The use of homotopy methods for solving nonlinear foam drainage equation

Foaming occurs in many distillation and absorption processes. The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. In this paper, the nonlinear foam drainage equation is solved by using the Adomianʹs decomposition method, modified Adomianʹs decomposition method, variational iteration method, modified variational iteration method, homotopy perturbation method, modified homotopy perturbation method and homotopy analysis method. The existence and uniqueness of the solution and convergence of the proposed methods are proved in details. Finally an example shows the accuracy of these methods.