By assuming a balance in molar flux at a solid-liquid interface layer with thickness delta in a binary liquid alloy, we study the interfacial instability and a critical radius of a homogeneous nucleation. The interfacial instability criterion, the periodic width of the cellular interface and the limit of absolute stability front the present model, were compared with those from Mullins-Sekerka's theory. Moreover, from the molar flux balance, we derive the Gibbs-Thomson (G-T) effect, which are mostly equivalent to those in the classical theory. (C) 2004 Elsevier B.V. All rights reserved.