Modeling yield stress fluids in complex flow scenarios presents significant challenges, particularly because conventional rheological characterization methods often yield material parameters that are not fully representative of the intricate constitutive behavior observed in complex conditions. We propose a Bayesian uncertainty quantification framework for the calibration and selection of constitutive models for yield stress fluids, explicitly accounting for uncertainties in both modeling accuracy and experimental observations. The framework addresses the challenge of complex flow modeling by making discrepancies that emanate from rheological measurements explicit and quantifiable. We apply the Bayesian framework to rheological measurements and squeeze flow experiments on Carbopol 980. Our analysis demonstrates that Bayesian model selection yields robust probabilistic predictions and provides an objective assessment of model suitability through evaluated plausibilities. The framework naturally penalizes unnecessary complexity and shows that the optimal model choice depends on the incorporated physics, the prior information, and the availability of data. In rheological settings, the Herschel-Bulkley and biviscous power law models perform well. However, when these rheological outcomes are used as prior information for a rheo-informed squeeze flow analysis, a significant mismatch with the experimental data is observed. This is due to the yield stress inferred from rheological measurements not being representative of the complex squeeze flow case. In contrast, an expert-informed squeeze flow analysis, based on broader priors, yields accurate predictions. These findings highlight the limitations of translating rheological measurements to complex flows and underscore the value of Bayesian approaches in quantifying model bias and guiding model selection under uncertainty.

翻译：在复杂流动场景中对屈服应力流体进行建模存在显著挑战，这主要是因为传统的流变表征方法获得的材料参数通常无法完全代表复杂条件下观察到的精细本构行为。我们提出了一种用于屈服应力流体本构模型标定与选择的贝叶斯不确定性量化框架，该框架明确考虑了模型精度与实验观测中的不确定性。该框架通过将流变测量中产生的差异显式化与可量化，应对了复杂流动建模的挑战。我们将贝叶斯框架应用于Carbopol 980的流变测量与挤压流动实验。分析表明，贝叶斯模型选择能够产生稳健的概率预测，并通过评估的似然度为模型适用性提供客观评估。该框架自然惩罚不必要的复杂性，并表明最优模型选择取决于所纳入的物理机制、先验信息以及数据的可获得性。在流变学设定中，Herschel-Bulkley模型与双幂律黏度模型表现良好。然而，当将这些流变学结果作为流变信息启发的挤压流动分析的先验信息时，观察到与实验数据的显著失配。这是由于从流变测量推断的屈服应力不能代表复杂挤压流动的情况。相比之下，基于更宽泛先验的专家知识启发的挤压流动分析能产生准确预测。这些发现凸显了将流变测量结果推广至复杂流动的局限性，并强调了贝叶斯方法在量化模型偏差及指导不确定性条件下模型选择方面的价值。