Unveiling non-Newtonian flow dynamics and rheology: data-driven constitutive modeling through differentiable simulations

Non-Newtonian and viscoelastic flows are ubiquitous in industrial and biological systems, yet modeling their behavior in realistic geometries and complex flow conditions remains challenging. Differentiable simulations, by enabling automatic gradient computations throughout fluid simulations, present a transformative approach for solving inverse problems. In this work, we present a fully differentiable non-Newtonian fluid solver developed using JAX, which enables efficient, data-driven parameterization of complex rheological behavior in arbitrary geometries. We incorporate a novel tensorial basis neural network to predict non-Newtonian and viscoelastic stresses from flow invariants. Our framework's interpretability allows for direct comparison to established constitutive models via Bayesian Information Criterion (BIC), facilitating model selection and parameter refinement from sparse experimental data. We demonstrate the efficacy of our approach by learning rheology directly from sparse flow measurements in complex geometries. Then, we present results from a new "rheofluidics" framework, where we learn the frequency-dependent rheology of droplets flowing through microfluidic channels with undulating walls from their deformation images. Ultimately, this work lays a data-driven groundwork for advanced digital rheometry to characterize the behavior of complex fluids under diverse and realistic in-situ conditions.