Plateau–Rayleigh instability in a capillary: assessing the importance of inertia

Liquid plug formation in thin channels due to the Plateau–Rayleigh instability of a liquid film is observed in a variety of fields. In this paper, complementarity between theoretical solutions and direct numerical simulations (DNS) based on a front-tracking algorithm is explored to evaluate the importance of inertia for the case of a cylindrical capillary. A linear stability analysis is first performed and DNS results are then used to investigate the spatial distributions of inertial, convective and viscous terms of the Navier–Stokes equation. The existence of both viscous and inertial regimes is evidenced with a threshold given by the film thickness. The presence of the core fluid slows down the instability. In the viscous regime, predictions of the lubrication theory are verified. An example of liquid water as the outer fluid film and water vapour as the inner core fluid is simulated with application to the fuel cells.