Contact line instability of a constant volume film down an incline

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

Mar del Plata, Argentina

Congreso; Pan-American Advanced Studies Institute (PASI) on Interfacial Fluid Dynamics: From Theory to Applications; 2007

National Science Foundation, EE. UU.

We study stability of a constant volume of fluid spreading down an incline. In contrast to the commonly considered flow characterized by constant fluid flux, in the present problem the base flow is time-dependent. We present a method to carry out consistently linear stability analysis, based on simultaneously solving the time evolution of the base flow and of the perturbations. The analysis is carried out numerically using a finite-difference method supplemented by a novel integral method developed here. 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.