Title: 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.