Bursting bubble in Herschel–Bulkley Fluids

Bursting bubble at a free surface is a canonical problem in multiphase fluid dynamics, with broad implications in geophysics, industry, and biology. While the Newtonian case has been extensively studied, much less is known about the bursting dynamics of complex fluids that exhibit yield stress and shear-dependent viscosity. In this work, we numerically investigate bubble bursting in Herschel–Bulkley fluids, which capture both shear-thinning and shear-thickening behavior with a finite yield stress. Using high-speed imaging and axisymmetric simulations performed with the open-source code Basilisk, we systematically explore a wide parameter space, including Bond number, Ohnesorge number, flow behavior index, and plastocapillary number, to capture the interplay of inertial, viscous, and viscoplastic effects. This framework reveals the interactions among different physical mechanisms, as reflected in the evolution of interfacial dynamics including capillary waves, cavity collapse, and jet formation and height. Our study lays the groundwork for understanding multiphase interface dynamics in complex media and provides a platform for interpreting phenomena in foams, food emulsions, and geophysical flows.