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Fluid Dynamics Seminar

Monday, Nov. 29, 2010,
4:00 PM

Cullimore, Room 611

New Jersey Institute of Technology

A liquid rivulet placed across on an inclined plane: Its stability

**Javier A. Diez**

Instituto de Fisica Arroyo Seco, Universidad Nacional del Centro de la
Provincia de Buenos Aires, Tandil, Argentina

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Abstract
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In this talk I will present some results on the stability of a viscous liquid rivulet placed across on an inclined plane under partial wetting conditions. The study is performed within the framework of lubrication approximation by employing a slipping model to overcome the contact line divergence. Both normal and parallel components of gravity are considered in the analysis. We find the stability regions for given area of the cross section of the rivulet, $A$, plane inclination angle, $\alpha$, and static contact angle, $\theta_0$ (which characterizes the wettability of the substrate). For $\alpha$ larger than some critical angle, $\alpha^{\ast}$, the static solution does no longer exist. For $\alpha<\alpha^{\ast}$, the static solution is characterized by rear/front contact angles which are smaller/larger compared to $\theta_0$ by the same amount. For given $A$ and $\theta_0$, this angle shift depends on $\alpha$, so that static solution ceases to exist when the rear angle becomes zero, and the front one practically doubles $\theta_0$. The linear stability analysis is performed by using a pseudo spectral Chebyshev method which yields the dispersion relation and the eigenfunctions of the perturbed problem. We analyze the effects of usual experimental parameters $A$, $\theta_0$ and $\alpha$ on the predictions of the model, such as dominant wavelength and maximum growth rate. For $\alpha>0$, the perturbation modes (eigenfunctions) are asymmetric, and the solution shows how they change for different wavenumbers and inclination angles. For the horizontal case, we compare the results of this model with the ones obtained by using a complementary model that introduces van der Waals forces to account for liquid-solid interaction.