Shear-migration in dense suspensions from the point of view of physics-informed neural networks

Phillips et al. [Phys. Fluids A 4 (1992) 30] proposed a  phenomenological model for the shear-induced migration of particles in a low-Reynolds-number flow. Since then, the model has been the workhorse for continuum modeling of migration phenomena in suspensions. However, being phenomenological, the model has only been calibrated for certain geometries. It is not clear if the model's parameters, determined by visually matching concentration profiles, for one flow scenario are valid in others. To address this knowledge gap, we apply the physics-informed neural networks (PINNs) approach. Specifically, the NN is constrained via the Phillips et al. model, and a suitable momentum equation for the unidirectional flow of the suspension. The NN is then trained against different experiments from the literature. We first verify the PINN approach for solving the inverse problem of radial particle migration in a non-Brownian suspension in an annular Couette flow. Then, we apply the PINN approach to analyze experiments on particle migration in both non-Brownian and Brownian suspensions in Poiseuille slot flow. For the latter, there is an additional model parameter, which has not been calibrated in prior literature, that we identify using the PINN. Significantly different values for the model parameters are obtained via the PINN upon analyzing Poiseuille flow experiments, although the parameters match Phillips et al. for the classical of an annular Couette flow. The PINN results also show that the best-fit model parameters vary with the Péclet number and the particle bulk volume fraction, instead of being constant as previously assumed.