Fluctuating Hydrodynamics and the Rayleigh-Plateau Instability

Abstract

The Rayleigh-Plateau instability occurs when surface tension makes a fluid column become unstable to small perturbations. At nanometer scales, thermal fluctuations are comparable to surface energy densities. Consequently, at these scales, thermal fluctuations play a significant role in the dynamics of the instability. These microscopic effects have previously been investigated numerically using particle-based simulations, such as molecular dynamics, and stochastic partial differential equation based hydrodynamic models, such as stochastic lubrication theory. In this paper we present an incompressible fluctuating hydrodynamics model with a diffuse-interface formulation for binary fluid mixtures designed for the study of stochastic interfacial phenomena. An efficient numerical algorithm is outlined and validated in numerical simulations of stable equilibrium interfaces. We present results from simulations of the Rayleigh-Plateau instability for long cylinders pinching into droplets for Ohnesorge numbers of Oh = 0.5 and 5.0. Both stochastic and perturbed deterministic simulations are analyzed and ensemble results show significant differences in the temporal evolution of the minimum radius near pinching. Short cylinders, with lengths less than their circumference, were also investigated. As previously observed in molecular dynamics simulations, we find that thermal fluctuations cause these to pinch in cases where a perturbed cylinder would be stable deterministically. Finally we show that the fluctuating hydrodynamics model can be applied to study a broader range of surface-tension driven phenomena.