Abstract

We study the dynamics of a radial liquid sheet produced by head-on impingement of two equal laminar liquid jets, which find application in atomization processes ranging from spray painting to combustion.  While previous work has focused on the interaction between the surrounding gas phase with the liquid sheet to understanding the sheet dynamics, our work focuses on the importance of sheet thickness variations on the overall dynamics. To this end, we derive linear stability equations from the inviscid flow equations for a radially expanding sheet that govern the time-dependent evolution of the two liquid interfaces. The analysis accounts for the varying liquid sheet thickness while the inertial effects due to the surrounding gas phase are ignored. The analysis results in stability equations for the sinuous and the varicose modes of sheet deformation that are decoupled at the lowest order of approximation. When the sheet is excited at a fixed frequency, a small sinuous displacement introduced at the point of impingement grows as it is convected downstream suggesting that the disturbance grows at all Weber numbers ($We=\rho_l U^2 h/\sigma$) in the absence of the gas phase. Here, $\rho_l$ is the density of the liquid, $U$ is the speed of the liquid jet, $h$ is the local sheet thickness, and $\sigma$ is the surface tension. The predictions are compared with measurements, where we use a simple non-contact optical technique based on the laser induced fluorescence to measure the instantaneous local sheet thickness and its displacement over a range of forcing frequencies and $We$. When the impingement point is forced sinusoidally, sinuous waves produced close to the impingement point travel radially outward. The measured growth rate of the sinuous wave envelope and the phase speed match the predictions of our theory suggesting that for the range of $We$ considered in the study, the mechanism for the growth of sinuous waves in liquid sheets is primarily due to the thinning of the liquid sheet (and not due to air interactions).