Fourth Order PDE: Model of Thin Film Flow Involving Surface Tension
Abstract
Surface wave on thin film is considered by involving surface tension. The fluid flows on an inclined channel. The model is based on lubrication theory, and presented in a single equation of the thickness of the fluid as wave movement, and the equation is strongly nonlinear. In solving the model, scaling and linearized processes are applied. So that three physical parameters play an important role in the wave propagation: bottom inclination, length of the scaling and the surface tension. Each of those parameters is represented as a term in the equation. Then, the equation is solved numerically by an implicit finite difference method for the linearized equation, so that the solution can be used to observe the effect of those physical quantities. We found that the surface wave propagates with different speed and reducing the amplitude. When the surface tension is involved, the profile of the wave slightly changes, beside it also effect to the movement of the wave. This is simulated in this paper.
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