Despite significant recent progress, dense, time-resolved imaging of complex, non-stationary 3D flow velocities remains an elusive goal. In this work we tackle this problem by extending an established 2D method, Particle Imaging Velocimetry, to three dimensions by encoding depth into color. The encoding is achieved by illuminating the flow volume with a continuum of light planes (a "rainbow"), such that each depth corresponds to a specific wavelength of light. A diffractive component in the camera optics ensures that all planes are in focus simultaneously. With this setup, a single color camera is sufficient for tracking 3D trajectories of particles by combining 2D spatial and 1D color information. For reconstruction, we derive an image formation model for recovering stationary 3D particle positions. 3D velocity estimation is achieved with a variant of 3D optical flow that accounts for both physical constraints as well as the rainbow image formation model. We evaluate our method with both simulations and an experimental prototype setup.

We investigate experimentally the breakup of the Edgerton crown due to Marangoni instability when a highly viscous drop impacts on a thin film of lower-viscosity liquid, which also has different surface tension than the drop liquid. The presence of this low-viscosity film modifies the boundary condition, giving effective slip to the drop along the solid substrate. This allows the high-viscosity drop to form a regular bowl-shaped crown, which rises vertically away from the solid and subsequently breaks up through the formation of a multitude of Marangoni holes. Previous experiments have proposed that the breakup of the crown results from a spray of fine droplets ejected from the thin low-viscosity film on the solid, e.g. Thoroddsen et al. (J. Fluid Mech., vol. 557, 2006, pp. 63–72). These droplets can hit the inner side of the crown forming spots with lower surface tension, which drives a thinning patch leading to the hole formation. We test the validity of this assumption with close-up imaging to identify individual spray droplets, to show how they hit the crown and their lower surface tension drive the hole formation. The experiments indicate that every Marangoni-driven patch/hole is promoted by the impact of such a microdroplet. Surprisingly, in experiments with pools of higher surface tension, we also see hole formation. Here the Marangoni stress changes direction and the hole formation looks qualitatively different, with holes and ruptures forming in a repeatable fashion at the centre of each spray droplet impact. Impacts onto films of the same liquid, or onto an immiscible liquid, do not in general form holes. We furthermore characterize the effects of drop viscosity and substrate-film thickness on the overall evolution of the crown. We also measure the three characteristic velocities associated with the hole formation: i.e. the Marangoni-driven growth of the thinning patches, the rupture speed of the resulting thin films inside these patches and finally the growth rate of the fully formed holes in the crown wall.

We use structured monochromatic volume illumination with spatially varying intensity profiles, to achieve 3D intensity particle tracking velocimetry using a single video camera. The video camera records the 2D motion of a 3D particle field within a fluid, which is perpendicularly illuminated with depth gradients of the illumination intensity. This allows us to encode the depth position perpendicular to the camera, in the intensity of each particle image. The light intensity field is calibrated using a 3D laser-engraved glass cube containing a known spatial distribution of 1100 defects. This is used to correct for the distortions and divergence of the projected light. We use a sequence of changing light patterns, with numerous sub-gradients in the intensity, to achieve a resolution of 200 depth levels.

CitationFunctional integrity of flexible n-channel metal-oxide-semiconductor field-effect transistors on a reversibly bistable platform 2015, 107 (17):174101 Applied Physics Letters

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