Influence of spatial curvature of a liquid jet on the rainbow positions: Ray tracing and experimental study

•Rainbows of a liquid jet with spatial curvature are analyzed experimentally.•A ray tracing method based on VCRM for explaining the interaction mechanism of the rays with the liquid jet is proposed.•The ray tracing method is flexible and can be applied to the light scattering of arbitrary 3D particles with complex shapes.•The spatial curvature of jet is responsible for the shifts of the rainbow positions.

Rainbow refractometry is largely used in optical metrology of particles thanks to its advantages of being non-intrusive, precise and fast. Many authors have contributed to its development and the application in the characterization of liquid jets/droplets. The researches reported in the literature are mainly for the spherical droplets or the liquid jets which can be considered as a cylinder of constant section. However, the section of a real liquid jet, even in the simplest configuration, varies with distance from the exit. The influence of the spatial curvature of the jets must, therefore, be taken into account. In this paper, we report experimental measurements of the shifts of the rainbow positions in the horizontal and vertical directions of a liquid jet and the theoretical investigation with the vectorial complex ray model. It is shown that the shifts of rainbow positions are very sensitive to the spatial curvature of the jets. This work is hoped to provide a new approach to characterizing the structure and the instability of liquid jets.