Three-dimensional nonlinear rupture theory of thin liquid films on a cylinder

The three-dimensional nonlinear rupture theory of thin liquid films on a cylinder is presented and studied in this note. The thin liquid film with the effect of intermolecular forces was modeled by a continuum theory, and the three-dimensional evolution equation of liquid films on a cylindrical surface was derived based on a long wavelength approximation. Both linear stability theory and nonlinear numerical method were adopted to solve this evolution equation. The linear stability analysis fails to distinguish the three-dimensional mode from the two-dimensional one in terms of maximum disturbance growth rate and always yields a rupture time larger than the nonlinear solution. In contrast, the nonlinear numerical results clearly show that among three disturbance modes, the two-dimensional annular disturbance one yields the longest rupture time, the two-dimensional axisymmetric disturbance one yields the second longest, and the three-dimensional disturbance one does the shortest. Accordingly, it can be concluded that the rupture status of thin films on cylinder is most likely evolved in the three-dimensional disturbance mode as predicted.