Drag on a partially immersed sphere at the capillary scale

Characterization of the drag on bodies in a background flow represents one of the most timeless and practical applications of fluid mechanics. For the case of objects partially immersed at a free surface, most prior work focuses on large scales where the effects of surface tension are negligible. In the present work, we use a custom benchtop flume to investigate the drag force on centimetric objects in steady flow constrained at the air-water interface. Surface profile reconstructions and particle image velocimetry measurements are presented in conjunction with direct force measurements. The experimental measurements are compared directly to numerical simulations performed using a variational multi-scale, mixed interface-capturing/interface-tracking formulation. In general, we observe that the drag force steadily increases with submergence, reaching a peak value which significantly exceeds the fully submerged case. Implications for the design of surface microrobots and other applications will be discussed.