Free surface topography of capillary flows using spatiotemporal phase shifting profilometry

We present a novel experimental technique for characterizing the free surface of capillary flows using the spatiotemporal phase shifting profilometry (ST-PSP) method. This study specifically addresses various regimes of capillary flows over inclined surfaces, including drops, rivulets, meanders, and braided films. The technique is explained step by step with a detailed discussion of the calibration process, which is carried out on a solid wedge to determine the optical distances required for the phase-to-height relationship. In addition, the minimal dye concentration for accurately reconstructing the free surface of a dyed water flow is investigated. The ST-PSP method is then applied to profile different liquid flows, achieving large signal-to-noise ratios in all experiments. Notably, the analysis of a sessile droplet shows excellent agreement between the ST-PSP results and side-view visualizations, as demonstrated by the precise recovery of its apparent contact angle. Moreover, free surface reconstructions of rivulet flows align well with previous theoretical predictions. These findings suggest that the ST-PSP method is highly effective for obtaining precise height maps of capillary flows, offering a valuable tool for future validation of theoretical models.