Gravity-driven flow of a viscoelastic liquid film along a vertical wall

The hydrodynamics of steady laminar film flow of a viscoelastic fluid down a vertical wall is considered. The rheological model used is known as Walters' liquid B ´´ and exhibits normal-stress differences even in simple shear flows. The equations governing the fluid motion are subject to boundary-layer type approximations. The momentum integral approach is then adopted to obtain the variation of film thickness with distance in the flow direction. The resulting analytical expression for the film thickness reveals that viscoelastic films develop more rapidly than Newtonian liquid films towards the downstream asymptotic state.