Linear and nonlinear instabilities in highly shear-thinning fluid flow through a pipe

Shear-thinning fluids flowing through pipes are crucial in many practical applications, yet many unresolved problems remain regarding their turbulent transition. Using highly robust numerical tools for the Carreau–Yasuda model, we discovered that linear instability can arise when the power-law index falls below 0.35. This inelastic non-axisymmetric instability can universally arise in generalised Newtonian fluids that extend the power-law model. The viscosity ratio from infinite to zero shear rate can significantly impact instability, even if it is small. Two branches of finite-amplitude travelling-wave solutions bifurcate subcritically from the linear critical point. The solutions exhibit sublaminar drag reduction, a phenomenon not possible in the Newtonian case.