Surface tension-induced instability in spatially developing subcritical liquid curtains

Abstract

An energy budget approach based on numerical simulations of a linear low-order model, combined with linear global stability analysis, is used to investigate the unsteady dynamics of subcritical (We < 1) gravitational liquid sheet flows. It is found that surface tension is the physical mechanism responsible for the modal flow instability as the Weber number is progressively decreased down to a critical threshold Weth for which the sheet is entirely subcritical. A transient algebraic growth of the perturbation characterized by the power law t13 is found in both asymptotically stable (Weth<We<1) and unstable (We<Weth) conditions. This finding agrees with a previous result of the literature obtained by employing a local spatiotemporal stability technique (for an infinite domain) for which in the subcritical regime an absolute instability occurs. However, in the present study, the temporal evolution of disturbances in the unstable case eventually follows an asymptotic modal growth, which is also recovered in the eigenvalue spectra evaluated using linear stability analysis. Asymptotic stability of the flow detected in the range Weth<We<1 is not caused by the damping effect of viscosity, but by the energy exchanges through the domain boundaries. Surface tension-induced instability is further studied by means of parametric analysis involving the Froude number Fr and the slenderness ratio parameter ε. It is found that decreasing ε and increasing Fr have the same destabilizing effect. The present work represents a further step toward a deeper understanding of liquid sheet dynamics in the subcritical regime, with the aim of providing a theoretical background to establish connections between results of two-dimensional modeling and three-dimensional observations of real occurrence.