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

The varicose dynamics of a forced gravitational liquid sheet (curtain) issuing into a quiescent gaseous ambient is numerically investigated in this work. The study is relevant for technological applications such as coating deposition, where varicose perturbations of the curtain interfaces can arise due to axial velocity fluctuations coming from the delivering pump placed upstream of the coating die. The investigation is performed in supercritical regime, namely, for Weber number We>1. Two methodologies are employed: a simplified one-dimensional (1D) linear model and two-dimensional (2D) volume-of-fluid simulations. Using harmonic forcing perturbations of the streamwise velocity applied at the inlet section, the curtain varicose dynamics is excited by varying the forcing frequency f and amplitude Au of the perturbations for different values of We. As a significant result, the 1D analysis reveals that the curtain oscillations amplitude reaches a maximum value for a certain forcing frequency f=fmax. In other terms, it is found that the flow manifests a resonance behavior, with the oscillation frequency fmax and corresponding amplitude Ah,max both scaling as We1/3, while the average wavelength λ¯max scales as We-1/3. These scaling laws are confirmed both by theoretical insights and 2D simulations. Moreover, it is found that the 2D curtain breaks up numerically by increasing the forcing amplitude Au. The numerical rupture is determined by a progressive curtain thinning induced by the varicose deformation, which moves upstream by increasing We, i.e., downstream by increasing the surface tension coefficient. In this respect, surface tension is found to play a stabilizing role on the varicose oscillations of the curtain.