Rifting of Extensional Flows on a Sphere

The front of a fluid that displaces a less viscous fluid in shear-dominated flows is known to be stable. We show that in predominantly extensional flows on a sphere, a similar front of a strain-rate-softening fluid can become unstable and evolve fingerlike patterns comprised of rifts and tongues. The number of rifts and tongues declines with time and is selected by competition between interfacial hoop stress, geometric stretching, momentum dissipation, and spatial curvature. Our results elucidate fracture dynamics in complex fluids under extension and are applicable to a wide range of systems, including planetary-scale ice shelves as in snowball epochs and icy moons.