TY - JOUR

T1 - Instability of a transverse liquid rivulet on an inclined plane

AU - Diez, Javier A.

AU - González, Alejandro G.

AU - Kondic, Lou

N1 - Funding Information:
J.A.D and A.G.G. acknowledge support from Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET, Argentina) and from Agencia Nacional de Promoción de Científica y Tecnológica (ANPCyT, Argentina) with Grant No. PICT 2498/06. L.K. acknowledges partial support by the National Science Foundation (NSF) Grant No. DMS-0908158.

PY - 2012/3/14

Y1 - 2012/3/14

N2 - This work concentrates on the stability of a viscous liquid rivulet positioned across an inclined plane under partial wetting conditions. The study is performed within the framework of lubrication approximation by employing a slip model. Both normal and parallel components of gravity are considered. We find the stability regions for given area of the cross section of the rivulet, A, plane inclination angle, α, and static contact angle, θ0, characterizing the wettability of the substrate. For α's smaller than some critical angle, α*, a static solution exists. This solution is characterized by rear/front contact angles given by θ0 ± δ. The linear stability analysis of this solution is performed using an efficient pseudo-spectral Chebyshev method. We analyze the effects of A, θ0, and α on the predictions of the model, such as the dominant wavelength, the maximum growth rate, and the behavior of the most unstable perturbation mode. To verify them, we also carry out experiments with silicone oils spreading on a coated glass substrate for several different fluid volumes and inclination angles. We find very good agreement between the wavelength of maximum growth rate given by the theory and the average distance between the drops after rivulet breakup. An analysis of finite size effects shows that the inclusion of normal gravity effects leads to a better agreement between theoretical and experimental results.

AB - This work concentrates on the stability of a viscous liquid rivulet positioned across an inclined plane under partial wetting conditions. The study is performed within the framework of lubrication approximation by employing a slip model. Both normal and parallel components of gravity are considered. We find the stability regions for given area of the cross section of the rivulet, A, plane inclination angle, α, and static contact angle, θ0, characterizing the wettability of the substrate. For α's smaller than some critical angle, α*, a static solution exists. This solution is characterized by rear/front contact angles given by θ0 ± δ. The linear stability analysis of this solution is performed using an efficient pseudo-spectral Chebyshev method. We analyze the effects of A, θ0, and α on the predictions of the model, such as the dominant wavelength, the maximum growth rate, and the behavior of the most unstable perturbation mode. To verify them, we also carry out experiments with silicone oils spreading on a coated glass substrate for several different fluid volumes and inclination angles. We find very good agreement between the wavelength of maximum growth rate given by the theory and the average distance between the drops after rivulet breakup. An analysis of finite size effects shows that the inclusion of normal gravity effects leads to a better agreement between theoretical and experimental results.

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U2 - 10.1063/1.3685802

DO - 10.1063/1.3685802

M3 - Article

AN - SCOPUS:84859311474

SN - 1070-6631

VL - 24

JO - Physics of Fluids

JF - Physics of Fluids

IS - 3

M1 - 032104

ER -