GRAVITY EFFECTS IN THE RETRACTION OF LIQUID FILAMENTS RESTING ON AN INCLINED PLANE

Abstract

We study the retraction of liquid filaments resting on inclined solid substrates under partially wetting condition. This one causes each extreme of the filament to retract and form a region of mass accumulation (head) that subsequently develops a neck at its rear part. This neck then breaks up into a separate drop, while the rest of the filament restarts the sequence. In the horizontal case, this process is symmetric and leads to a regular arrangement of evenly spaced drops. When the substrate is inclined, gravity acts differently at each end, thus modifying the distance retracted by each end, the retraction speed and the final distance between drops, which also ceases to be uniform. We find that, in the case of the inclined plane, the maximum distance retracted by the end that recedes against (in favor of) gravity decreases (increases) with respect to the horizontal case. This effect turns out to be a useful mechanism for the self–positioning of the resulting drops at the end of the process. Our experimental results, such as end positions, thickness profiles in the longitudinal section, etc., are contrasted with numerical simulations of the Navier–Stokes equations, obtaining a good agreement. This is achieved by using in the contact line the boundary condition known as Cox–Voinov–Blake (CVB) relationship, which includes both the effects of macroscopic hydrodynamics as well as molecular dynamics