Global linear stability analysis of falling films with inlet and outlet

In this paper, the stability of falling films with different flow conditions at the inlet is studied. This is done with an algorithm for the numerical investigation of stability of steady-state solutions to dynamical systems, which is based on an Arnoldi-type iteration. It is shown how this algorithm can be applied to free boundary problems in hydrodynamics. A volume-of-fluid solver is employed to predict the time evolution of perturbations to the steady state. The method is validated by comparison to data from temporal and spatial stability theory, and to experimental results. The algorithm is used to analyse the flow fields of falling films with inlet and outlet, taking the inhomogeneity caused by different inlet conditions into account. In particular, steady states with a curved interface are analysed. A variety of reasonable inlet conditions is investigated. The instability of the film is convective and perturbations at the inlet could be of importance since they are exponentially amplified as they are transported downstream. However, the employed algorithm shows that there is no significant effect of the inlet condition. It is concluded that the flow characteristics of falling films are stable with respect to the considered time-independent inlet conditions.