A long-wave model for a falling Upper Convected Maxwell film inside a tube

In this talk, a long-wave asymptotic model will be presented for a viscoelastic falling film along the inside of a tube; viscoelasticity is incorporated using an Upper Convected Maxwell model. The dynamics of the resulting model in the inertialess limit are determined by three parameters: Bond number, Weissenberg number, and a film thickness parameter. The free surface is unstable to long waves due to the Plateau-Rayleigh instability; linear stability analysis of the model equation quantifies the degree to which viscoelasticity increases both the rate and wavenumber of maximum growth of instability. Elasticity also affects the classification of instabilities as absolute or convective, with elasticity promoting absolute instability. Numerical solutions of the nonlinear evolution equation demonstrate that elasticity promotes plug formation by reducing the critical film thickness required for plugs to form. Turning points in traveling wave solution families may be used as a proxy for this critical thickness. By continuation of these turning points, it is demonstrated that in contrast to Newtonian films in the inertialess limit, in which plug formation may be suppressed for a film of any thickness so long as the base flow is strong enough relative to surface tension, elasticity introduces a maximum critical thickness past which plug formation occurs regardless of the base flow strength.