Molecular Dynamics Study of Rayleigh-Plateau Instability at Liquid-Liquid Interfaces

TL;DR

The study addresses Rayleigh-Plateau instability at a liquid–liquid interface with equal viscosities using molecular dynamics to test macroscopic predictions under nanoscale conditions. It employs two initial conditions (perturbed and unperturbed) and analyzes growth via breakup time and Fourier amplitude to compare with Stone–Brenner dispersion relations, while quantifying thermal-fluctuation effects. Key findings show that for perturbed cylinders, growth rates converge to the classical theory as the radius increases (with $r_0$ down to about 15 atomic diameters showing good agreement), whereas unperturbed cases reveal a power-law breakup behavior with exponent $\alpha$ that increases with radius, indicating stronger fluctuations at smaller sizes. The results demonstrate that macroscopic RP theory can hold at nanoscale radii under controlled perturbations and highlight how thermal fluctuations shape breakup dynamics in microscopic systems, guiding when continuum models remain valid and where stochastic effects must be accounted.

Abstract

We investigated the Rayleigh-Plateau instability at the interface between two immiscible liquids of equal viscosity using molecular dynamics simulations. Two types of initial conditions were considered, one with an imposed single-mode perturbation at the interface and the other without any imposed perturbation. Under the single-mode perturbation, the growth rate deviated from the theoretical prediction for small cylinder radii, but progressively approached and agreed with classical macroscopic theory as the radius increased. In contrast, for the unperturbed initial condition, we found a systematic relationship between the breakup time and the minimum radius, in which the power-law exponent increased with increasing radius. These results demonstrate that, even in extremely microscopic systems with cylinder radii on the order of only about fifteen atomic diameters, the growth of the instability can follow macroscopic theoretical predictions when appropriate conditions are imposed, and that the influence of thermal fluctuations on the breakup dynamics becomes increasingly significant as the system radius decreases.

Figures (13)

• Figure 1: The generation of the initial configuration. (a) We first thermalized a single-component system. (b) After relaxation of the single-component system, we changed the labels of atoms in a cylinder of a specified radius.
• Figure 2: The snapshots of the simulations. (a) The breakup process of the cylinder with the imposed perturbation. The cylinder breaks up at evenly spaced intervals due to the imposed perturbation. (b) The breakup process of the cylinder without an imposed perturbation. The constriction occurs irregularly due to no perturbation.
• Figure 3: The schematic view of the cylinder with the imposed perturbation. (a) The schematic view of the cylinder at $t=0$ with the radius $r_0$, the amplitude $A$ and the wavelength of the perturbation $\lambda$. (b) The schematic view of the cylinder at time $t$. If only the perturbation with wavelength $\lambda$ grows, the amplitude evolves as $A\exp (\omega t)$ over time.
• Figure 4: The schematic diagram of the cylinder without an imposed perturbation. (a) The schematic view of the cylinder with the initial radius $r_0$. (b) The schematic view of the cylinder at time $t$, when the minimum radius $r_{\min} (t)$ was measured in order to investigate the effects of the thermal fluctuations on the cylinder.
• Figure 5: The dispersion relation calculated by the breakup time. The horizontal axis is the wavenumber, and the vertical axis is the growth rate. The growth rate does not become zero at $\tilde{k} = 0$ or $\tilde{k} \geq 1$.