Quantifying mass transport limitations in a microfluidic CO₂ electrolyzer with a gas diffusion cathode

Electrochemical CO₂ reduction (CO₂ER) using renewable energy is a promising pathway for sustainable chemical production. Traditional planar electrodes suffer from low current densities due to poor CO₂ mass transport. Gas diffusion electrodes (GDEs) offer a significant improvement by delivering CO₂ directly to the catalyst surface in the gas phase, enabling higher CO₂ conversion rates. However, the performance of GDE-based CO₂ electrolyzers is complex, influenced by coupled transport of gases, liquids, and ions, along with electrochemical reaction kinetics. Understanding these multi-physical processes is crucial for optimizing device design and performance. Continuum modeling provides a powerful tool to analyze these coupled processes and quantify their influence on the local chemical environment and overall performance of the electrolyzer. While previous 1D models have provided insights, they lack the ability to capture the in-plane concentration gradients. Recent 2D models have addressed this, but often with simplifying assumptions that limit their accuracy, particularly at high current densities. This study aims to develop a comprehensive 2D model that overcomes these limitations and provides a more accurate representation of the system's behavior, ultimately guiding the design of efficient and industrially relevant CO₂ electrolyzers.

Numerous studies have investigated CO₂ER, focusing on catalyst development and reactor design. Planar electrodes, while providing fundamental kinetic insights, suffer from mass transport limitations due to CO₂'s low solubility and diffusivity in aqueous electrolytes. GDEs offer a solution, providing a pathway to improve mass transfer by delivering CO₂ directly to the catalytic sites. 1D GDE models have been successful in explaining the enhanced mass transfer compared to planar electrodes, but fail to capture lateral concentration gradients. 2D models are emerging, but often rely on simplifying assumptions, like equilibrium water dissociation and constant Henry's constant, which are not valid at high current densities. This paper addresses the shortcomings of existing models by incorporating more comprehensive descriptions of the coupled transport and reaction processes.

A 2D volume-averaged model of a GDE integrated with electrolyte and CO₂ flow channels was developed using COMSOL Multiphysics. The model accounts for mass transport of gaseous and aqueous species, electrochemical reactions (COER and HER), homogeneous reactions (carbonate formation and water dissociation), and phase transfer reactions between gaseous and aqueous CO₂. Two catalyst layer (CL) wetting scenarios were considered: ideally wetted (I.W) and fully flooded (F.F). The model solves for species concentrations, electrode and electrolyte potentials, and flow fields using a coupled system of governing equations (Navier-Stokes for electrolyte flow, Darcy's law for gas flow in the GDE, Nernst-Plank for aqueous species transport, and a mixture-averaged diffusion model for gas-phase transport). Electrochemical reactions were modeled using Tafel kinetics, considering concentration dependence for COER and independence for HER. Homogeneous reactions were modeled using equilibrium constants and rate constants, and phase transfer reactions were modeled using mass transfer coefficients incorporating the Sechenov effect (for CO₂ solubility). The model was validated against experimental data from previous studies. The impact of operating parameters (applied potential, electrolyte flow rate, CO₂ flow rate) and CL properties (porosity, anisotropy in diffusivity) were systematically investigated through parametric sweeps.

The model accurately predicted the experimental CO PCD, particularly in the fully flooded CL scenario. The model revealed two distinct regimes: a kinetically controlled regime at lower potentials, followed by a mass transport controlled regime at higher potentials where CO PCD peaks before declining due to CO₂ depletion and decreased solubility resulting from increased ionic strength (OH^- and CO₃^2-). H₂ production remained relatively unaffected by mass transport. Increasing electrolyte flow rate significantly enhanced CO PCD (400% increase from 1 to 100 ml/min), while increasing CO₂ flow rate yielded a 50% increase but reduced conversion efficiency. 2D simulations revealed significant heterogeneity in current distribution, with most current generation concentrated near the CL-GDL interface. Introducing heterogeneity in CL porosity (exponentially increasing from 0.5 to 0.9 from bottom to top) improved current distribution uniformity and increased peak CO PCD. Increasing anisotropy in CL diffusivity in the x-direction (through-plane) alleviated mass transport limitations, leading to higher CO PCD and FE.

The findings highlight the significance of considering mass transport limitations in designing efficient CO₂ electrolyzers. The observed decline in CO PCD at high potentials is primarily attributed to the interplay between CO₂ consumption in electrochemical and homogeneous reactions, and the decrease in CO₂ solubility due to rising ionic strength. The model's ability to capture this behavior demonstrates the importance of incorporating detailed descriptions of coupled transport and reaction processes. The improved performance with increased flow rates underscores the necessity of optimizing fluid dynamics for efficient mass transfer. The impact of CL porosity and anisotropy reveals promising strategies for engineering improved electrode structures to address mass transport limitations and improve performance. These insights contribute to the development of more efficient and scalable CO₂ electrolysis technologies.

This study presents a comprehensive 2D model of a GDE-based CO₂ electrolyzer, accurately predicting experimental behavior and revealing crucial mass transport limitations. Strategies for improving performance, including adjusting electrolyte and CO₂ flow rates, CL porosity heterogeneity, and CL diffusivity anisotropy, are proposed and validated. Future work should focus on incorporating the ionomer layer in the model and expanding the model to consider the impact of bubble formation and two-phase flow.

The model makes several simplifying assumptions, including constant water concentration in the CL, which could overestimate OH^- production and affect pH predictions. The model also does not explicitly simulate bubble formation and two-phase flow. Furthermore, the kinetics of COER on silver nanoparticles were assumed to be the same as those on metallic silver foil, and the effect of temperature variations and electrode degradation were not explicitly included. While these assumptions enable efficient computations, it is important to note that their removal may lead to more accurate representations of the complex phenomena under consideration. Future studies should relax these constraints to gain more realistic insights.