Unstable bidimensional grid of liquid filaments: Drop pattern after breakups

DIEZ, JAVIER A.; CUELLAR, INGRITH; RAVAZZOLI, PABLO D.; GONZÁLEZ, ALEJANDRO G.

Denver - Colorado

Congreso; 70 th Annual Meeting of Division of Fluid Dynamics (DFD) of the American Physical Society (APS)); 2017

American Physical Society

A rectangular grid formed by liquid filaments on a partially wetting substrate evolves in a series ofbreakups leading to arrays of drops with different shapes distributed in a rather regular bidimensionalpattern. Our study is focused on the configuration produced when two long parallel filaments ofsilicone 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 thiskind of grids is that there are two qualitatively different types of drops. While one set is formedat the crossing points, the rest are consequence of the breakup of shorter filaments formed betweenthe crossings. Here, we analyze the main geometric features of all types of drops, such as shapeof the footprint and contact angle distribution along the drop periphery. The formation of a seriesof short filaments with similar geometric and physical properties allows us to have simultaneouslyquasi identical experiments to study the subsequent breakups. We develop a simple hydrodynamicmodel 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 andits predictions are successfully compared with the experimental data as well as with numericalsimulations of the full Navier?Stokes equation that provide a detailed time evolution of the dewettingmotion of the filament till the breakup into drops. Finally, the prediction for finite filaments iscontrasted with the existing theories for infinite ones.