Universal Scaling Law for the Collapse of Viscous Nanopores

Abstract

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.

Dynamical transitions during the collapse of inertial holes

“…Moreover, in the early stages of contraction, the experiments confirm the existence of an inertial regime (top red line) in which the data approximately follow the rate of collapse expected for an inviscid liquid 20,34,38 . Similarly, in the vicinity of pinch off, when the minimum hole radius r m → 0, the dynamics enters a final viscous regime (bottom red line) in which the data follow the theoretical rate of collapse corresponding to a Stokes liquid 21,24,35 . The results are also consistent with the findings in 23 .…”

“…This is significant because in a series of careful experiments conducted in highly-viscous liquid sheets, small holes were observed to contract at constant velocity 8,41 . Specifically, in the limit , when inertial forces are negligible, small cavities contract in a Stokes regime in which the force balance between viscous forces and capillary forces leads to a constant velocity of contraction v m = 1/2 21,24,35 . The implication is that, despite , the inertial hole in the low-viscosity liquid sheet of Fig.…”

“…Mesh independence studies were carried out at various resolutions, and meshes with degrees of freedom between approximately 15000 and 20000 degree of freedom were selected depending on the Oh . We have previously benchmarked and successfully applied this numerical scheme to simulate similar free-surface flows, including drop coalescence 32 , breakup of Newtonian and non-Newtonian liquid filaments 33 , collapse of viscous and inertial pores 34,35 , and contraction of surfactant-laden pores and filaments 36,37 .…”

Contraction of Surfactant-Laden Pores

“…The pore is considered axisymmetric around the z-axis, initially at rest, and symmetry boundary conditions are applied on the plane of symmetry z = 0. The numerical scheme has been described previously in Lu et al 14,20,23 and so only a brief summary is given. Following Lu and Corvalan, 13 the set of governing equations was discretized in space using the finite-element method, along with an arbitrary Lagrangian− Eulerian scheme, in which the location of the free interface is traced using the method of spines introduced by Kistler and Scriven.…”

Deformation and removal of viscous thin film by submerged jet impingement

“…Displacing a thin fluid film deposited on a solid surface using the impingement of a jet of another fluid is of critical importance in many industrial applications ranging from polymer processing and jet stripping for thickness control of liquid coating to cleaning and rinsing of food processing surfaces . More recently, the development of micro‐rheology measurement technologies based on carefully characterized free surface flows such as microscopic pores and indentations has motivated the possibility of tracing deformation and removal of a thin film using jet impingement as an nonintrusive and controlled method to measure mechanical property of biofilms, cells, and adhesion strength of powder coating …”