Universal Scaling Law for the Collapse of Viscous Nanopores

Below a threshold size, a small pore nucleated in a fluid sheet will contract to minimize the surface energy. Such behavior plays a key role in nature and technology, from nanopores in biological membranes to nanopores in sensors for rapid DNA and RNA sequencing. Here we show that nanopores nucleated in viscous fluid sheets collapse following a universal scaling law for the pore radius. High-fidelity numerical simulations reveal that the scaling is largely independent of the initial conditions, including the size, shape, and thickness of the original nanopore. Results further show that the scaling law yields a constant speed of collapse as observed in recent experiments. Nanopores in fluid sheets of moderate viscosity also attain this constant terminal speed provided that they are sufficiently close to the singularity.