Diffuse-interface approach to competition between viscous flow and diffusion in pinch-off dynamics

TL;DR

This paper investigates the competition between viscous flow and diffusion in liquid pinch-off dynamics using a minimal model, revealing how the dominant mechanism influences the scaling behavior of the pinch-off process.

Contribution

It introduces a characteristic length scale to quantify the competition between diffusion and viscous flow in pinch-off dynamics, supported by numerical and analytical analysis.

Findings

Identification of a nanometer to micrometer scale for the competition length

Numerical demonstration of different pinch-off regimes

Analytical insight into the crossover between regimes

Abstract

The pinch-off dynamics of a liquid thread has been studied through numerical simulations and theoretical analysis. Occurring at small length scales, the pinch-off dynamics admits similarity solutions that can be classified into the Stokes regime and the diffusion-dominated regime, with the latter being recently experimentally observed in aqueous two-phase systems [Phys. Rev. Lett. 123, 134501 (2019)]. Derived by applying Onsager's variational principle, the Cahn-Hilliard-Navier-Stokes model is employed as a minimal model capable of describing the interfacial motion driven by not only advection but also diffusion. By analyzing the free energy dissipation mechanisms in the model, a characteristic length scale is introduced to measure the competition between diffusion and viscous flow in interfacial motion. This length scale is typically of nanometer scale for systems far from the critical point, but can approach micrometer scale for aqueous two-phase systems close to the critical point. The Cahn-Hilliard-Navier-Stokes model is solved by using an accurate and efficient spectral method in a cylindrical domain with axisymmetry. Ample numerical examples are presented to show the pinch-off processes in the Stokes regime and the diffusion-dominated regime respectively. In particular, the crossover between these two regimes is investigated numerically and analytically to reveal how the scaling behaviors of similarity solutions are to be qualitatively changed as the characteristic length scale is inevitably accessed by the pinching neck of the interface. Discussions are also provided for numerical examples that are performed for the breakup of long liquid filaments and show qualitatively different phenomena in different scaling regimes.