A class and home problem on electrolyte transport: constant electric field implies electroneutrality, but electroneutrality does not imply a constant electric field

TL;DR

This paper clarifies that while electroneutrality is necessary, it does not guarantee a constant electric field, using electrochemical models and problems for educational purposes.

Contribution

It introduces a teaching problem demonstrating that electroneutrality does not imply a constant electric field in electrochemical systems.

Findings

Electroneutrality is necessary but not sufficient for a constant electric field.

A closed-form solution illustrates the relationship between concentration, potential, and electric field.

Educational problems clarify misconceptions in electrochemical transport phenomena.

Abstract

We present a class and home problem in graduate transport phenomena and electrochemical engineering that clarifies a common misconception: electroneutrality implies the electric field is constant. Starting with one-dimensional Poisson--Nernst--Planck equations for a silver electroplating cell, students obtain concentration and potential profiles. A companion home problem with added background electrolyte introduces a new dimensionless ratio and admits a closed-form solution. Students conclude that electroneutrality is necessary but not sufficient for a constant electric field.