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

Area of Science:

• Fluid dynamics
• Non-Newtonian fluid mechanics
• Rheology

Background:

• Fluid instabilities are crucial for mixing, but often inhibited in low-inertia systems like microfluidics.
• Kolmogorov flow, a benchmark system, is examined for instability emergence near zero Reynolds number.
• Non-Newtonian fluid behavior, specifically finite-time viscosity changes, is key to instability onset.

Purpose of the Study:

• Investigate the emergence of fluid instabilities in Kolmogorov flow at vanishing fluid inertia (low Reynolds number).
• Identify the critical role of finite-time shear-induced microstructural transitions and viscosity changes in instability formation.
• Determine the conditions under which instabilities emerge in different classes of non-Newtonian fluids.

Main Methods:

• Renormalized perturbative expansions (multiple-scale expansions) were employed.
• Energy-based arguments on linearized equations of motion were utilized.
• Numerical analysis of eigenvalue problems from linear stability analysis provided key data.

Main Results:

• Instabilities emerge in rheopectic fluids due to finite-time, shear-induced order-disorder transitions and viscosity increases.
• No instabilities were observed in shear-thinning or shear-thickening fluids with instantaneous viscosity adjustments.
• Thixotropic fluids, despite finite viscosity adjustment times, also did not exhibit instabilities at low Reynolds numbers.

Conclusions:

• Finite-time viscosity changes are essential for hydrodynamic instabilities in low-inertia flows.
• Non-Newtonian fluids offer potential solutions for triggering mixing in microfluidic applications.
• The findings open new avenues for research in smart fluid materials and hydrodynamic control.