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 threedimensional 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 threedimensional disturbance mode as predicted. (C) 2002 Elsevier Science (USA).