What are steric effects? A purely continuum model

In electrolyte solutions, the application of an external voltage elicits a series of complex microscopic phenomena. When there is no charge transfer between solution and electrodes (non-Faradaic processes), an extremely thin electric double layer is formed on each of the electrodes, screening the bulk of the solution from the external electric field. In the simplest double layer models, the volume of ions in the solution is neglected. For relatively small voltage values, one can easily reach values of concentrations in the double layers over the physical packing limit. To address this issue, steric effects associated with the finite volume of ions are introduced, toward limiting the maximum concentration in the double layers. These effects are often introduced at a microscopic scale, through modifications of the entropy of mixing. However, the macroscopic interpretation of these models remains elusive. Here, we propose a purely continuum model of steric effects in electrolyte solutions. We show that including steric effects at a microscopic scale is equivalent to requiring that each constituent of the solution is incompressible at a macroscopic level. Incidentally, the macroscopic model easily extends steric effects to multiple ions of different sizes, a challenging task for microscopic models. We highlight the consequences of our model on electrolyte solutions and ionic membranes. In particular, we show how our model constitutes a simple mathematical formulation for actuators with ionic liquid solvents. Our effort supports the creation of physics-based models of ionic actuators, facilitating their mathematical description.