Columnlike free-interface flows: symmetry breaking and linear instability

This thesis is dedicated to the analysis of a subclass of interfacial flows, columnlike free-interface flows, from two view angles: (i) the symmetry breaking under geometry-induced or external forces, (ii) their stability against infinitesimal disturbances. We employ the domain perturbation method to address three flow types by means of linear stability analysis. First, we examine the flow down an eccentric vertical fibre: the non-axisymmetric base flow brings interfacial shear into play to deform the capillary-driven Rayleigh-Plateau modes. A large enough eccentricity destabilises extra whirl modes despite the surface energy barrier to coil the interface. The linear analysis concludes according with our experiments that the combination of a thin fibre (with respect to the liquid column), a large Bond number ($Bo$, that compares gravitational forces with surface tension), and large eccentricity leads to the destabilisation and dominance of the whirl mode. We secondly study numerically and theoretically the draining liquid film coating the inside of a horizontal tube at moderate $Bo$. The buoyancy-driven rising interface deforms as $Bo$ increases, and a large enough deformation can suppress the Rayleigh-Plateau instability at large times. The linear analysis seconds pre-existing experiments in the literature, showing that the critical stabilising $Bo$ increases with the average film thickness, irrespective of finite inertia and transient growth of the perturbations. Thirdly, we explore the draining film down a horizontal cylinder, a configuration suitable for the co-existence of the Rayleigh-Plateau and Rayleigh-Taylor instabilities. The base flow either reaches a quasi-static pendant equilibrium or keeps falling until a two-dimensional rupture occurs. Nonlinear simulations suggest that the critical $Bo$ to maintain a pendant curtain scales inversely with mean film thickness. The resulting quasi-static state is linearly unstable and the collective action of capillary and gravitational effects can form two distinct patterns: (i) pearls enveloping the cylinder when surface tension dominates, (ii) vertical fingers underneath the cylinder when gravity dominates. The most linearly amplified mode will either form an array of pendant drops or result in a three-dimensional rupture, a threshold found unaffected by the transient growth of the perturbations. Lastly, we inspect numerically an electrified liquid jet falling vertically from a nozzle by coupling the flow and electric field equations. When electrical forces dominate surface tension (at large electric Bond number), the interface smoothly transitions to a conical meniscus at the nozzle tip emitting a fine jet downstream. This is due to the tangential electrical stress at the interface that folds the streamlines in the vicinity of the nozzle tip. Further raising the electrical Bond number reinforces the thinning, increases the cone half-angle, and sets in a recirculating cell at the nozzle tip to conserve the flow rate.