Abstract
The nonlinear stability analysis of Walters B' viscoelastic falling fluid film with countercurrent gas flow has been investigated. A normal mode approach is first employed to compute the linear stability solution for the film flow. The results of linear analysis indicate that the viscoelasticity parameter and Weber number have stabilizing effects, and the Reynolds number has a destabilizing effect, while the countercurrent shear stress parameter has a dual role on the stability of the flow system. The method of multiple scales is then used to obtain the weak nonlinear dynamics of the film flow in the form of the Ginzburg-Landau equation. It is shown that both subcritical instability and supercritical stability conditions are possible when the gas flows in the countercurrent direction. The results further indicate that in the subcritical unstable region, the threshold amplitude increases (and then decreases) depending on the wave number value by increasing the viscoelasticity parameter and the countercurrent shear stress parameter, while in the supercritical stable region, it decreases by increasing the viscoelasticity parameter and Weber number, and it increases by increasing the countercurrent shear stress parameter and Reynolds number. It is found also that the nonlinear wave speed decreases by increasing the Weber number, and it decreases and then slightly increases by increasing the Reynolds number in the subcritical unstable region, while it increases by increasing Weber number, countercurrent shear stress parameter, viscoelasticity parameter, and it decreases by increasing Reynolds number in the supercritical stable region.