Measurements of sinuous waves on mechanically forced radially expanding free planar liquid sheets using chromatic confocal measurements

The chromatic confocal measurement technique is used to investigate the dynamics of radially expanding free liquid sheets generated by liquid jet impingement onto the flat end of a harmonically excited cylinder. Measurements of the sinuous-mode capillary waves are compared to experimental results reported by Bremond et al. (2007) and analytical solutions from two inviscid linear theories: The "aerodynamic (wave-growth)" theory by Bremond et al. (2007), which considers the interaction between the liquid film and the surrounding gas phase, and the linear theory by Tirumkudulu and Paramati (2013) which neglects the gas phase surrounding the liquid sheet but predicts growth of forced sinuous disturbances due to higher-order inertia terms associated with the thinning of the radially expanding sheet ("thinning" theory). For liquid Weber numbers Wed based on impinging jet velocity and jet diameter which are larger than 800 and aerodynamically stable forcing conditions, agreement with "thinning" theory is found in terms of radial positions of nodes and anti-nodes of the sheet disturbance envelope as well as growth of envelope maxima and minima. However, absolute amplitude values are significantly overpredicted in this case. For all other investigated operating conditions where instability due to film thinning is expected to dominate film dynamics (according to "thinning theory"), no such instability was observed experimentally. For most investigated cases, "aerodynamic wave-growth" theory agreed better with the experimentally observed film behavior. The importance of the naturally most-amplified aerodynamic mode was considered but could not be quantified as part of the present investigation.