Oscillatory pipe flow of a wormlike micellar solution

The oscillatory pipe flow of the wormlike micellar solution CPyCl/NaSal [100:60] mM has been studied by means of time-resolved Particle Image Velocimetry (PIV) measurements in a meridional plane of the cylinder. The flow is inertialess (Re<1) and dominated by fluid elasticity (De>>1).

In the first part of the talk I will discuss results obtained at small driving amplitudes (rectilinear-laminar flow) for a large range of driving frequencies [1]. The velocity magnitude at the tube axis peaks at well-defined resonance frequencies, where the phase lag with the forcing changes abruptly. The velocity field is increasingly reversing at increasing driving frequencies. I will compare these results with theoretical predictions based on the upper-convected Maxwell and Oldroyd-B models of the linear shear rheology of the solution [2].

In the second part of the talk I will focus on the destabilization of the rectilinear-laminar flow and the formation of vortex rings at larger driving amplitudes [3]. The stability boundaries between rectilinear, axisymmetric-vortical, and non-axisymmetric-vortical flow 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 vertical tube length reveal that the flow destabilization and the subsequent formation of vortex rings is favoured at the bottom part of the cylinder, close to the driving piston. As the driving amplitude is increased, the vortical flow expands vertically upward, 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 have uncovered an additional temporal evolution of the vortical flow. I will end up by discussing possible mechanisms of destabilization of the rectilinear flow in this system.

[1] L. Casanellas, J. Ortin. Laminar oscillatory flow of Maxwell and Oldroyd-B fluids: theoretical analysis. J. Non-Newtonian Fluid Mech. 166 (2011) 1315-1326. [2] L. Casanellas, J. Ortin. Experiments on the laminar oscillatory flow of wormlike micellar solutions. Rheol. Acta 51 (2012) 545-557. [3] L. Casanellas, J. Ortin. Vortex ring formation in oscillatory pipe flow of wormlike micellar solutions. Submitted to Journal of Rheology (2013).