We looked for conditions to carry out the electrodeposition of metal nanowires in ion track-etched polycarbonate membranes under diffusion control, to facilitate contrasting experimental results with a suitable mathematical model taking into account the various mechanisms of mass transport during the successive stages of the process. Such conditions were found electrodepositing Cu nanowires from 0.05 M CuSO4, 2 M Na2SO4 and 0.5 M H2SO4 solution at -500 mV vs Cu/CuSO4 in 20 mu m thick membranes, with the working electrode in the upper side of the cell and nanowires growing downwards, toward the gravitational field. We described the growth of nanowires in terms of the evolution of the diffusion fields inside the pores considering mass transport control under four possibilities; linear flux within the pores; localized hemispherical fluxes at the mouths of the pores; semi-infinite linear diffusion to the entire electrode surface, and mixed diffusive-convective flux to the electrode. After analyzing the different stages of advance of the diffusion fronts we found that under these experimental conditions the onset of a natural-convective instability is unavoidable before completing the growth of nanowires within the pores. (C) 2014 The Electrochemical Society.