Instability of sliding viscoplastic films

The stability of sliding spreading films of Herschel–Bulkley fluid is investigated theoretically, motivated by a dramatic fingering pattern observed experimentally and proposed theoretically to originate from an extensional flow instability of shear-thinning fluids. Considering the thin-film limit, we construct axisymmetric base states and then test their stability towards non-axisymmetric perturbations by numerically solving the initial-value problem. We complement the numerics with analytical solutions for early and late times. The stability analysis demonstrates that spreading thinning films are unstable. At late times, where the spreading of the base state becomes self-similar, non-axisymmetric patterns can develop strongly if the fluid has a yield stress or is sufficiently shear thinning.