Flow of a infinite thin strip of fluid on an incline: Stability study of the contact line

J. M. GOMBA; J. DIEZ; R. GRATTON; A. G. GONZÁLEZ; L. KONDIC

Salt Lake City, Utah. EE.UU.

Conferencia; 60th Annual Meeting of the Division of Fluid Dynamics, American Physical Society; 2007

American Physical Society

We consider the flow of a strip of fluid spreading on an incline. The infinte lenght of the strip allows us to study the pure destabilizating capillary effects on the contact line, thus avoiding the effects of boundaries. In contrast with the commonly considered flow that admit a travelling wave solution, in the present problem the base state depends on time. So, the equations that governs both the base state and the perturbation must be solved simultaneously. The computations show that, after a short transient stage, imposed perturbations travel with the same velocity as the leading contact line. The spectral analysis of the modes evolution shows that their growth rates are in general time-dependent. The wavelength of maximum amplitude (dominant wavelength) decreases with time until it reaches an asymptotic value which is in good agreement with experimental results. We also explore the dependence of the dominant wavelength on the cross sectional fluid area and on the inclination angle of the substrate. For considered small cross sectional areas, corresponding to small Bond numbers, we find that the dependence of the dominant wavelenght on the cross sectional area is in good agreement with experimental data. This dependence differs significantly from the one observed for the films characterized by much larger cross sectional areas and Bond numbers. We also predict the dependence of the dominant wavelength on the inclination angle