3D-3C measurements of flow reversal in small sessile drops in shear flow

Abstract

Sessile drops play an important role in nature and the operation of many technical and biological systems as for instance fuel cells, cleaning processes, lab-on-a-chip devices and single-cell analysis. Nonetheless, their dynamic behavior in a shear flow is still not fully understood (e. g. detachment mechanism). Challenges exist regarding the precise simulation of two-phase flows as well as difficulties in conducting flow measurements with sufficient temporal resolution of more than 1 kHz. In this article, we present the first three-dimensional flow measurements in strongly oscillating drops stemming from a shear flow by using a monocular 3D localization microscope based on a Double-Helix Point Spread Function combined with Particle Tracking Velocimetry. The high temporal resolution and the large measurement volume - in terms of microscopy - make it possible to measure the time- and phase-averaged flow in small drops with Bond numbers ($\mathrm{Bo}$) smaller than 1. Water drops were placed in an air flow channel and measurements were conducted for Reynolds numbers (${\mathrm{Re}}_d$) from about 750 to 1700. Our measurements show that the results of previous investigations for drops with $\mathrm{Bo}>1$ concerning vortex pattern and flow reversal inside the drop apply for smaller drops as well. In addition, we are able to reveal the three-dimensional flow structure and multiple vortex-pattern in time and space. We discover a periodic 3D vortical flow pattern that corresponds to the first and second eigenfrequency of the drop. Moreover, we demonstrate the potential of adaptive optics to correct measurement errors stemming from time-varying light refraction when conducting measurements through the fluctuating drop surface, in particular for opaque substrates. The results may help in understanding the coupling of inner and outer flow for sessile drops in shear flow which allows for an analysis of the onset motion of these drops, i.e. drop removal. Removal of sessile drops plays a crucial role in many applications, which includes among other things the water management of fuel cells where small drops with $\mathrm{Bo}<1$ predominantly occur.