ZERO-INERTIA INSTABILITIES IN RHEOPECTIC FLUIDS

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The emergence of fluid instabilities in the relevant limit of vanishing fluid inertia (i.e., arbitrarily close to zero Reynolds number) has been investigated for the well-known Kolmogorov flow. The time-lagged viscosity change from lower to higher values due to shear changes is the crucial ingredient for the instabilities to emerge. This behavior characterizes the so-called rheopectic fluids. The instability does not emerge in shear-thinning or -thickening fluids where viscosity adjustment to local shear occurs instantaneously. No instability arbitrarily close to zero Reynolds number is either observed in thixotropic fluids, even though the viscosity adjustment time to shear is finite like in rheopectic fluids. Numerical tools (through suitable eigenvalue problems from the linear stability analysis) and multiple-scale homogenization techniques are utilized to lead to our conclusions. Our findings may have important consequences in all situations where purely hydrodynamic fluid instabilities or mixing are inhibited due to negligible inertia, such as in microfluidics. To trigger mixing in these situations, suitable (not necessarily viscoelastic) non-Newtonian fluid solutions appear as a valid answer. Our results open interesting questions and challenges in the field of smart (fluid) materials.