The Nernst-Planck-Poisson (NPP) finite difference method is used to simulate a moving boundary experiment of an aqueous system with HCl and CdCl2 salts, as used to determine the transference number of H+ according to the classical method [D. A. MacInnes et al., Chem. Rev. 11 (1932) 171-230]. Theoretical predictions used in inferring transference numbers from moving boundary experiments are confirmed, and the presence of charge separation in the vicinity of the moving boundary is demonstrated. This is the first simulation of the moving boundary experiment using a full NPP scheme. (C) 2011 Elsevier B. V. All rights reserved.