Revisiting viscoelastic liquid films flowing down a slippery substrate: Linear and nonlinear viscoelastic waves

Abstract

This paper revisits the flow of a viscoelastic film on a slippery substrate (Phys. Rev. Fluids 7 (6), 064007, 2022) using the Navier-slip boundary condition, ${\tau }_{xz}=\lambda u$ ($\lambda$ represents the friction coefficient of the substrate). Here, ${\tau }_{xz}$ represents the total tangential shear stress, comprised of both a viscous and an elastic component. A model equation for the film thickness is derived based on the long-wave theory. The study investigates both the linear and nonlinear dynamics of the film flow. It reveals that the presence of a slippery substrate and viscoelasticity promote the instability of linear viscoelastic waves. Additionally, they affect the speed and height of nonlinear viscoelastic waves. Our present study suggests that neglecting the elastic component of ${\tau }_{xz}$ at the slippery wall could result in an overestimation of the linear stability threshold while underestimating the speed and height of nonlinear waves.