Theoretical model for breakup of a liquid filament on a solid surface

We theoretically studied how a liquid filament on a substrate breaks down. This instability problem has been broadly explored due to several applications particularly for surface patterning, e.g., metal nanoparticle patterning, multiple-droplet coating, and liquid metal wires for flexible devices. Previous studies are mostly studied by experiments and numerical simulations. Thus, we developed a theoretical model for the instability of a liquid filament on a substrate where the solid-liquid interaction is crucial. Based on the extended lubrication theory, linear perturbation approximations, and additional no-slip boundary condition, finally, we obtained simplified non-linear governing equations, which are only function of the axial direction and time. We found that the theoretical model can predict a breakup of the filament and the satellite droplet formation, which show that the boundary condition on a stationary surface plays an important role to make satellite droplets. In addition, we presented that radii of the satellite droplets have a linear relation with the aspect ratio of the wavelength and the mean radius of a liquid filament.