Capillary instability and breakup of a viscous thread

Papageorgiou derived a similarity solution that describes the asymptotic behavior of a thinning viscous thread suspended in vacuum, near the critical time and around the location of breakup. The motion is driven by surface tension, and the fluid inertia is neglected throughout the evolution. To assess the physical relevance of the similarity solution, the evolution of an infinite thread immersed in an ambient fluid with arbitrary viscosity, subject to periodic axisymmetrtic perturbations is simulated through solution of the equations of Stokes flow by a boundary integral method. The results show that when the thread is suspended in vacuum, the similarity solution accurately describes the process of thinning over an extended length of the thread between the developing bulges, and captures the late stages of breakup for a broad range of initial conditions. But a small amount of ambient fluid viscosity, as small as 0.05 times the viscosity of the thread fluid, drastically alters the nature of the motion by shifting the location of the breakup points toward the bases of developing bulges, and causing the thread to develop locally asymmetric shapes.