Editors' Choice—Critical Review—Mathematical Formulations of Electrochemically Gas-Evolving Systems

Abstract

Electrochemically gas-evolving systems are utilized in alkaline water electrolysis, hydrogen production, and many other applications. To design and optimize these systems, high-fidelity models must account for electron-transfer, chemical reactions, thermodynamics, electrode porosity, and hydrodynamics as well as the interconnectedness of these phenomena. Further complicating these models is the production and presence of bubbles. Bubble nucleation naturally occurs due to the chemical reactions and impacts the reaction rate. Modeling bubble growth requires an accurate accounting of interfacial mass transfer. When the bubble becomes large, detachment occurs and the system is modeled as a two-phase flow where the bubbles can then impact material transport in the bulk. In this paper, we review the governing mathematical models of the physicochemical life cycle of a bubble in an electrolytic medium from a multiscale, multiphysics viewpoint. For each phase of the bubble life cycle, the prevailing mathematical formulations are reviewed and compared with particular attention paid to physicochemical processes and the impact the bubble. Through the review of a broad range of models, we provide a compilation of the current state of bubble modeling in electrochemically gas-evolving systems.

Oscillating Hydrogen Bubbles at Pt Microelectrodes

“…Alkaline water electrolysis is still the most mature and least platinum-consuming technology, albeit one suffering from inadequate efficiency. The latter can be increased by reducing the Ohmic losses [15][16][17][18][19] arising from the reduction of conductivity and the deactivation of the electrode by the nonconducting bubbles. If the hydrogen bubbles are to be transported away from the electrodes faster, this inherently requires a better understanding of bubble growth and detachment.…”

“…Tremendous efforts to resolve the growth dynamics of hydrogen bubbles during the past five decades have brought evidence on the growth law for the bubble radius R b ∝ t x , where the exponent is equal to 1=2 if the growth is controlled by the bulk diffusion of dissolved hydrogen and equal to 1=3 if the hydrogen injection occurs at the foot of the bubble and mostly by coalescence with smaller bubbles [20,21]. By contrast, the current understanding of the force balance [19,[22][23][24] does not cover the variety of existing observations. Among the unresolved phenomena, one of the most prominent is the sudden jump off of bubbles from the electrode, and their subsequent reattachment [25][26][27].…”

Influence of Bubbles on the Energy Conversion Efficiency of Electrochemical Reactors

“…This review introduces the reader to a growing body of interdisciplinary literature on the effects of bubbles in the energy and mass transfer efficiency of electrochemical systems. While previous reviews have focused on the mathematical modeling of electrochemical gas evolving systems or discussed the interactions of bubbles and electrocatalyst surfaces, 19,27,28 we provide a complementary viewpoint covering electrochemical engineering aspects of devices for the production of electrofuels and chemicals. Specifically, we will focus on hydrogen evolution in water electrolyzers given its relevance to energy research but most of the equations shown in the following sections are applicable for most gas evolving system.…”

3D‐QSAR, Molecular Docking and Molecular Dynamics Analysis of 1,2,3,4‐Tetrahydroquinoxalines as BRD4/BD2 Inhibitors

“…Density generalization theory (DFT) is part of a powerful tool for dealing with the electronic structure and geometry of interacting multi-electron systems [24] . In order to evaluate the electronic structure details of small molecule orbital energy levels and to accurately calculate various electronic properties, compounds were modeled on GaussView 6.0 and the relevant properties of small molecule compounds were investigated using density general-ization theory.…”