Shear-thickening and thinning behaviors are often observed in the rheological measurements of dilute surfactant solutions with drag-reducing ability in wall-bounded turbulent flows. This study proposes a simple rheological modeling method based on combining constitutive equations, such as Giesekus and FENE-P models, with a fluidity equation to determine both thickening and thinning behaviors in simple shear flows simultaneously. The Giesekus and FENE-P models, which are typically used in numerical studies on turbulent drag reduction, cannot capture such complex behaviors. However, the proposed models, called f-Giesekus and f-FENE-P models, can predict the shear-thickening properties. The developed models are inspired by the Bautista–Manero–Puig model, where the Oldroyd-B model (upper-convected Maxwell model) is coupled with the fluidity equation. Parametric studies prove that the proposed models can accurately predict both the shear-thickening and shear-thinning properties. Notably, the f-FENE-P model shows prominent flexibility to determine the plateau region of the shear viscosity as a function of the shear rate. We verify that the analytical solutions of the f-FENE-P model agree with the experimental data of the shear viscosity in dilute drag-reducing surfactant solutions, except for the remarkable steep increase in the shear viscosity. The start-up shear flow is also studied to confirm various transitions accompanied by the overshoot and undershoot of the f-FENE-P model.

在稀表面活性剂溶液的流变学测量中经常观察到剪切增稠和稀化行为，并且在具有边界的湍流中具有减阻能力。这项研究提出了一种简单的流变建模方法，该方法是将本构方程（例如Giesekus模型和FENE-P模型）与流动性方程相结合的基础上，同时确定简单剪切流中的增稠和稀疏行为。Giesekus和FENE-P模型通常用于湍流减阻的数值研究中，但无法捕获此类复杂的行为。但是，建议的模型称为f-Giesekus和f-FENE-P模型，可以预测剪切增稠特性。所开发的模型受Bautista–Manero–Puig模型的启发，其中Oldroyd-B模型（上部对流Maxwell模型）与流动性方程耦合。参数研究证明，所提出的模型可以准确预测剪切稠化和剪切稀化特性。值得注意的是，f-FENE-P模型显示出显着的灵活性，可以根据剪切速率确定剪切粘度的平稳区域。我们验证了f-FENE-P模型的解析溶液与稀减阻表面活性剂溶液中的剪切粘度的实验数据相符，除了剪切粘度显着急剧增加外。还研究了启动剪切流，以确认伴随f-FENE-P模型的上冲和下冲的各种过渡。f-FENE-P模型显示出显着的灵活性，可以根据剪切速率确定剪切粘度的平稳区域。我们验证了f-FENE-P模型的解析溶液与稀减阻表面活性剂溶液中的剪切粘度的实验数据相符，除了剪切粘度显着急剧增加外。还研究了启动剪切流，以确认伴随f-FENE-P模型的上冲和下冲的各种过渡。f-FENE-P模型显示出显着的灵活性，可以根据剪切速率确定剪切粘度的平稳区域。我们验证了f-FENE-P模型的解析溶液与稀减阻表面活性剂溶液中的剪切粘度的实验数据相符，除了剪切粘度显着急剧增加外。还研究了启动剪切流，以确认伴随f-FENE-P模型的上冲和下冲的各种过渡。