On the breakup of fluid rivulets

We study the stability of rivulets on horizontal substrates. The implemented model includes the effects of capillarity, fluid-solid interaction, and gravity if appropriate, within the framework of the lubrication approximation. We find that the results compare favorably with those in literature, in the regime where previous analyses are valid. By isolating the effect of van der Waals interactions for nanoscale rivulets, and of gravity for macrosize rivulets, we are able to analyze the influence of these forces on the stability. We discuss in detail the scaling of the emerging wavelengths (distance between drops formed after the breakup process) with the rivulet cross-sectional area. Perhaps surprisingly, we uncover close connection between this scaling and the one for the breakup of a free-space fluid jet (Rayleigh-Plateau instability). Finally, we consider rivulets of finite length and find that the finite size effects are considerably different from the ones obtained previously for semi-infinite fluid films.