Disorder suppresses viscoelastic instability

At critically large strain rates or Weissenberg numbers, viscoelastic fluids are known to undergo a transition to a time dependent, chaotic flow(i.e. elastic turbulence), characterized by spatio-temporal velocity fluctuations. In this work, we quantify the flow of a viscoelastic fluid through a microfluidic device consisting of an array of cylindrical pillars, which are tuned from an ordered hexagonal lattice to a disordered medium. Measurement of the temporal fluctuations of the velocity field illustrates that flow through the ordered lattice undergoes a bifurcation at a critical Weissenberg number Wi=0.5. However, the introduction of a finite disorder to the pillar array completely suppresses this critical behavior, as the flow stabilizes along preferential flow paths characterized by a 2-5 fold increase in the velocity field correlation length. Spectral analysis of the Lagrangian strain rate reveals that in addition to a high Wi number, a high quality factor of the strain rate spectrum - observed only in highly ordered systems - is crucial for the onset of the viscoelastic instability.