Universal self-similar attractor in the bending-driven levelling of thin viscous films

We study theoretically and numerically the bending-driven levelling of thin viscous films within lubrication approximation. derive Green’s function linearized thin-film equation further show that it represents a universal self-similar attractor at long times. As such, rescaled perturbation film profile converges in time towards function, for any summable initial profile. In addition, stepped axisymmetric conditions, we demonstrate existence another, short-term one-dimensional-like regime. also characterize convergence long-term terms relevant physical geometrical parameters, provide local hydrodynamic fields global elastic energy regime as functions time. Finally, extend our analysis to nonlinear through numerical simulations.