Instabilities in falling films of thixotropic fluids

Thixotropic fluids with a non-monotonic flow curve display viscosity bifurcations at certain stresses. It has been proposed that these transitions can introduce interfaces (or shear bands) into thin films that can destabilize inertialess flows over inclined planes. This proposition is confirmed in the present paper by formulating a thin-film model, then using this model to construct sheet-like base flows and test their linear stability. It is also found that viscosity bifurcations, and the associated interfaces, are not necessary for instability, but that the time-dependent relaxation of the microstructure responsible for thixotropy within the bulk of the film can promote instability instead. Computations with the thin-film model demonstrate that instabilities saturate supercritically into steadily propagating nonlinear waves that travel faster than the mean flow.