Universal Thinning of Liquid Filaments under Dominant Surface Forces

TL;DR

This paper develops a theory and simulations showing that liquid filaments thin exponentially under dominant surface forces, with a universal regime useful for measuring surface viscosities.

Contribution

It introduces a universal asymptotic regime for liquid filament thinning where surface tension balances surface viscous stresses, supported by theory and numerical simulations.

Findings

Exponential thinning regime identified under dominant surface forces.

Universal function relates thinning rate to surface viscosity coefficients.

Potential application in measuring surface viscosities.

Abstract

Theory and numerical simulations of the thinning of liquid threads at high superficial concentration of surfactants suggest the existence of an asymptotic regime where surface tension balances surface viscous stresses, leading to an exponential thinning with an $e$-fold time $F(\Theta)\,(3\mu_s + \kappa_s)/\sigma$, where $\mu_s$ and $\kappa_s$ are the surface shear and dilatational viscosity coefficients, $\sigma$ is the interfacial tension, $\Theta=\kappa_s/\mu_s$, and $F(\Theta)$ is a universal function. The potential use of this phenomenon to measure the surface viscosity coefficients is discussed.