Theoretical study on Rayleigh-Plateau instability with an inner boundary condition

Abstract

Rayleigh-Plateau(R-P) instability of viscous liquid is widely observed in engineering problems, such as inkjet printing and optical fiber coating. R-P instability occurs in both a viscous liquid thread and a liquid film on a fiber where the capillary effect is predominant. However to date these cases have been separately studied. In particular, it has been rarely considered how the solid structure affects the R-P instability. In this study, to consider both breakup phenomena simultaneously, we derived a new theoretical model with an additional inner boundary condition at the solid-liquid interface where we assumed that axisymmetric stokes flow and long-wave ansatz to consider the perturbation. Based on this, we obtained time-marching surface profiles and dispersion relations for any fiber radii. Finally, we found that periodic breakup and satellite droplet formation were caused by viscous stress from no-slip boundary condition at the solid-liquid interface. To evaluate our model, we compared with previous experimental and numerical results. In conclusion, we confirmed that the current theoretical model well predicts the R-P instability with a better accuracy. We hope that the current model helps to move one step forward to understand R-P instability theoretically.