Dynamics of viscoplastic filament stretching

•Comparison of the slender filament model and 2D simulations.•2D simulations performed with the PAL method.•Study of the effect of inertia in the pinching process of viscoplastic filaments. We use numerical simulations to study the stretching and pinching of a viscoplastic material that is confined by two coaxial disks when they are pulled apart. The material initially forms a cylindrical bridge between the disks, follows the Heschel-Bulkley model and yields according to the von Mises criterion. We solve the governing equations numerically in their 2D, axisymmetric form using the PAL algorithm (Dimakopoulos et al. (2018)) and the slender filament approximation using the Bercovier and Engelman (1980) regularization. This approximation is valid when the disk radius to the initial length of the bridge, ε=R˜/L˜o, is small, but it is often used even when this aspect ratio is O(1). The results from the 2D solution agree with the experiments of Balmforth et al. (2010) for both a Carbopol gel and a Kaolin suspension, which can be classified as materials of medium and high viscoplasticity, respectively. Depending on the values of the aspect ratio and the yield stress of the material, we show that stretching can or cannot be accurately described by the slender filament approximation. By varying the yield stress and the pulling velocity, we find that discrepancies arise when the viscoplastic character of the flow increases, even though R˜/L˜o