Extensional Dynamics of viscoplastic and shear thinning liquid bridges

The elongational rheology of fluids with yield stress has not been examined as thoroughly as their shear rheology, hence there are many open questions. We study the extension of a liquid bridge confined by two coaxial disks. The material follows the Herschel-Bulkley model and yields according to the von Mises criterion. The upper disk is pulled upwards and the evolution of the bridge shape, particularly its minimum radius, velocity and stress fields are monitored. Assuming axial symmetry, our newly developed Penalized Augmented Lagrangian method (Dimakopoulos et al. JNNFM, 2018) is used to solve the governing equations in 2D. The code is validated by comparing its predictions to experiments by Balmforth et al. (JNNFM, 2010) and finding very good agreement. We examine the effect of the Bingham number (ratio of yield stress to capillary forces), shear thinning, stretching velocity and initial aspect ratio of the bridge and compare our predictions with those by the same authors, who used the 1D slender filament approximation. As these parameters increase, deviation between the approximate results and our computations is observed, owing to the increasing complexity of the yielded domains inside the bridge.