Shifting and breakup instabilities of squeezed elliptic jets

Abstract

Liquid jets are inherently unstable and breakup into drops due to capillary instability driven by surface tension. Elliptic jets have been studied and reported to be more unstable than circular jets. The reason for their increased instability has been often ascribed to the axis-switching of elliptic jets. We theoretically elucidate, for the first time, that even in the absence of axis-switching, an elliptic jet exhibits greater instability compared to circular jets solely due to interfacial curvature effects. For this purpose, we analyse the stability of a jet with elliptic cross-section subject to a non-uniform ambient pressure. This azimuthally dependent pressure distribution in the ambient fluid helps to prescribe a static base state for the elliptic jet and maintain the azimuthally varying curvature of the interface. Physically, this mathematical treatment implies that the jet is squeezed into an elliptic configuration by a non-uniform pressure distribution in the passive ambient fluid and therefore cannot exhibit axis-switching. The jet is assumed to be incompressible and inviscid. The stability of such a jet is analyzed using Rayleigh’s Work Principle (RWP) and linear stability theory. It is also shown that in addition to capillary breakup, analogous to that of classical circular jets, squeezed elliptic jets are found to exhibit a shifting mode instability, in which the entire jet translates parallel to its major axis. Both capillary breakup and shifting modes are rendered more unstable by an increase in ellipticity. For low ellipticity, the breakup mode exhibits higher growth rates as compared to the shifting mode. We show that there exists a critical ellipticity beyond which the shifting mode starts to dominate the capillary breakup mode. Predictions from both RWP and linear stability theory converge to Rayleigh’s classic results for a circular cylindrical jet.