The article by Bazant, Thornton, and Ajdari analyzes the response of a model micro-electrochemical system to a time-dependent applied voltage. The study begins with a historical review of electrochemistry, colloidal science, and microfluidics, followed by a detailed mathematical analysis of the system. The model consists of a symmetric binary electrolyte between parallel-plate, blocking electrodes, with compact Stern layers on the electrodes. The Nernst-Planck-Poisson equations are linearized and solved using Laplace transforms for small voltages, and numerical solutions are obtained for large voltages. The "weakly nonlinear" limit of thin double layers is analyzed using matched asymptotic expansions, revealing that the system initially behaves like an RC circuit with a response time of $\lambda_D L / D$. However, nonlinearity introduces multiple time scales, slowing down the charging process and coupling neutral-salt adsorption to bulk diffusion. In the "strongly nonlinear" regime, this effect produces bulk concentration gradients and transient space charge at very large voltages. The article concludes with an overview of more general situations involving surface conduction, multi-component electrolytes, and Faradaic processes.The article by Bazant, Thornton, and Ajdari analyzes the response of a model micro-electrochemical system to a time-dependent applied voltage. The study begins with a historical review of electrochemistry, colloidal science, and microfluidics, followed by a detailed mathematical analysis of the system. The model consists of a symmetric binary electrolyte between parallel-plate, blocking electrodes, with compact Stern layers on the electrodes. The Nernst-Planck-Poisson equations are linearized and solved using Laplace transforms for small voltages, and numerical solutions are obtained for large voltages. The "weakly nonlinear" limit of thin double layers is analyzed using matched asymptotic expansions, revealing that the system initially behaves like an RC circuit with a response time of $\lambda_D L / D$. However, nonlinearity introduces multiple time scales, slowing down the charging process and coupling neutral-salt adsorption to bulk diffusion. In the "strongly nonlinear" regime, this effect produces bulk concentration gradients and transient space charge at very large voltages. The article concludes with an overview of more general situations involving surface conduction, multi-component electrolytes, and Faradaic processes.