Drop pattern resulting from the breakup of a bidimensional grid of liquid filaments

Abstract

A rectangular grid formed by liquid filaments on a partially wetting substrate evolves in a series of breakups leading to arrays of drops with different shapes distributed in a rather regular bidimensional pattern. Our study is focused on the configuration produced when two long parallel filaments of silicone oil, which are placed upon a glass substrate previously coated with a fluorinated solution, are crossed perpendicularly by another pair of long parallel filaments. A remarkable feature of this kind of grids is that there are two qualitatively different types of drops. While one set is formed at the crossing points, the rest are consequence of the breakup of shorter filaments formed between the crossings. Here, we analyze the main geometric features of all types of drops, such as shape of the footprint and contact angle distribution along the drop periphery. The formation of a series of short filaments with similar geometric and physical properties allows us to have simultaneously quasi identical experiments to study the subsequent breakups. We develop a simple hydrodynamic model to predict the number of drops that results from a filament of given initial length and width. This model is able to yield the length intervals corresponding to a small number of drops and its predictions are successfully compared with the experimental data as well as with numerical simulations of the full Navier-Stokes equation that provide a detailed time evolution of the dewetting motion of the filament till the breakup into drops. Finally, the prediction for finite filaments is contrasted with the existing theories for infinite ones.

Self-assembly of a drop pattern from a two-dimensional grid of nanometric metallic filaments

“…as confirmed by the experiments in [27]. Therefore, the characteristic length of a filament needed for the formation of a single drop is L 1 = L l + L s = 4.697 w. Figure 7a illustrates the introduced quantities.…”

“…Although the scale of the experiments considered in [27] is different, visual similarity of the instabilities to the ones considered in the present paper suggests that the instability mechanism may be similar. The macroscopic experiments from [27] provide however significantly more detailed information about grid evolution, that is useful in explaining the present experimental results for which such detailed information is not available. Figure 5 illustrates the instability mechanism discussed extensively in [27]; here we provide a brief overview of the main features.…”

“…The macroscopic experiments from [27] provide however significantly more detailed information about grid evolution, that is useful in explaining the present experimental results for which such detailed information is not available. Figure 5 illustrates the instability mechanism discussed extensively in [27]; here we provide a brief overview of the main features. The first step (between Fig.…”

“…Here we consider the fluid mechanical description recently reported by Cuellar et al [27] in the context of microfluidic experiments carried out with the silicon oil grids. Although the scale of the experiments considered in [27] is different, visual similarity of the instabilities to the ones considered in the present paper suggests that the instability mechanism may be similar. The macroscopic experiments from [27] provide however significantly more detailed information about grid evolution, that is useful in explaining the present experimental results for which such detailed information is not available.…”

Electrostatic control of dewetting dynamics

“…We find that for 0.3 < L x ≤ 1 the droplet is in the capillary rim regime and for L x ≤ 0.3 the droplet is in the spherical cap regime. As shown in supplementary video S1 in the final stages of relaxation the droplet spreads slightly along the short axis of the rivulet (ydirection) while along the long axis (x-direction) the contact line continues to retract, this gives rise to a slightly elliptical final contact line shape 27,28 . It is clear from Fig.…”