Nonlinear regime of radially spreading extensional flows. Part 2. Power-law fluids

Radially spreading extensional flows can become unstable and develop tearing patterns consisting of rifts and tongues. Such patterns have been observed in laboratory experiments with strain-rate-softening (shear-thinning) polymer solutions and in spreading ice shelves. Linear stability analysis predicts that axisymmetric spreading of power-law fluids becomes unstable when the fluid is shear thinning. However, understanding the emergence and evolution of rifts requires analysis of the nonlinear flow regime. In Part 1 of this study we developed a numerical simulation of the full nonlinear equations and showed that Newtonian fluids remain globally stable, consistently with theoretical predictions and experimental observations. Here we extend that framework to explore power-law fluids. We demonstrate that purely viscous shear-thinning fluids can develop rifts, and evolve rift-tongue patterns consistently with theoretical and experimental findings. Starting from an axisymmetric base state, we examine the resulting flow under monochromatic perturbations over a range of amplitudes, wavenumbers, fluid properties, and boundary and initial conditions. We find that for shear-thinning fluids, rift formation depends strongly on perturbation amplitude, while being less sensitive to the perturbation wavenumber. The mechanism reflects competition between a destabilising radial force associated with hoop stresses and a stabilising force arising from radial normal-stress divergence. As the fluid gets more shear thinning, the stabilising contribution weakens, facilitating rift formation. These results provide new insights into the nonlinear mechanisms governing rift formation in polymer solutions and in spreading ice shelves.