Flow of an infinite fluid strip down an inclined plane: Contact line stability

J. GOMBA, J. DIEZ, R. GRATTON, A. G. GONZALEZ

Salt Lake City, Utah, USA.

Conferencia; 60th Annual Meeting of APS Division of Fluid Dynamics; 2007

American Physical Society

We present a computational study on the flow of afluid strip down an inclined plane. Unlike the commonly considered caseof constant film thickness far behind the contact line, this flow involvesa finite cross section and therefore it does not admit a traveling wavesolution; instead, the base flow is time- dependent. Consequently, theequations that governs the evolution of both the base state and of theperturbation must be solved simultaneously. The computations showthat, imposed perturbations travel with the same velocity as the leadingcontact line. The spectral analysis of the modes evolution shows thattheir growth rates are time-dependent. The wavelength of the mode withmaximum amplitude decreases with time until it reaches an asymptoticvalue, Lmax. We explore the dependence of Lmax on the cross sectionalfluid area, A, and on the inclination angle of the plane, . For the consideredsmall A, corresponding to small Bond numbers, we find that thedependence of Lmax on A is in good agreement with experimental data(Gomba et al, Phys. Rev. E 71, 016304, 2005). This dependence differsfrom the one observed for films characterized by much larger crosssectional areas and Bond numbers.