The thin film lubrication approximation has been studied extensively for moving contact lines of Newtonian fluids. However, many industrial and biological applications of the thin film equation involve shear-thinning fluids, which often also exhibit a Newtonian plateau at low shear. This study presents new numerical simulations of the three-dimensional (i.e. two-dimensional spreading), constant-volume, gravity-driven, free surface flow of an Ellis fluid. The numerical solution was validated with a new similarity solution, compared to previous experiments, and then used in a parametric study. The parametric study centered around rheological data for an example biological application of thin film flow: topical drug delivery of anti-HIV microbicide formulations, e.g. hydroxyethylcellulose (HEC) polymer solutions. The parametric study evaluated how spreading length and front velocity saturation depend on Ellis parameters. A lower concentration polymer solution with smaller zero shear viscosity (η₀), τ_1/2, and λ values spread further. However, when comparing any two fluids with any possible combinations of Ellis parameters, the impact of changing one parameter on spreading length depends on the direction and magnitude of changes in the other two parameters. In addition, the isolated effect of the shear-thinning parameter, λ, on the front velocity saturation depended on τ_1/2. This study highlighted the relative effects of the individual Ellis parameters, and showed that the shear rates in this flow were in both the shear-thinning and plateau regions of rheological behavior, emphasizing the importance of characterizing the full range of shear-rates in rheological measurements. The validated numerical model and parametric study provides a useful tool for future steps to optimize flow of a fluid with rheological behavior well-described by the Ellis constitutive model, in a range of industrial and biological applications.

薄膜润滑近似已被广泛研究用于牛顿流体的移动接触线。然而，薄膜方程的许多工业和生物应用都涉及剪切稀化流体，这些流体通常在低剪切下也表现出牛顿平台。这项研究提出了 Ellis 流体的三维（即二维扩展）、恒定体积、重力驱动、自由表面流动的新数值模拟。与之前的实验相比，数值解用新的相似性解进行验证，然后用于参数研究。参数研究集中在薄膜流动的生物应用示例的流变学数据上：抗 HIV 杀微生物剂制剂的局部给药，例如羟乙基纤维素 (HEC) 聚合物溶液。参数研究评估了扩展长度和锋面速度饱和度如何取决于 Ellis 参数。具有较小零剪切粘度的较低浓度聚合物溶液（η ₀ )、τ _1/2和λ值进一步扩展。然而，当将任意两种流体与 Ellis 参数的任何可能组合进行比较时，改变一个参数对铺展长度的影响取决于其他两个参数变化的方向和幅度。此外，剪切稀化参数λ对前沿速度饱和的孤立影响取决于τ _1/2. 该研究强调了各个 Ellis 参数的相对影响，并表明该流中的剪切速率处于流变行为的剪切稀化和平台区域，强调了在流变测量中表征全范围剪切速率的重要性. 经过验证的数值模型和参数研究为未来步骤提供了有用的工具，以优化具有 Ellis 本构模型在一系列工业和生物应用中充分描述的流变行为的流体流动。