Breakup of Liquid Nano-threads Simulated by Molecular Dynamics

A circular liquid thread of radius R will break up into drops if the axial wavelength of surface perturbation L $>$ 2$\pi $R. If L $<$ 2$\pi $R, the thread is stable and will remain intact. This is Rayleigh's stability criterion based on a continuum model. We use molecular dynamics to simulate the evolution of Lennard-Jones liquid threads with equilibrium radius R = 2.25-6.59, where R has been non-dimensionalized by the distance at which the Lennard-Jones potential equals zero. Periodic conditions are imposed at the boundaries of the simulation box so that the thread length is the wavelength L. We find that if R is fixed, there exists a range of L bounded by L$_{min}$ and L$_{max}$ such that for L $\ge $ L$_{max}$ the thread always breaks up into drops and stays as drops, and for L $\le $ L$_{min}$, the thread remains connected but the shape varies continuously among a series of shapes including a cylinder, unduloids, and sinusoids. For L$_{min} <$ L $<$ L$_{max}$, the thread can break up temporarily into drops and then resume connected. As R increases, L$_{min} \to $ L$_{max}$, and L$_{max}$ is slightly smaller than 2$\pi $R. The appearance of various shapes can be explained by the energy fluctuation of the system.