Simple theory for the electrochemical study of reversible ion transfer processes at micro- and nano-liquid vertical bar liquid interfaces supported on a capillary is presented. Closed-form expressions are obtained for the response in normal pulse and differential double pulse voltammetries, which describe adequately the particular behaviour of these systems due to the 'asymmetric' ion diffusion inside and outside the capillary. The use of different potential pulse techniques for the determination of the formal potential and diffusion coefficients of the ion is examined. For this, very simple analytical expressions are presented for the half-wave potential in NPV and the peak potential in DDPV. (C) 2014 Published by Elsevier B.V.