A model accounting for the role of convection in macroscopically immobile solutions (viz., not submitted to any macroscopic flow or any density gradient) is developed to predict the resulting alterations on electrochemical experiments performed at long time durations. The model is based on a seminal idea introduced by Levich, and shows that in macroscopically still solutions microscopic chaotic motion has the same effect as an apparent diffusion coefficient that depends on the distance from the electrode, x. When the electrochemical perturbation affects only the viscous sub-layer adjacent to the electrode, this apparent diffusion coefficient varies as x(4). The model remarkably predicts the experimental distortions of chronoamperometric currents from their ideal Cottrellian behavior. The model is thoroughly tested with success by comparing its predictions to experimental results (current and concentration profiles) obtained for the oxidation of Fe(CN)(6)(4-) in aqueous KCl.