A new elastic instability in gravity-driven viscoelastic film flow

We examine the linear stability of gravity-driven flow a viscoelastic fluid film down an inclined plane. The is modeled using Oldroyd-B constitutive equation and, therefore, exhibits constant shear viscosity and positive first normal stress difference in viscometric shearing flows; latter class flows includes aforesaid film-flow configuration. show that configuration susceptible to two distinct purely elastic instabilities inertialess limit. instability owes its origin entirely existence free surface has been examined earlier [Shaqfeh et al., “The gravity driven at low moderate Reynolds number,” J. Non-Newtonian Fluid Mech. 31, 87–113 (1989)]. second one analog centermode recently discovered plane Poiseuille [Khalid “Continuous pathway between elasto-inertial turbulent states channel flow,” Phys. Rev. Lett. 127, 134502 (2021)] base-state shear; it example with rectilinear streamlines. One may draw analogy pair unstable modes inertial free-surface shear-driven known for analogous Newtonian fluid. While tension expected stabilizing effect on modes, corresponding is, surprisingly, more complicated. For both mode centermode, plays dual role, there being parameter regimes where acts as destabilizing influence. remains limit vanishing tension, becomes only when appropriate non-dimensional exceeds threshold. In infinitely dominant, boundary conditions reduce centerline symmetry satisfied by flow. As result, regime identical original channel-flow centermode. At intermediate values parameter, however, exist even counterpart stable. end discussion added role inertia aforementioned instabilities.