Using an extension of a recently developed model describing phase transformations based on a sharp interface [M. Buchmann, M. Rettenmayr, Scripta Mater. 57 (2007) 169], steady-state melting of an Al-Cu alloy is numerically modelled. The conditions are varied such that the 'contact conditions' range from local equilibrium to pronounced deviations thereof, corresponding to 'solute trapping' conditions during solidification. The rigorously derived model that includes realistic free energies ensures physical consistency and allows for the treatment of non-ideal systems. Aspects of the asymmetry between melting and solidification become apparent in the contact conditions, i.e. the concentrations at the interface in the liquid and solid phase, respectively, at elevated velocities. (c) 2008 Elsevier B.V. All rights reserved,