In this paper, the liquid–vapour–solid system near triple-phase contact line in a microchannel heat sink is studied numerically. Molecular dynamics (MD) method is employed aiming to get a microscopic insight into the complex liquid–vapour–solid system. In the present model, the Lennard-Jones potential is applied to mono-atomic molecules of argon as liquid and vapour, and platinum as solid substrates, to perform a simulation of non-equilibrium molecular dynamics. The results of numerical simulation suggest that for a completely wetting system of mono-atomic fluid and substrates, there is a non-evaporating liquid film with thickness in nanometres existing on the heating solid surface. The film thickness in the triple-phase contact line under different conditions of substrate temperature is predicted. The thickness of such an ultra-thin liquid film varies only slightly with the number of argon molecules but decreases with the increase of heating substrate temperature. The potential energy in the thin liquid film decreases considerably toward the heating wall; this indicates that the interactions of solid and liquid molecules are very strong.