This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License 4.0 (CC BY-NC-ND 4.0), which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
The moving contact line of a thin fluid film can often corrugate into fingers, which is also known as a fingering instability. Although the fingering instability of Newtonian fluids has been studied extensively, there are few studies published on contact line fingering instability of non-Newtonian fluids. In particular, it is still unknown how shear-thinning rheological properties can affect the formation, growth, and shape of a contact line instability. Our previous study (Hu and Kieweg, 2012) showed a decreased capillary ridge formation for more shear-thinning fluids in a 2D model (i.e. 1D thin film spreading within the scope of lubrication theory). Those results motivated this study's hypothesis: more shear-thinning fluids should have suppressed finger growth and longer finger wavelength, and this should be evident in linear stability analysis (LSA) and 3D (i.e. 2D spreading) numerical simulations. In this study, we developed a LSA model for the gravity-driven flow of shear-thinning films, and carried out a parametric study to investigate the impact of shear-thinning on the growth rate of the emerging fingering pattern. A fully 3D model was also developed to compare and verify the LSA results using single perturbations, and to explore the result of multiple-mode, randomly imposed perturbations. Both the LSA and 3D numerical results confirmed that the contact line fingers grow faster for Newtonian fluids than the shear-thinning fluids on both vertical and inclined planes. In addition, both the LSA and 3D model indicated that the Newtonian fluids form fingers with shorter wavelengths than the shear-thinning fluids when the plane is inclined; no difference in the most unstable (i.e. emerging) wavelength was observed at vertical. This study also showed that the distance between emerging fingers was smaller on a vertical plane than on a less-inclined plane for shear-thinning fluids, as previously shown for Newtonian fluids. For the first time for shear-thinning fluids, these results connect trends in capillary ridge and contact line finger formation in 2D models, LSA, and 3D simulations. The results can provide us insights on how to optimize non-Newtonian fluid properties to minimize a fingering instability in many industrial and biological applications.
Hu, B., & Kieweg, S. L. (2015). Contact Line Instability of Gravity-Driven Flow of Power-Law Fluids. Journal of Non-Newtonian Fluid Mechanics, 225, 62–69. http://doi.org/10.1016/j.jnnfm.2015.09.002
Items in KU ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.
We want to hear from you! Please
share your stories
about how Open Access to this item benefits YOU.
Except where otherwise noted, this item's license is described as: This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License 4.0 (CC BY-NC-ND 4.0), which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
The University of Kansas prohibits discrimination on the basis of race, color, ethnicity, religion, sex, national origin, age, ancestry, disability, status as a veteran, sexual orientation, marital status, parental status, gender identity, gender expression and genetic information in the University’s programs and activities. The following person has been designated to handle inquiries regarding the non-discrimination policies: Director of the Office of Institutional Opportunity and Access, IOA@ku.edu, 1246 W. Campus Road, Room 153A, Lawrence, KS, 66045, (785)864-6414, 711 TTY.