The electrochemical processes in electrolytic cells are the basis for modern energy technology such as batteries. Electrolytic cells consist of an electrolyte (an salt dissolved in solution), two electrodes, and a battery. The Poisson–Nernst–Planck equations are the simplest mathematical model of steady state ionic transport in an electrolytic cell. We find the matched asymptotic solutions for the ionic concentrations and electric potential inside the electrolytic cell with mass conservation and known flux boundary conditions. The mass conservation condition necessitates solving for a higher order solution in the outer region. Our results provide insight into the behaviour of an electrochemical system with a known voltage and current, which are both experimentally measurable quantities.

Join bestselling author Simon Singh and Oxford mathematician turned educator Junaid Mubeen for a session on maths communication! Learn how to present mathematics in a way that is both accessible and engaging, and how to apply these principles in a teaching context. Simon and Junaid will draw on their experiences in the Parallel Academy https://parallel.org.uk, an online initiative they set up in 2023, which has since grown to support thousands of keen and talented students to pursue maths beyond the curriculum. 

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