Analysis of Contact Occurrence in Fluid–Structure Interaction System Under the Thin Film Approximation

Abstract

In this paper, we consider the interactions between a 2D film of an incompressible viscous fluid deposited on a solid substrate and an elastic 2D structure delimiting the upper boundary of the film. The system is strongly coupled since we assume continuity of velocities and normal stresses at the fluid/structure interface. A general model including a fractional power of the laplacian is chosen to model the structure dynamics. We derive two asymptotic models in the thin film approximation depending on the relative size of the structure mechanical parameters. We then discuss the influence of the power exponent on possible collapse of the film in the various reduced models.