Contactless generation and trapping of hydrodynamic knots in sessile droplets by acoustic screw dislocations

Abstract

Hydrodynamics knots are not only promising elementary structures to study mass and momentum transfer in turbulent flows, but also potent analogs for other topological problems arising in particle physics. However, experimental studies of knots are highly challenging due to the limited control over knot generation and difficult observation of the resulting fast-paced multiscale flow evolution. In this paper, we propose using acoustic streaming to tie hydrodynamic knots in fluids. The method is contactless, almost instantaneous and is relatively insensitive to viscosity. Importantly, it allows starting from quite arbitrary three dimensional flow structures without relying on external boundary conditions. We demonstrate our approach by using an acoustic screw dislocation to tie a knot in a sessile droplet. We observe an inversion of the knot chirality (measured by the hydrodynamic helicity) as the topological charge of the screw dislocation is increased. Combined with recent progress in acoustic field synthesis, this work opens a window to study more complex hydrodynamic knot topologies at a broader range of space and timescales.