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.

We study the hydrodynamic mechanisms involved in the motion of the contact line formed at the end region of a liquid filament laying on a planar and horizontal substrate. Since the flow develops under partially wetting conditions, the tip of the filament recedes and forms a bulged region (head) that subsequently develops a neck region behind it. Later the neck breaks up leading to a separated drop, while the rest of the filament restarts the sequence. One main feature of this flow is that the whole dynamics and final drop shapes are strongly influenced by the hysteresis of the contact angle typical in most of the liquid-substrate systems. The time evolution till breakup is studied experimentally and pictured in terms of a hybrid wettability theory which involves the Cox-Voinov hydrodynamic approach combined with the molecular kinetic theory developed by Blake. The parameters of this theory are determined for our liquid-substrate system (silicone oil-coated glass). The experimental results of the retracting filament are described in terms of a simple heuristic model and compared with numerical simulations of the full Navier-Stokes equations. This study is of special interest in the context of pulsed laser-induced dewetting.

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