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.

薄的流体膜的移动接触线经常会波纹成手指状，这也被称为指状不稳定性。尽管已对牛顿流体的指弹不稳定性进行了广泛的研究，但有关非牛顿流体的接触线指弹不稳定性的研究很少。尤其是，仍不清楚剪切稀化的流变性质如何影响接触线不稳定性的形成，生长和形状。我们先前的研究（Hu和Kieweg，2012）表明，在二维模型（即在润滑理论范围内扩展的一维薄膜）中，剪切剪切稀疏的流体可减少毛细管脊的形成。这些结果激发了这项研究的假设：更多的剪切稀化液应该抑制了手指的生长，延长了手指的波长，这在线性稳定性分析（LSA）和3D（即2D扩展）数值模拟中应该很明显。在这项研究中，我们为剪切稀化薄膜的重力驱动流动开发了LSA模型，并进行了参数研究，以研究剪切稀化对新兴指状图案生长速率的影响。还开发了一个完整的3D模型，以使用单个扰动来比较和验证LSA结果，并探索随机施加的多模式扰动的结果。LSA和3D数值结果均证实，牛顿流体的接触线指形在垂直和倾斜平面上的生长都比剪切稀化流体的生长快。此外，LSA和3D模型均表明，当平面倾斜时，牛顿流体形成的手指的波长比剪切稀疏流体的手指的波长短。在垂直方向上，没有观察到最不稳定（即出射）波长的差异。这项研究还表明，对于剪切稀化流体，新兴手指之间的距离在垂直平面上要比在不太倾斜平面上的手指间距离小，如先前对牛顿流体所示。这些结果首次用于剪切稀化流体，连接了2D模型，LSA和3D模拟中毛细管脊和接触线指形物形成的趋势。结果可为我们提供有关如何优化非牛顿流体特性以最大程度减少许多工业和生物应用中指弹不稳定性的见解。在垂直方向观察到波长）。这项研究还表明，对于剪切稀化流体，新兴手指之间的距离在垂直平面上要比在不太倾斜平面上的手指间距离小，如先前对牛顿流体所示。这些结果首次用于剪切稀化流体，连接了2D模型，LSA和3D模拟中毛细管脊和接触线指形物形成的趋势。结果可为我们提供有关如何优化非牛顿流体特性以最大程度减少许多工业和生物应用中指弹不稳定性的见解。在垂直方向观察到波长）。这项研究还表明，对于剪切稀化流体，新兴手指之间的距离在垂直平面上要比在不太倾斜平面上的手指间距离小，如先前对牛顿流体所示。这些结果首次用于剪切稀化流体，连接了2D模型，LSA和3D模拟中毛细管脊和接触线指形物形成的趋势。结果可为我们提供有关如何优化非牛顿流体特性以最大程度减少许多工业和生物应用中指弹不稳定性的见解。这些结果联系了2D模型，LSA和3D模拟中毛细脊和接触线手指形成的趋势。结果可为我们提供有关如何优化非牛顿流体特性以最大程度减少许多工业和生物应用中指弹不稳定性的见解。这些结果联系了2D模型，LSA和3D模拟中毛细脊和接触线手指形成的趋势。结果可为我们提供有关如何优化非牛顿流体特性以最大程度减少许多工业和生物应用中指弹不稳定性的见解。