Micro-electro-mechanical (MEMS), plasma or powder spray deposition, surface coating, semiconductor technology, splat cooling, single and twin-roller melt-spinning, strip and slab casting, melt-extraction, etc. are usually characterized by solidification of a thin liquid layer on a cold substrate. A one-dimensional model of enthalpy formation of the energy and species conservation equations with thermodynamic relationships from ternary equilibrium diagram are solved to study the solidification processes for ternary alloys molten liquid layer on the ternary eutectic solid substrate. The solidification path of the liquid layer may pass through the primary, cotectic and eutectic solidification regions. The melting and re-solidification of the substrate happens at the ternary eutectic point. The thermal physical properties of the splat and substrate are identical and imperfect contact of contact surface between the splat and substrate is considered. The temperature functions as compositions are assumed as linear along the liquidus surface and cotectic curves. The temperature distributions of the solidified splat and the melted, re-solidified substrate, the thicknesses of the different mushy layers of splat and melting of substrate subject to different process parameters and thermal physical properties are quantitatively and extensively investigated. The initiation times for primary, cotectic mushy and eutectic solid fronts of splat and the complete re-solidification times of the substrate are affected by different parameters, these are also investigated. Results of this study are compared with experimental data provided by Aitta et al. The growth rates of the cotectic and eutectic fronts are found to agree well with experimental data. The effects of initial solute concentrations of liquid layer, solute concentrations and temperatures at the binary and ternary eutectic points on the thicknesses of different mushy layers are important and presented. (c) 2006 Elsevier Ltd. All rights reserved.