Exact solution for capillary waves on fluid sheets

Using the Schwarz function method, we have obtained a new exact solution for the problem of capillary waves on a fluid sheet. The reliability of the solution was confirmed by the results of numerical verification of the main boundary equation. It was revealed that the pressure coefficient is the determining physical parameter. Its value makes it possible to predict that one should expect either the capillary wave of a certain type (symmetric or antisymmetric) or the disintegration of the fluid sheet into individual drops. It is shown that the maximum possible length of the capillary wave is approximately 1.6 times the thickness of the fluid sheet, regardless of the wave type. The question of reproducing the known exact solution of W. Kimmersley for this problem remains open.