(584b) Self-Similar Dynamics of Axisymmetric Point Rupture of Highly Viscous Liquid Sheets

In numerous coating flow and polymer processing operations, a highly viscous fluid is ejected from a nozzle or a die as a liquid sheet. If sufficiently thin, sheets can rupture due to van der Waals (vdW) forces and exhibit self-similar dynamics near breakup. Witelski et. al (PoF 2001) investigated the phenomenon of axisymmetric point rupture in freely suspended liquid sheets under the influence of inertia and viscosity. These authors uncovered the self-similar nature of the rupture dynamics, highlighting a balance between inertial, viscous, and vdW forces as the film approaches breakup. 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 scale of the rupture zone, and the lateral velocity with time remaining to rupture. Additionally, they highlighted sheet rupture in three practically important geometries: axisymmetric point, line (translationally-symmetric), or ring. Subsequently, Thete et al. (PoF 2016) built on the pioneering work of these authors to investigate line rupture in the limits of low and high viscosity. In the high viscosity or Stokes limit, Thete et al. showed that the pinch-off dynamics exhibits self-similarity of the second kind with a dominant balance between viscous and vdW forces for sheets undergoing line rupture. They calculated scaling exponents using both numerical simulations and analytical techniques. In this talk, we investigate the dynamics of both axisymmetric point and ring rupture under Stokes flow conditions, unveiling unexpected findings in the point rupture case indicating a heretofore unknown dependence of the rupture dynamics on the nature or geometry of the initial perturbation of the sheet's surface(s).