Contact line instability of a liquid rivulet partially wetting an inclined plane

A. G. GONZÁLEZ; J. A. DIEZ; L. KONDIC

Baltimore

Conferencia; 64th Annual Meeting of the APS Division of Fluid Dynamics; 2011

American Physical Society

We analyze the stability of a liquid rivulet of cross section, $A$, positioned across a plane with inclination angle, $\alpha$. The liquid partially wets the substrate with a static contact angle, $\theta_0$ , when the substrate is horizontal. The contact line stability is studied using the lubrication approximation and with a slip model. Both normal and parallel components of gravity are considered. A static solution exists for small $\alpha$'s and its stability is considered using a linear stability analysis. We use an efficient pseudo-spectral Chebyshev method with a combination of basis functions that automatically satisfies the conditions at the contact lines. We analyze the effects of $A$, $\theta_0$ and $\alpha$ on the predictions of the model, such as stability regions, the maximum growth rate and the behavior of most unstable perturbation mode. Experiments with silicone oils spreading on a coated glass substrate are considered for a number of different fluid volumes and inclination angles. We find a good agreement between the wavelength of maximum  growth rate predicted by the model and the experimental average distance between the drops after rivulet breakup.