On The Thinning and Pinch-Off Dynamics for a Newtonian Liquid Thread Draining in a Viscoplastic Medium

The spatiotemporal thinning and consequential pinch-off of a Newtonian liquid thread surrounded by a Newtonian medium is dominated by competition between interfacial tension stresses and flow-general viscous stresses. While this system has been comprehensively studied, understanding becomes limited when the external medium exhibits viscoplastic properties. To investigate the complex behavior of a Newtonian thread embedded in a viscoplastic medium described by the Herschel-Bulkley model, we employ direct numerical simulations. We characterize the flow by generating regime maps in the Ohnesorge and plastocapillary number space, for varying viscosity ratios. Across different viscosity ratios, thread breakup occurs below an approximately consistent threshold, while distinct boundaries are captured. By implementing a regular perturbation analysis followed by a scaling analysis, we also identify and include scalings for the minimum interfacial height and the axial velocity; we observe a close match between simulations and theoretical predictions. Insights arising from this work are expected to contribute towards the optimization of embedded additive manufacturing processes and other relevant industrial sectors.