Trajectory analysis of a liquid filament under Rayleigh breakup conditions created from laminar rotary spraying of oil-in-water emulsions

- High-speed video data from a rotary sprayer's laminar liquid filament were analyzed.
- Filament Plateau-Rayleigh instabilities were traced across high-speed video frames.
- Fluid velocity and dominant forces were determined from tracking instabilities.
- The liquid filament arc-shape is described using parametric equations.
- The model was validated against image data and was in good agreement.

A liquid jet resulting from the laminar rotary spraying of an oil-in-water emulsion (O/W) with a zero shear viscosity of 60 mPa s and a surface tension on the order 40 mN/m has been studied by means of a high-speed camera. The liquid flow rate and rotational speed of the rotary sprayer are tuned so that the liquid filament breaks up into droplets under Rayleigh breakup conditions. From the high-speed imagery we consider in detail the dominant forces, which define the shape of the liquid jet near the nozzle exit. We use the formation of Rayleigh disturbances as a tracing mechanism across multiple high-speed video frames to determine the role that rotational forces, surface tension, viscous forces and wind resistance play on the shape of the liquid filament as well as the formation of resulting droplets. From this analysis it is determined that rotational forces play the dominant role, thus resulting in a simplified parametric model of the liquid jet trajectory based on the Rossby number only. This model is compared to a previous model defined in the Frenet-Serret frame of reference and shown to be the same under our simplifying assumptions. Image analysis of the liquid filament trajectories shows that the assumptions made in the model are valid under the experimental conditions considered here.