Instabilities of nanoscale liquid metal films
(Supported by the NSF Grant CBET-1235710)

In this work, the nontrivial influence of the initial geometry on the evolution of a liquid filament deposited on a substrate is studied, with a particular focus on the thin liquid strips of nano-scale thickness. Based on the analogy to the classical Rayleigh-Plateau (R-P) instability of a free-standing liquid jet, an estimate of the minimal distance between the final states (sessile drops) 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 stage 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.


Roberts, N., Fowlkes, J., Mahady, K., Afkhami, S., Kondic, L., Rack, P.,

We consider the evolution and related instabilities of thin metal films liquefied by laser pulses.   The films are patterned by large-scale perturbations and we discuss how these perturbations influence the dynamics.   In the experiments,  we find that the considered thin films dewet, leading to the formation of primary and secondary drops, with the locations of the primary ones coinciding with the original perturbations.  Based on the results of the fully nonlinear time-dependent  simulations, we discuss the details of the evolution   leading
to these patterns.  Furthermore, in both experiments and simulations, we discuss the influence of the shape of the initial perturbations on the properties of the final patterns.
The figure shows combined simulations and experimental results illustrating the instability mechanism.   The bottom row shows simulations where initial stochastic noise was included in the simulations.   The simulations are carried out withing the long-wave model, reducing the problem to a nonlinear 4th order PDE.

Metallic nanoparticles, liquefied by fast laser irradiation, go through a rapid change of shape attempting to minimize their surface energy. The resulting nanodrops may be ejected from the substrate when the mechanisms leading to dewetting are sufficiently strong, as in the experiments involving gold nanoparticles [Habenicht et al., Science 309}, 2043 (2005)].   We use a direct continuum-level approach to accurately model the process of liquid nanodrop formation and the subsequent ejection from the substrate.   Our computations show a significant role of inertial effects and an elaborate interplay of initial geometry and wetting properties: e.g., we can control  the direction of ejection by prescribing appropriate initial shape and/or wetting properties. The basic insight regarding ejection itself can be reached by considering  a simple effective model based on an energy balance. We validate our computations by comparing directly with the experiments specified above  involving the length scales measured in hundreds of nanometers, and with molecular dynamics simulations on much shorter scales measured in tens of atomic diameters, as in  M. Fuentes-Cabrera et al., Phys.~Rev. E 83, 041603 (2011).  The quantitative agreement, in addition to illustrating how to controlling particle ejection, shows utility of continuum-based simulation in describing dynamics on nanoscale quantitatively, even in a complex setting as considered here. 

The figure shows the experimental images of two stagest of instability with metal showing as light and the substrate as dark. 

We consider nanometer-sized fluid annuli (rings) deposited on a solid substrate and ask whether these rings break up into droplets due to the instability of Rayleigh-Plateau type modified by the presence of the substrate, or collapse to a central drop due to the presence of azimuthal curvature. The analysis is carried out by a combination of atomistic molecular dynamics simulations and a continuum model based on a long-wave limit of Navier Stokes equations. We find consistent results between the two approaches, and demonstrate characteristic dimension regimes which dictate the assembly dynamics. 

The figure shows breakup (or lack of it) in MD simulations of rings and filaments.

Nguyen, T., Fuentes-Cabrera, M., Fowlkes, J., Diez, J., Gonzalez, A.G., Kondic, L., Rack, P.,  Competition between collapse and breakup in nanometer-sized thin rings using molecular dynamics and continuum modeling,  Langmuir, 28, 13960 (2012).

We study the stability of a viscous incompressible fluid ring on a partially  wetting substrate within the framework of long-wave theory.  We discuss the conditions under which a static equilibrium of the ring is possible in the presence of contact angle hysteresis. A linear stability analysis (LSA) of this equilibrium solution is carried out by using a slip model to account for the contact line divergence. The LSA provides specific  predictions regarding the evolution of unstable modes. In order to describe the evolution of the ring for longer times, a quasi-static approximation of Wentzel-Kramers-Brillouin (WKB) type is implemented.  This approach assumes a quasi-static evolution and takes into account the concomitant variation of the instantaneous growth rates of the modes responsible for either collapse of the ring  into a single central drop or breakup into a number of droplets along the ring periphery.  We compare the results of the LSA and WKB with those obtained from nonlinear numerical simulations using a complementary disjoining pressure model.  We find remarkably good agreement between the predictions of  the two models regarding the expected number of drops forming during the breakup process.