On the influence of initial geometry on the evolution of fluid filaments

In this work, the influence of the initial geometry on the evolution of a fluid filament deposited on a substrate is studied, with a particular focus on the thin fluid strips of nano-scale thickness. Based on the analogy to the classical Rayleigh-Plateau (R-P) instability of a free-standing fluid jet, an estimate of the minimal distance between the final states (sessile droplets) can be obtained. However, this numerical study shows that while the prediction based on the R-P instability mechanism is highly accurate for an initial perturbation of a sinusoidal shape, it does not hold for a rectangular waveform perturbation. The numerical results are obtained by directly solving fully three-dimensional Navier-Stokes equations, based on a Volume of Fluid interface tracking method. The results show that (i) rectangular-wave perturbations can lead to the formation of patterns characterized by spatial scales that are much smaller than what is expected based on the R-P instability mechanism; (ii) the nonlinear stages of the evolution and end states are not simply related, with a given end state resulting from possibly very different types of evolution; and (iii) a variety of end state shapes may result from a simple initial geometry, including one- and two-dimensional arrays of droplets, a filament with side droplets, and a one-dimensional array of droplets with side filaments. Some features of the numerical results are related to the recent experimental study by Roberts et al. ["Directed assembly of one- and two-dimensional nanoparticle arrays from pulsed laser induced dewetting of square waveforms," ACS Appl. Mater. Interfaces 5, 4450 (2013)].