Theoretical Studies of Liquid Sheet Interfacial Instabilities Pertinent to Air Assisted Water and Acoustically Modulated Ink Mixtures

Abstract

The study focuses on the theoretical characterization of interfacial instability in the Rayleigh zone of water sheet in the presence of co-flowing air and acoustically modulated ink-jet mixtures in stagnant ambient. The present analytical models are based on linear stability theory to predict the temporal progression of sinusoidal (anti-symmetrical) and dilatational (symmetrical) perturbations for gas Weber number (Weg) less than 0.4. The first model is a modified version of KelvinHelmholtz (K-H) instability that includes the effects of surface tension and viscous forces, whereas the second model a refined version of the former destined for ink jet printing applications. In the framework of ink jet printing applications, the previous model has been restructured for stagnant ambient conditions by including the contribution of acoustic forcing. Both analyses extract the complex variable that describes the corresponding phase velocity and the amplification factor for the introduced Fourier modes of perturbation. Utilizing this information, the critical wavelength that ultimately leads to the disintegration of a liquid sheet can be delineated and thereby the associated breakup frequency can be obtained. The frequency plot for the air-assisted model reveals funnel-like behavior that exhibits a cross-over tendency by the sinusoidal mode as the Weber number reaches the upper limit of the Rayleigh zone. In other words, by considering the breakup frequency as the benchmark for instability, the supremacy of dilatational instability has been established. The high-speed flow visualization studies carried out to validate the theoretical models elucidated the existence of a low-frequency (primary) and high-frequency (intermediate) breakup processes. The low-frequency event matches with the sinusoidal mode, whereas the high frequency has been traced by the dilatational mode. It has to be noted that, the empirical average breakup frequency tracks reasonably well with the dilatational data. The present work distinguishes..