Time-dependent 3D dynamics in viscoelastic pressure-driven channel flow*

Dilute polymer solutions do not flow like Newtonian fluids. Their flows exhibit instabilities at very low Reynolds numbers that are driven not by inertia, but rather by anisotropic elastic stresses. Further increase of the flow rate results in a chaotic flow, often referred to as purely elastic turbulence (PET). The mechanism of this new type of chaotic motion is poorly understood.

We consider a model shear-thinning viscoelastic fluid driven by an applied pressure gradient through 2D and 3D channels. By starting from a linearly unstable mode recently discovered by Khalid et al. (Khalid et al., Phys. Rev. Lett. 127, 134502 (2021)) at very large flow rates and very low polymer concentrations, we demonstrate the existence of 2D travelling-wave solutions in such flows. We show that this state sub-critically connects to significantly higher values of polymer concentration and lower flow rates (Morozov, Phys. Rev. Lett. 129, 017801 (2022)), rendering travelling-wave solutions experimentally relevant.

Upon embedding the 2D coherent states in a 3D domain, we observe the emergence of a time-dependent, turbulent-like state, that becomes more complex with increasing Weissenberg number. We perform extensive characterisation of the ensuing dynamics and demonstrate its strong connection to PET.