Capillary-driven horseshoe vortex forming around a micro-pillar

Horseshoe vortices are known to emerge around large-scale obstacles, such as bridge pillars, due to an inertia-driven adverse pressure gradient forming on the upstream-side of the obstacle. We contend that a similar flow structure can arise in thin-film Stokes flow around micro-obstacles, such as used in textured surfaces to improve wettability. This could be exploited to enhance mixing in microfluidic devices, typically limited to creeping-flow regimes.

Numerical simulations based on the Navier-Stokes equations are carried out to elucidate the flow structure associated with the wetting dynamics of a liquid film spreading around a 50 μm diameter micro-pillar. The employed multiphase solver, which is based on the volume of fluid method, accurately reproduces the wetting dynamics observed in current and previous (Mu et al., Langmuir, 2019) experiments.

The flow structure within the liquid meniscus forming at the foot of the micro-pillar evinces a horseshoe vortex wrapping around the obstacle, notwithstanding that the Reynolds number in our system is extremely low. Here, the adverse pressure gradient driving flow reversal near the bounding wall is caused by capillarity instead of inertia. The horseshoe vortex is entangled with other vortical structures, leading to an intricate flow system with high-potential mixing capabilities.