Extensional dynamics of viscoplastic filaments: I. Long-wave approximation and the Rayleigh instability

We derive an asymptotic reduced model for the extensional dynamics of long, slender, axisymmetric threads of incompressible Herschel–Bulkley fluids. The model describes the competition between viscoplasticity, gravity, surface tension and inertia, and is used to explore the viscoplastic Rayleigh instability. A finite-amplitude initial perturbation is required to yield the fluid and initiate capillary-induced thinning. The critical amplitude necessary for thinning depends on both the wavelength of the perturbation and on the yield stress. We also numerically examine the inertialess growth of the instability and the progression towards pinch-off. The final self-similar form of inertialess pinch-off is similar to that for a power-law fluid.