Varicose dynamics of liquid curtain: Linear analysis and volume-of-fluid simulations

The varicose dynamics of gravitational liquid sheet flows issuing into a quiescent gaseous ambient is relevant for technological applications such as coating deposition, where varicose perturbations of the curtain shape can arise due to velocity fluctuations coming from the delivering pump placed upstream of the coating die. We investigate this problem using a one-dimensional linear model and two-dimensional nonlinear simulations, finding novel scaling laws for the curtain oscillation frequency and amplitude with the Weber number. Moreover, an interesting numerical break-up phenomenon of the curtain is outlined, driven by the progressive curtain thinning induced by the varicose disturbances.