Flow field around a swimming droplet close to a wall

Micro-swimmers rarely evolve in a 3D infinite and unbounded medium. Instead, they are confined by external geometries which strongly modify their behavior. There is however no exact theoretical knowledge of the flow fields in this context and experimental data are scarce. Here we consider a swimming water droplet [1], denser than the continuous phase, which performs a linear steady motion parallel to the bottom wall. The flow field around the droplet, measured using 3D confocal PIV, is quantitatively characterized. Besides we propose an analytical formulation derived from a simplified description of the swimmer as the superposition of dipolar and quadrupolar singularities and an exact treatment of the wall [2]. The effect of the wall on quadrupole terms is very well captured. Although lower terms suffer from the approximation, they show that the long-range interaction between droplets can not be reduced to a simple description in terms of pushers or pullers.

[1] Izri et al. PRL 113, 248302 (2014).
[2] Blake et al. JEM 8 (1) (1974).