Universal Scaling Law for the Collapse of Viscous Nanopores

Dynamical transitions during the collapse of inertial holes

At the center of a collapsing hole lies a singularity, a point of infinite curvature where the governing equations break down. It is a topic of fundamental physical interest to clarify the dynamics of fluids approaching such singularities. Here, we use scaling arguments supported by high-fidelity simulations to analyze the dynamics of an axisymmetric hole undergoing capillary collapse in a fluid sheet of small viscosity. We characterize the transitions between the different dynamical regimes —from the initial inviscid dynamics that dominate the collapse at early times to the final Stokes dynamics that dominate near the singularity— and demonstrate that the crossover hole radii for these transitions are related to the fluid viscosity by power-law relationships. The findings have practical implications for the integrity of perforated fluid films, such as bubble films and biological membranes, as well as fundamental implications for the physics of fluids converging to a singularity.

Coalescence dynamics of viscous conical drops

When two oppositely charged drops come into light contact, a liquid meniscus bridge with double-cone geometry forms between the drops. Recent experiments have demonstrated the existence of a critical cone angle above which the meniscus bridge pinches off and the drops do not coalesce. This striking behavior-which has implications for processes ranging from the coarsening of emulsions to electrospray ionization in mass spectrometry-has been studied theoretically and experimentally for inertial liquid drops. Little is known, however, about the influence of the liquid viscosity on the critical cone angle. Here, we use high-fidelity numerical simulations to gain insight into the coalescence dynamics of conical drops at intermediate Reynolds numbers. The simulations, which account for viscous, inertial, and surface tension effects, predict that the critical cone angle increases as the viscosity of the drops decreases. When approaching the inertial regime, however, the predicted critical angle quickly stabilizes at approximately 27°, as observed in experiments.