Bayesian model selection for the squeeze flow of soft matter

Soft matter - such as polymeric liquids and particle suspensions - have a microstructure due to which the constitutive behavior is dependent on its state (e.g. deformation or stress). To optimize industrial processes such as additive manufacturing, injection molding and extrusion, characterizing the flow behavior is essential. However, due to the increase in complexity of the flow setting (e.g. type of flow or material), the calibration of the accompanying models using relatively simple experiments can be difficult.

 

The concept of Bayesian uncertainty quantification provides a modeling framework for flow predictions of soft matter, especially for systems surrounded by uncertainties. In this framework, we calibrate and compare models to determine which one best explains the experimental data. The predictive error of a model is a balance between accuracy and uncertainty. A complex model gives a low modeling error but a larger parametric error because of the larger number of parameters. A simple model has a relatively large modeling error due to more assumptions being made to it but a low parametric error because of the relatively small number of parameters. In the end, the best model is the simplest valid model. Simplicity refers to the number of parameters in a model, where a simpler model has less parameters.

 

Bayesian model selection has already been applied to a viscoelastic fluid in a rheological flow, which is a simple flow. In this contribution, we apply Bayesian model selection on a squeeze flow using a Newtonian, a generalized Newtonian and a viscoplastic fluid. In this type of flow a fluid is compressed between two parallel plates. This is a more complex flow because it combines shear and elongational deformation. First, we calibrate the models through Bayesian inference with data obtained through a tailored experimental setup. The models vary in constitutive behavior and additional complexities such as slip and Laplace pressure inclusion. Next, we compare the calibrated models using Bayesian model selection through the Bayesian posterior plausibility’s.