Minimal model for zero-inertia instabilities in shear-dominated non-Newtonian flows

摘要

The emergence of fluid instabilities in the relevant limit of vanishing fluid inertia (i.e., arbitrarily close to zeronReynolds number) has been investigated for the well-known Kolmogorov flow. The finite-time shear-inducednorder-disorder transition of the non-Newtonian microstructure and the corresponding viscosity change fromnlower to higher values are the crucial ingredients for the instabilities to emerge. The finite-time low-to-highnviscosity change for increasing shear characterizes the rheopectic fluids. The instability does not emerge innshear-thinning or -thickening fluids where viscosity adjustment to local shear occurs instantaneously. The lack ofninstabilities arbitrarily close to zero Reynolds number is also observed for thixotropic fluids, in spite of the factnthat the viscosity adjustment time to shear is finite as in rheopectic fluids. Renormalized perturbative expansionsn(multiple-scale expansions), energy-based arguments (on the linearized equations of motion), and numericalnresults (of suitable eigenvalue problems from the linear stability analysis) are the main tools leading to ournconclusions. Our findings may have important consequences in all situations where purely hydrodynamic fluidninstabilities or mixing are inhibited due to negligible inertia, as in microfluidic applications. To trigger mixing innthese situations, suitable (not necessarily viscoelastic) non-Newtonian fluid solutions appear as a valid answer.nOur results open interesting questions and challenges in the field of smart (fluid) materials.