Electroconvective Instability in annular geometry

Electroconvective instability associated with concentration polarization near a charge selective interface in the overlimiting current, has been extensively studied in the past years. These theoretical studies mainly rely on the parallel electrodes geometry where the concentration profile of electrolyte is linear in the electro-neutral bulk region. But less has been explored in an annular geometry (inner electrode at R₁ and outer one at R₂), in which the concentration profile is logarithmic in the electro-neutral bulk. Consequently, the limiting current depends on both the direction of electric field and the radius ratio R₁/R₂. When the inner electrode radius R₁ is much larger than the Debye length ε, the electro-osmotic slip at a charge selective interface is similar to the one in parallel electrodes geometry. By employing the slip formula and Nernst-Plank equations, we perform a linear stability analysis of the quiescent electric conduction in annular geometry.