Fluctuation-driven dynamics of liquid nano-threads with external hydrodynamic perturbations

TL;DR

This paper investigates the stability and rupture dynamics of liquid nano-threads under external hydrodynamic perturbations using a stochastic lubrication model, revealing regimes dominated by external forces or thermal fluctuations.

Contribution

It introduces a stochastic lubrication equation incorporating external perturbations and thermal noise, providing a combined theoretical and numerical analysis validated by molecular dynamics.

Findings

External perturbations can dominate surface tension effects, leading to uniform ruptures.

Thermal fluctuations can cause non-uniform ruptures when external forces are weak.

The transition between regimes depends on perturbation amplitude and wavenumber.

Abstract

Instability and rupture dynamics of a liquid nano-thread, subjected to external hydrodynamic perturbations, are captured by a stochastic lubrication equation (SLE) incorporating thermal fluctuations via Gaussian white noise. Linear instability analysis of the SLE is conducted to derive the spectra and distribution functions of thermal capillary waves influenced by external perturbations and thermal fluctuations. The SLE is also solved numerically using a second-order finite difference method with a correlated noise model. Both theoretical and numerical solutions, validated through molecular dynamics, indicate that surface tension forces due to specific external perturbations overcome the random effects of thermal fluctuations, determining both the thermal capillary waves and the evolution of perturbation growth. The results also show two distinct regimes: (i) the hydrodynamic regime, where external perturbations dominate, leading to uniform ruptures, and (ii) the thermal-fluctuation regime, where external perturbations are surpassed by thermal fluctuations, resulting in non-uniform ruptures. The transition between these regimes, modelled by a criterion developed from the linear instability theory, exhibits a strong dependence on the amplitudes and wavenumbers of the external perturbations.