockage or salt formation within the flow pattern. , In contrast, design C1 exhibits an exceptionally low pressure drop as shown in Figure (iii) while maintaining an average CO₂ concentration nearly equivalent to that of serpentine flow. This can be attributed to its hybrid bioinspired design, which synergistically combines features of avian lung and V. amazonica leaf. The gradual tapering of the channel width along the flow direction, mimicking the avian parabronchial structure, accelerates the gas velocity, enhances convective transport, and prevents stagnant zones. The C1 design achieves efficient CO₂ utilization with minimal pumping power requirements, highlighting its potential as an energy efficient and scalable flow field for CO₂ electrolyzers. Figure (ii) represents the CO₂ streamline corresponding to C1, depicting the gas flow distribution within the flow pattern at a flow rate of 40 sccm. The average CO₂ on the catalyst surface of C1 and D1 design at different flow rates (20, 40, 60, and 80 sccm) is shown in Figures S7 and S9, respectively.

9.

Simulated data for the flow pattern inspired by avian lung and wave flow. (i) Average CO₂ concentration on the catalyst surface, (ii) CO₂ streamline showing the direction of the flow for C1, (iii,iv) pressure drop at different flow rates for C1, D1, and D2.

Figure represents the fraction of the catalyst surface area exhibiting a CO₂ concentration of 0 mM at varying flow rates ranging from 20 to 80 sccm. The data corresponds to the best performing flow patterns A1, B4, C1, and D1 and are derived from the cumulative data obtained from COMSOL simulations, as shown in Figures S4, S6, S8, and S10, respectively. At lower flow rates (≤30 sccm), a significant portion of the catalyst surface experiences complete CO₂ depletion. This occurs because the reactant is rapidly consumed near the inlet region, leaving the remaining section of the catalyst with a very low CO₂ concentration. Under such conditions, these inactive zones are prone to favor HER, thereby reducing the overall selectivity toward CO₂RR. This plot can be useful in determining the conditions, such as the flow rate, necessary at a particular current density at which the complete surface of the catalyst can be utilized and limited hydrogen is produced. As the flow rate increases, CO₂ is available to a larger area of the catalyst, reflecting improved convective replenishment and more uniform gas distribution across the catalyst interface. Beyond a flow rate of approximately 40 sccm, nearly the entire catalyst surface remains covered with CO₂, ensuring the effective utilization of the active area and minimizing HER participation. This observation highlights the importance of maintaining an adequate gas feed rate at high current densities (e.g., 500 mA cm^–2) to sustain efficient CO₂ reduction and maximize the product selectivity.

10.

Percentage of the catalyst surface area exhibiting 0 mM CO₂ concentration for different flow field designs as a function of the inlet flow rate.

Among the simulated designs, A1 exhibits a relatively larger area with a 0 mM concentration at low flow rates but shows the steepest decline in zero-concentration surface fraction with an increasing flow rate. This behavior can be attributed to its diagonal inlet configuration, which directs the gas feed nonuniformly at low flow conditions but rapidly equalizes the distribution as the flow velocity increases. Overall, this analysis provides valuable insight into the critical interplay among flow rate, mass transport, and catalyst utilization, offering a quantitative basis for optimizing operating parameters to achieve high-performance CO₂ electrolysis with minimal parasitic losses.

3.2. Quantitative Assessment of CO₂ Concentrations on the Catalyst Surface

Based on the comparative analysis of the pressure drop and average CO₂ concentration on the catalyst surface, the most efficient flow patterns were selected for detailed evaluation against the conventional serpentine flow pattern. A three-parameter logistic growth model as represented by eq was used to fit the simulated data, quantitatively describe the dependence of the CO₂ concentration on the flow rate, and assess the transport efficiency of each design. It effectively captures the behavior of gas-fed electrochemical systems, where the CO₂ concentration transitions from a diffusion limited flow regime at low flow rates to a convection dominated system at higher flow rates. A plateau is achieved when the increasing flow rate no longer affect the CO₂ concentration significantly. The fitted parameters provide valuable quantitative indicators, enabling a direct comparison of performance of different flow patterns.

$$y(x)=\frac{a}{1+e^{-k(x-x_c)}}$$ 14

Here, y and x are the average CO₂ concentration and flow rate, respectively.

Figure represents the simulated data points, represented by the discrete solid markers and fitted curve represented by the dashed line. The three major fitted parameters obtained from the model include the asymptotic concentration (a), the inflection point (x_c), and the growth rate constant (k) serving as the key descriptor of the designs. The parameter “a” represents the maximum concentration of CO₂ that can be attained at the catalyst surface under high flow conditions, reflecting the overall efficiency of gas transport achieved by the flow pattern. The parameter “x_c” represents the flow rate at which the concentration on the catalyst surface is half of the maximum value, and “k” represents the rate at which the concentration is enhancing on the surface of the catalyst. Together, these parameters provide a quantitative framework to compare the different flow fields. Table summarizes the fitted parameters obtained from the model and is subsequently discussed with respect to the performance of the flow patterns.

11.

Sigmoidal growth model fitting of simulated data.

