Spatiotemporal Filter Velocimetry With Arbitrary-Shaped Measurement Region For Accurate Measurement In The Vicinity Of A Boundary

Abstract

Viscous stress at a boundary or an interface is a source of drag acting on a body or a fluid particle and therefore its measurement is of great importance for understanding the motion of the body or the fluid particle. In this study, spatiotemporal filter velocimetry (SFV: Hosokawa & Tomiyama, 2012) is extended to arbitrary quadrilateral measurement areas fitted to an interface shape for accurate measurement of flow about a deformed drop, and it is applied to flows about single drops of glycerol-water solution falling in stagnant silicon oil under clean and contaminated conditions. Figure 1 shows the trajectories of tracer particles and the measured velocity distributions. No separation is observed for the spherical and ellipsoidal drops. On the other hand, the stagnant region is observed in the dimple region of the tail of the cap drop. These results clearly indicate that the flow about the deformed drop is successfully measured by SFV with arbitrary quadrilateral measurement areas. Figure 2 shows the trajectories of tracer particles and the measured velocity distributions of single ellipsoidal drops in clean and contaminated systems. Triton X-100 was used as the surfactant and its concentration C in the drop ranges from 0.0 to 0.1 mol/m3 . The drop tail becomes flat and then slightly dimpled shape, and the internal circulation becomes weak as C increases. The internal circulation remains even at the high surfactant concentration condition under which the internal circulation in single spherical drop is fully damped (Hosokawa et al., 2017). We also evaluate interfacial velocity, interfacial shear stresses, the Marangoni stress and surfactant concentration at the interface from measured velocity distributions in the vicinity of the interface. As a result, we confirmed that SFV enables us to measure velocity distribution about a single deformed drop and enables us to evaluate interfacial velocity, interfacial shear stresses, the Marangoni stress and surfactant concentration at the interface.