Bayesian uncertainty quantification for the squeeze flow of soft matter

Soft matter have a microstructure due to which the constitutive behavior is dependent on its state (e.g., deformation or stress). The characterization of the flow is essential to optimize industrial processes such as additive manufacturing. Because of the increase in complexity of the flow settings and the materials, the calibration of the constitutive models can be a daunting task.

Uncertainty quantification (UQ) provides a modeling approach for systems surrounded by uncertainties. We use a Bayesian approach to calibrate our model using the Markov Chain Monte Carlo (MCMC) method. We perform a full UQ analysis of Newtonian and non-Newtonian fluids in a squeeze flow, which combines the elongational en shear deformations. In addition to model calibration based on experimental data, model selection is also considered in our work to determine which calibrated model best explains the data.

First, we apply Bayesian inference on steady shear measurements to quantify the uncertainty in the constitutive model parameters, which are used as priors for the squeeze flow. We continue by applying uncertainty propagation (UP) and Bayesian inference (BI) on the squeeze flow, using simulations and experiments. To get a grasp on the parametric uncertainties, a tailored experimental setup is developed. Using the well-defined parametric uncertainties, UP is used to determine the quantity of interest: the outward motion of the fluid. Finally, we show how BI is used to infer the model parameters from squeeze flow measurements.