2. Parameters Obtained From Sigmoidal Model Fitting for Best Performing Flow Field Designs.

design	a	x c (sccm)	k
Serpentine	28.93	26.99	0.0700
A1	30.31	25.86	0.0603
B4	28.11	30.37	0.0626
C1	28.65	27.18	0.0716
D1	29.78	26.96	0.0696

From Table , it can be observed that the designs A1 and D1 have the highest “a” values (30.3 and 29.7, respectively), indicating superior gas transport and high surface coverage under high flow conditions as compared to the other flow patterns. However, the two designs show contrasting hydrodynamic behavior with D1 showing highest pressure drop as shown in Figure (iv), suggesting that the periodic oscillations increase the convective mass transfer but also lead to increased frictional losses and pressure drop. This pressure drop arises primarily from differences in channel curvature and branching density; designs with complex or oscillatory flow paths promote stronger mixing but also increase viscous losses. In contrast, design A1 achieved the highest asymptotic concentration with the lowest pressure drop (Figure (iv)) showcasing its effective design in efficient mass transport with minimal flow resistance. Table S2 presents the maximum CO₂ concentration predicted by the model, along with the corresponding maximum pressure drop. A1 and D1 designs showcase a lower x_c value as compared to that of serpentine, indicating that the designs attain efficient gas utilization at a lower flow rate. In contrast, B4 requires a higher flow rate to achieve the same x _c value, indicating less effective gas utilization compared with other designs. Moreover, its relatively high pressure drop further reflects increased flow resistance, making it the least efficient among the designs evaluated. The parameter “k” ranges between 0.0603 and 0.0716, with C1 showing the highest value, suggesting a steeper transition and faster improvement in CO₂ availability on the catalyst surface among all the designs. It also has a moderate “a” value and low pressure drop, as shown in Figure (iii) suggesting that the design can achieve uniform gas distribution with minimal pressure drop and also at a faster rate. The serpentine flow pattern, used as the baseline for all comparisons, exhibits a moderate pressure drop owing to its unidirectional flow path, which could be mitigated by designing symmetric flow-field patterns that promote more uniform pressure distribution and reduced flow resistance across the geometry.

Considering all of the parameters derived from the model and the corresponding pressure drop values, A1 and C1 designs exhibit an optimal balance between mass transport efficiency and hydrodynamic performance. Both flow patterns ensure efficient CO₂ availability at the catalyst surface with a comparatively low flow resistance. They provide efficient CO₂ concentration on the catalyst surface with a minimal energy loss due to a low pressure drop. Conversely, D1 demonstrates superior CO₂ delivery at the catalyst surface through enhanced convective mass transfer but incurs significantly higher pressure drops, which can impose higher energy demands during operation. These results emphasize that the optimization of the flow-field pattern in CO₂ electrolyzers must carefully balance mass-transport enhancement against hydrodynamic losses. Consequently, the A1 and C1 designs emerge as promising candidates for scalable electrolyzer systems where both reactant utilization and energy efficiency are critical to achieving sustainable performance.

3.3. Implications for Scalable Electrolyzer Design

The present analysis underscores the potential of bioinspired flow patterns based on design perspective to achieve efficient CO₂ transport with minimal hydrodynamic losses. Hierarchical and interconnected vein networks, exemplified by the V. amazonica leaf and avian lung inspired designs, demonstrate superior flow uniformity, which directly enhances catalyst utilization and suppresses local concentration gradients. The bioinspired flow fields proposed in this study, particularly A1 and C1 provide a promising foundation for future experimental validation and scale-up efforts. Their capability to sustain high reactant accessibility at low energy input positions them as strong candidates for next-generation CO₂ electrolyzers that integrate both efficiency and sustainability.

4. Conclusion

In this study, we developed a Multiphysics model to evaluate bioinspired flow field designs for cathodic compartment of CO₂ electrolyzers, highlighting how bioinspired designs can enhance CO₂ mass transport and reduce the overall pressure drop for efficient working of the electrolyzers. We developed various designs inspired by V. amazonica, camel’s turbinate, avian lungs, and wave flow and observed that the designs inspired by V. amazonica leaf (A1) and avian lungs (C1) emerged as the most promising designs, achieving high average CO₂ concentration on the catalyst surface with minimal pressure drop. Their hierarchical and tapered channel structures facilitate effective reactant delivery and mitigate concentration gradients, thus enhancing catalyst utilization and selectivity. Conversely, while the wave flow (D1) design promoted superior convective mass transfer, it incurred a high pressure drop, illustrating the intrinsic trade-off between mixing enhancement and energy efficiency. A quantitative sigmoidal growth model was used to compare the designs, and the derived parameters confirmed the better performance of A1 and C1 design. Thus, this study demonstrates that adopting bioinspired designs can overcome key mass-transport limitations in CO₂ electrolyzers and reduce the pressure drop, paving the way for the development of scalable and energy-efficient electrochemical systems, bridging the gap between laboratory research and practical deployment.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.5c13375.

• Mesh-independence study; validation of the serpentine flow-field model, including spatial CO₂ distribution, CAD geometry, and literature-based validation results; CO₂ concentration profiles and corresponding zero-CO₂ catalyst-surface area analyses at different flow rates for designs A1, B4, C1, and D1; and comparative performance metrics and dimensional details of the investigated flow-field designs, including maximum average CO₂ concentration, pressure drop, and geometric parameters of the best-performing configurations (PDF)

The authors declare no competing financial interest.