The characteristic of precursor film in Navier-Stokes equations frame

This paper studies a model for a fluid lumpspreading with a precursor film. In the description, the fluid lump and theprecursor film are calculated as a whole using order parameter coupledNavier-Stokes equations, CHW (Cahn, Hilliard and van der Waales) equationand GNBC (Generalized Navier boundary condition). The fluid lump spreads underthe actions of certain long-range force -VW (van der Waals) intermolecularlong-range force, surface tension and viscous force. A film of nanoscopicthickness emerges as VW force reaches a certain value. The profile of thefilm after spreading a long time approaches to 1/x power law, which agreeswell with the theoretical results of Ref.1. The frontal position of thefilm is found to has a power-law dependence on time, which is also shown inthe results of some experiments6. The interfacial stretching has apower-law dependence on time as well. The exponent of the later is a littlebigger than that of the former.