The use of homotopy methods for solving nonlinear foam drainage equation

Abstract

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 Adomian's decomposition method , modified Adomian's 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.

Numerical Solution of Nonlinear the Foam Drainage Equation via Hybrid Method

“…Foams are usually utilized in foods and, personal care products, acoustic cladding and textured wallpapers, etc. Also, there are important foam applications in the foods, chemical industries, fire fighting, mineral processing, and structural material sciences [1]. In nature, chemical, physical and biological events, as well as foams are often modeled with nonlinear equations.…”

“…In nature, chemical, physical and biological events, as well as foams are often modeled with nonlinear equations. In the literature, several methods were described and implemented for the numerical solution of these models [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. We, therefore, preferred a robust hybrid method to solve the following nonlinear foam drainage equation [1]:…”

“…Various analytical methods were used to obtain the solution of foam drainage equation, such as Tanh method [6], spatial finite difference method, generalized G /G − expansion method [5], Adomian method [6], Homotopy analysis method etc. [1]. In the literature review, it was observed that the hybrid method was never used to solve the foam drainage equation.…”