Self-similar dynamics of axisymmetric point rupture of highly viscous liquid sheets

High-viscosity liquid sheets arise in coating flows and polymer processing. If sufficiently thin, sheets rupture due to van der Waals (vdW) forces and exhibit self-similar dynamics. Witelski et al. (2001) investigated the axisymmetric point rupture of liquid sheets under the influence of inertia and viscosity. They uncovered the self-similar nature of the dynamics, highlighting a balance between inertial, viscous, and vdW forces as the film thins. Moreover, they showed that the similarity is of the first kind with rational power-law scaling exponents that relate the free surface height, lateral length, and lateral velocity with time remaining to rupture. They highlighted sheet rupture in three practically important geometries: axisymmetric point, line, or ring. Subsequently, Thete et al. (2016) built on their pioneering work to investigate line rupture in the low and high viscosity (Stokes) limits. In the latter, Thete et al. showed that the dynamics exhibits self-similarity of the second kind with a dominant balance between viscous and vdW forces in line rupture. Here, we investigate the dynamics of axisymmetric point and ring rupture under Stokes flow conditions, unveiling unexpected findings during point rupture indicating a heretofore unknown dependence on initial conditions.