Single theoretical model for breakup of viscous thread with and without a fiber

We present a theoretical model for viscous liquid systems exhibiting Rayleigh-Plateau instability, considering cases with and without a solid fiber. Using the lubrication approach and hydrodynamic interactions at the solid-liquid interface, we derive one-dimensional evolution equations for the breakup of viscous liquid threads and films on fibers. Our model aligns well with experimental results, unifying Goren's liquid film on a fiber and Rayleigh's viscous liquid thread findings. It identifies the most unstable mode as proportional to the wavenumber quadratically and reveals the exponential decay of satellite droplet volume with increasing wavenumber.