Technology Category
Machine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: Relational Probabilistic ModelsIntelligent Robots: State Estimation
Bayesian Model Selection for Complex Flows of Yield Stress Fluids
🤖 AI Summary
This study addresses the limited extrapolation capability of yield-stress fluid parameters obtained via conventional rheometry when applied to complex flows, which often leads to significant predictive errors in constitutive models. To overcome this, the work proposes the first Bayesian uncertainty quantification framework tailored for complex flows, integrating expert prior knowledge to calibrate and select among models such as Herschel–Bulkley and the bi-viscosity power law. The framework explicitly accounts for both experimental and modeling uncertainties while automatically penalizing unnecessary model complexity. Experiments on Carbopol 980, combining rheometric and extrusion flow data, demonstrate that despite excellent fits to rheological data, direct extrapolation yields substantial prediction errors in extrusion flows. In contrast, the Bayesian approach markedly improves predictive accuracy and effectively exposes the limitations of parameter extrapolation, thereby validating its superiority in modeling yield-stress fluids.
Technology Category
Application Category
📝 Abstract
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.
Problem
Research questions and friction points this paper is trying to address.
yield stress fluids
complex flows
constitutive modeling
rheological characterization
model selection
Innovation
Methods, ideas, or system contributions that make the work stand out.
Bayesian model selection
yield stress fluids
uncertainty quantification
constitutive modeling
squeeze flow
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