Learning rheological parameters of non-Newtonian fluids from velocimetry data

TL;DR

This paper presents a Bayesian inverse Navier-Stokes approach to jointly reconstruct flow fields and learn rheological parameters of non-Newtonian fluids from velocimetry data, validated with flow-MRI experiments on blood analogue fluids.

Contribution

It introduces an algorithm that learns Carreau shear-thinning parameters and their uncertainties solely from velocimetry data, extending to complex non-Newtonian fluid models.

Findings

Successful reconstruction of flow fields and rheological parameters.

Good agreement between learned parameters and rheometry measurements.

Algorithm can be extended to more complex non-Newtonian fluids.

Abstract

We solve a Bayesian inverse Navier-Stokes (N-S) problem that assimilates velocimetry data in order to jointly reconstruct the flow field and learn the unknown N-S parameters. By incorporating a Carreau shear-thinning viscosity model into the N-S problem, we devise an algorithm that learns the most likely Carreau parameters of a shear-thinning fluid, and estimates their uncertainties, from velocimetry data alone. We then conduct a flow-MRI experiment to obtain velocimetry data of an axisymmetric laminar jet through an idealised medical device (FDA nozzle) for a blood analogue fluid. We show that the algorithm can successfully reconstruct the flow field by learning the most likely Carreau parameters, and that the learned parameters are in very good agreement with rheometry measurements. The algorithm accepts any algebraic effective viscosity model, as long as the model is differentiable, and it can be extended to more complicated non-Newtonian fluids (e.g. Oldroyd-B fluid) if a viscoelastic model is incorporated into the N-S problem.