Defocused shadowgraphy $\mu$PTV for analyzing the spreading mechanism of an impacting droplet onto a thin liquid film

This study investigates the flow of a radially spreading lamella, generated by a droplet impacting onto a thin liquid film. The use of shadow imaging based defocusing microparticle tracking velocimetry (SDμPTV) enables one to acquire time- and height-resolved radial velocity profiles. The post-processing method was optimized for this application so that the spatial position was determined from changes in particle image diameter relative to the focal plane. Thanks to a structured process that transforms raw measurements into interpretable scientific knowledge, it was possible to measure simultaneously the temporal evolution of the lamella thickness, the radial velocity profiles in two planes, and the rate of momentum transfer a<sub>r</sub> (t). To validate the measurements, a holistic approach is chosen that includes theoretical considerations and a direct comparison with experimental findings. An analytic expression is found that directly links the exponential decay of the function a<sub>r</sub> (t) to the decay of the pressure force, thereby matching the experimentally observed trends. Moreover, two distinct dissipative mechanisms are identified, namely shear losses in the boundary layer and dissipation losses due to deformation of the lamella in the vertical and radial direction. The latter, also termed biaxial extensional viscous dissipation, strongly hampers the capability of viscous fluids to radially expand, leading to an enhanced deceleration of the spreading lamella. The opposite occurs in low-viscosity fluids, where the radial expansion is basically unhindered and shear stresses represent the dominant mechanism for viscous dissipation.