Vortex ring formation in oscillatory pipe flow of wormlike micellar solutions

Abstract

The destabilization of rectilinear oscillatory pipe flow and the formation of vortex rings in a wormlike micellar solution, CPyCl/NaSal [100:60] mM, oscillated in a vertical cylinder of large aspect ratio, has been studied by means of time-resolved-particle image velocimetry measurements in a meridional plane of the cylinder. The flow was inertialess (Re<1) and dominated by fluid elasticity (De≫1). The oscillatory pipe flow of a Newtonian fluid under equivalent conditions would remain rectilinear and laminar. For the micellar solution, instead, the reversing character of the rectilinear flow induces vortex ring formation. The stability boundaries between rectilinear, axisymmetric-vortical, and non-axisymmetric-vortical flows in the middle region of the cylinder have been determined from the root-mean-square fluctuations of the measured vertical and radial velocity components. Measurements performed over the whole tube length reveal that the flow destabilization and the subsequent formation of vortex rings is favored at the bottom part of the cylinder, close to the driving piston. As the driving amplitude is increased, the vortical flow expands vertically upwards, giving rise to a number of coaxial toroidal vortices distributed over the vertical pipe. On short-time scales these axisymmetric vortex rings are periodic in time with the periodicity of the driving. On long time scales, much longer than the relaxation time of the fluid, we uncover an additional temporal evolution of the vortical flow which makes the spatiotemporal structure of the oscillatory flow more involved.