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

Abstract

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.