Measurements of the ion-depletion zone evolution in a micro/nano-channel

Ion-depletion and ion-enrichment are the most important phenomena found in a hybrid micro/nano-channel. This depletion process significantly decreases the ion concentration at the anodic end of the nano-channels and lower concentration propagation in the microchannel. The present paper focuses on measurement and analyzes the extension of the depletion zone with time and propagation of concentration perturbation. The systemic experiments were conducted using the nano-porous membranes with different pore diameters (ϕ15 nm, ϕ50 nm), the applied electric voltages (20–100 V) and the buffer solution pH values (pH 5.4, 9.2). According to dimensionless analysis, the extension of the depletion boundary was initially found to be independent of time and to have a non-linear variation for larger times. Based on Nernst–Planck equation, a one-dimensional wave equation is obtained under certain hypothesis, which also shows the propagation of concentration perturbation in depletion zone with constant speed at the initial time.